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q9f committed Jan 9, 2020
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69 changes: 47 additions & 22 deletions docs/Secp256k1.html
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Expand Up @@ -116,7 +116,11 @@ <h2>
Overview
</h2>

<p>expose the secp256k1 module</p>
<p>Implements 256-bit <code><a href="Secp256k1.html">Secp256k1</a></code> Koblitz elliptic curve.
Ref: <a href="https://www.secg.org/sec2-v2.pdf" target="_blank">secg.org/sec2-v2.pdf</a></p>

<p><code><a href="Secp256k1.html">Secp256k1</a></code> has the characteristic prime <code>p</code>, it is defined over the prime field ℤ_p.
Ref: <a href="https://en.bitcoin.it/wiki/Secp256k1" target="_blank">en.bitcoin.it/wiki/Secp256k1</a></p>



Expand All @@ -141,35 +145,35 @@ <h2>
</h2>


<a href="https://github.com/q9f/secp256k1.cr/blob/90277a931d1866de696bde9fe0ca31871b26b7c4/src/bitcoin.cr#L16" target="_blank">
<a href="https://github.com/q9f/secp256k1.cr/blob/74ab83c5d3f91e1df45b16e61e56af6fa02eddff/src/bitcoin.cr#L16" target="_blank">
bitcoin.cr
</a>

<br/>


<a href="https://github.com/q9f/secp256k1.cr/blob/90277a931d1866de696bde9fe0ca31871b26b7c4/src/constants.cr#L19" target="_blank">
<a href="https://github.com/q9f/secp256k1.cr/blob/74ab83c5d3f91e1df45b16e61e56af6fa02eddff/src/constants.cr#L22" target="_blank">
constants.cr
</a>

<br/>


<a href="https://github.com/q9f/secp256k1.cr/blob/90277a931d1866de696bde9fe0ca31871b26b7c4/src/structs.cr#L16" target="_blank">
<a href="https://github.com/q9f/secp256k1.cr/blob/74ab83c5d3f91e1df45b16e61e56af6fa02eddff/src/structs.cr#L20" target="_blank">
structs.cr
</a>

<br/>


<a href="https://github.com/q9f/secp256k1.cr/blob/90277a931d1866de696bde9fe0ca31871b26b7c4/src/version.cr#L16" target="_blank">
<a href="https://github.com/q9f/secp256k1.cr/blob/74ab83c5d3f91e1df45b16e61e56af6fa02eddff/src/version.cr#L20" target="_blank">
version.cr
</a>

<br/>


<a href="https://github.com/q9f/secp256k1.cr/blob/90277a931d1866de696bde9fe0ca31871b26b7c4/src/secp256k1.cr#L26" target="_blank">
<a href="https://github.com/q9f/secp256k1.cr/blob/74ab83c5d3f91e1df45b16e61e56af6fa02eddff/src/secp256k1.cr#L30" target="_blank">
secp256k1.cr
</a>

Expand All @@ -194,13 +198,18 @@ <h2>
<strong>EC_BASE_G</strong> = <code><span class="t">EC_Point</span>.<span class="k">new</span>(<span class="t">EC_BASE_G_X</span>, <span class="t">EC_BASE_G_Y</span>)</code>
</dt>

<dd class="entry-const-doc">
<p>The commonly used base point <code>G</code> coordinates <code>x</code>, <code>y</code>;
any other point that satisfies <code>y^2 = x^3 + 7</code> would also do.</p>
</dd>


<dt class="entry-const" id="EC_BASE_G_COMPRESSED">
<strong>EC_BASE_G_COMPRESSED</strong> = <code><span class="t">BigInt</span>.<span class="k">new</span>((<span class="t">Secp256k1</span><span class="t">::</span><span class="t">Util</span>.public_key_compressed_prefix(<span class="t">EC_BASE_G</span>)), <span class="n">16</span>)</code>
</dt>

<dd class="entry-const-doc">
<p>The base point G in compressed form is:</p>
<p>The base point <code>G</code> in compressed form.</p>
</dd>


Expand All @@ -209,7 +218,7 @@ <h2>
</dt>

<dd class="entry-const-doc">
<p>The base point G in uncompressed form is:</p>
<p>The base point <code>G</code> in uncompressed form.</p>
</dd>


Expand All @@ -218,61 +227,77 @@ <h2>
</dt>

<dd class="entry-const-doc">
<p>The commonly used base point G coordinates x, y;
any other point that satisfies y^2 = x^3 + 7 would also do:</p>
<p>The <code>x</code>-coordinate of the base point <code>G</code>.</p>
</dd>


<dt class="entry-const" id="EC_BASE_G_Y">
<strong>EC_BASE_G_Y</strong> = <code><span class="t">BigInt</span>.<span class="k">new</span>(<span class="s">&quot;483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8&quot;</span>, <span class="n">16</span>)</code>
</dt>

