I'd like to propose a patch for adding RSA 4096 in a generic way (and hence should be easy to adapt for RSA 3072 as well)
for now it's just a simple addition instead of replace so it can be worked on independently

diff -ura package.orig/pynitrokey/pynitrokey/cli/nk3/piv.py package.new/pynitrokey/pynitrokey/cli/nk3/piv.py
--- package.orig/pynitrokey/pynitrokey/cli/nk3/piv.py	2025-12-10 21:24:30.510769406 +0100
+++ package.new/pynitrokey/pynitrokey/cli/nk3/piv.py	2025-12-10 22:36:39.852806689 +0100
@@ -55,7 +55,9 @@
             assert isinstance(padding, PKCS1v15)
             assert isinstance(algorithm, hashes.SHA256)
 
-            return self._device.sign_rsa2048(data, self._key_reference)
+            #return self._device.sign_rsa2048(data, self._key_reference)
+            bits = self.key_size  # 2048 or 4096
+            return self._device.sign_rsa(data, self._key_reference, bits)
 
         def decrypt(self, ciphertext: bytes, padding: AsymmetricPadding) -> bytes:
             raise NotImplementedError()
@@ -394,7 +396,7 @@
     )
     @click.option(
         "--algo",
-        type=click.Choice(["rsa2048", "nistp256"], case_sensitive=False),
+        type=click.Choice(["rsa2048", "rsa4096", "nistp256"], case_sensitive=False),
         default="nistp256",
         help="Algorithm for the key.",
     )
@@ -448,12 +450,25 @@
         algo = algo.lower()
         if algo == "rsa2048":
             algo_id = b"\x07"
+        elif algo == "rsa4096":
+            algo_id = b"\x16"
         elif algo == "nistp256":
             algo_id = b"\x11"
         else:
             local_critical("Unimplemented algorithm", support_hint=False)
 
-        body = Tlv.build([(0xAC, Tlv.build([(0x80, algo_id)]))])
+        if algo == "rsa2048":
+            key_selector = b"\x10"
+        elif algo == "rsa4096":
+            key_selector = b"\x20"
+
+
+        #body = Tlv.build([(0xAC, Tlv.build([(0x80, algo_id)]))])
+        body = Tlv.build([(0xAC, Tlv.build([
+            (0x80, algo_id),
+            (0x81, key_selector)
+        ]))])
+
         ins = 0x47
         p1 = 0
         p2 = key_ref
@@ -481,7 +496,7 @@
                 cryptography.hazmat.primitives.asymmetric.ec.SECP256R1(),
             )
             public_key_ecc = public_numbers_ecc.public_key()
-        elif algo == "rsa2048":
+        elif algo in ("rsa2048", "rsa4096"):
             modulus_data = find_by_id(0x81, data)
             exponent_data = find_by_id(0x82, data)
             if modulus_data is None or exponent_data is None:
@@ -609,7 +624,7 @@
             certificate = certificate_builder.public_key(public_key_ecc).sign(
                 P256PivSigner(device, key_ref, public_key_ecc), hashes.SHA256()
             )
-        elif algo == "rsa2048":
+        elif algo in ("rsa2048", "rsa4096"):
             if key_ref == 0x9C:
                 device.login(pin)
             csr = csr_builder.sign(
diff -ura package.orig/pynitrokey/pynitrokey/nk3/piv_app.py package.new/pynitrokey/pynitrokey/nk3/piv_app.py
--- package.orig/pynitrokey/pynitrokey/nk3/piv_app.py	2025-12-10 21:24:30.511426525 +0100
+++ package.new/pynitrokey/pynitrokey/nk3/piv_app.py	2025-12-10 22:27:20.067101562 +0100
@@ -39,6 +39,22 @@
     assert len(total) == 256
     return total
 
+def prepare_for_pkcs1v15_sign(data: bytes, key_size_bytes: int) -> bytes:
+    digest = hashes.Hash(hashes.SHA256())
+    digest.update(data)
+    hashed = digest.finalize()
+
+    # ASN.1 DigestInfo prefix for SHA-256
+    prefix = bytearray.fromhex("3031300d060960864801650304020105000420")
+
+    # PKCS#1 v1.5 block:
+    #  0x00 0x01 FF FF ... FF 0x00 prefix hash
+    padding_len = key_size_bytes - 3 - len(prefix) - len(hashed)
+    padding = b"\x00\x01" + (b"\xff" * padding_len) + b"\x00"
+
+    total = padding + prefix + hashed
+    assert len(total) == key_size_bytes
+    return total
 
 class StatusError(Exception):
     def __init__(self, value: int):
@@ -306,6 +322,12 @@
         payload = prepare_for_pkcs1v15_sign_2048(data)
         return self.raw_sign(payload, key, 0x07)
 
+    def sign_rsa(self, data: bytes, key: int, bits: int) -> bytes:
+        key_size_bytes = bits // 8
+        payload = prepare_for_pkcs1v15_sign(data, key_size_bytes)
+        algo_id = 0x07 if bits == 2048 else 0x16
+        return self.raw_sign(payload, key, algo_id)
+
     def raw_sign(self, payload: bytes, key: int, algo: int) -> bytes:
         body = Tlv.build([(0x7C, Tlv.build([(0x81, payload), (0x82, b"")]))])
         result = self.send_receive(0x87, algo, key, body)

I tried to test with openssl and openSC-pkcs11 - but it's limited to rsa3072
however: as the token is able to generate a full rsa4096 signature for its self-signed cert and I'm able to communicate with it via javax.smartcardio I guess I can replicate it this way (I'm currently working on a BouncyCastle extension to combine javax.smartcardio to be able to use piv-capable tokens like yubikey or nitrokey)

openssl x509 -in 82.crt -noout -text -certopt ext_parse
Certificate:
    Data:
        Version: 3 (0x2)
        Serial Number:
            01:e1:23:e8:8b:5d:35:90:bd:7a:e8:9d:4d:1d:93:83:6e:23:7d:f4
        Signature Algorithm: sha256WithRSAEncryption
        Issuer: CN=82
        Validity
            Not Before: Jan  1 00:