<dd class="entry-const-doc">
<p>The <code>y</code>-coordinate of the base point <code>G</code>.</p>
</dd>


<dt class="entry-const" id="EC_COFACTOR_H">
<strong>EC_COFACTOR_H</strong> = <code><span class="t">BigInt</span>.<span class="k">new</span>(<span class="s">&quot;01&quot;</span>, <span class="n">16</span>)</code>
</dt>

<dd class="entry-const-doc">
<p>The elliptic curve cofactor <code>h</code>.</p>
</dd>


<dt class="entry-const" id="EC_FACTOR_A">
<strong>EC_FACTOR_A</strong> = <code><span class="t">BigInt</span>.<span class="k">new</span>(<span class="s">&quot;0000000000000000000000000000000000000000000000000000000000000000&quot;</span>, <span class="n">16</span>)</code>
<strong>EC_FACTOR_A</strong> = <code><span class="t">BigInt</span>.<span class="k">new</span>(<span class="s">&quot;00&quot;</span>, <span class="n">16</span>)</code>
</dt>

<dd class="entry-const-doc">
<p>The curve E: y^2 = x^3 + ax + b over F_p is defined by a, b:
As the a constant is zero, the ax term in the curve equation is always zero,
hence the curve equation becomes y^2 = x^3 + 7.</p>
<p>The curve <code>E</code>: <code>y^2 = x^3 + ax + b</code> over <code>F_p</code> is defined by <code>a = 0</code>.
As the <code>a</code> constant is zero, the <code>ax</code> term in the curve equation is always zero,
hence the curve equation becomes <code>y^2 = x^3 + b</code>.</p>
</dd>


<dt class="entry-const" id="EC_FACTOR_B">
<strong>EC_FACTOR_B</strong> = <code><span class="t">BigInt</span>.<span class="k">new</span>(<span class="s">&quot;0000000000000000000000000000000000000000000000000000000000000007&quot;</span>, <span class="n">16</span>)</code>
<strong>EC_FACTOR_B</strong> = <code><span class="t">BigInt</span>.<span class="k">new</span>(<span class="s">&quot;07&quot;</span>, <span class="n">16</span>)</code>
</dt>

<dd class="entry-const-doc">
<p>The curve <code>E</code>: <code>y^2 = x^3 + b</code> over <code>F_p</code> is defined by <code>b = 7</code>,
hence the curve equation becomes <code>y^2 = x^3 + 7</code>.</p>
</dd>


<dt class="entry-const" id="EC_ORDER_N">
<strong>EC_ORDER_N</strong> = <code><span class="t">BigInt</span>.<span class="k">new</span>(<span class="s">&quot;fffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141&quot;</span>, <span class="n">16</span>)</code>
</dt>

<dd class="entry-const-doc">
<p>Finally, the order n of G and the cofactor h are:</p>
<p>The order <code>n</code> of <code>G</code> defines the finite size of the Secp256k1 field <code>E</code>.</p>
</dd>


<dt class="entry-const" id="EC_PARAM_PRIME">
<strong>EC_PARAM_PRIME</strong> = <code><span class="t">BigInt</span>.<span class="k">new</span>(<span class="s">&quot;fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f&quot;</span>, <span class="n">16</span>)</code>
<dt class="entry-const" id="EC_PRIME_P">
<strong>EC_PRIME_P</strong> = <code><span class="t">BigInt</span>.<span class="k">new</span>(<span class="s">&quot;fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f&quot;</span>, <span class="n">16</span>)</code>
</dt>

<dd class="entry-const-doc">
<p>The elliptic curve domain parameters over F_p associated with a Koblitz curve
Secp256k1 are specified by the sextuple T = (p, a, b, G, n, h) where the finite
field F_p is defined by p = 2^256 - 2^32 - 2^9 - 2^8 - 2^7 - 2^6 - 2^4 - 1:</p>
<p>The elliptic curve domain parameters over <code>F_p</code> associated with a Koblitz curve
Secp256k1 are specified by the sextuple <code>T = (p, a, b, G, n, h)</code> where the finite
field <code>F_p</code> is defined by the prime <code>p = 2^256 - 2^32 - 2^9 - 2^8 - 2^7 - 2^6 - 2^4 - 1</code>.</p>
</dd>


<dt class="entry-const" id="VERSION">
<strong>VERSION</strong> = <code><span class="s">&quot;0.2.0&quot;</span></code>
<strong>VERSION</strong> = <code><span class="s">&quot;0.2.1&quot;</span></code>
</dt>

<dd class="entry-const-doc">
<p>The <code><a href="Secp256k1.html#VERSION">VERSION</a></code> of the <code><a href="Secp256k1.html">Secp256k1</a></code> module.</p>
</dd>


</dl>

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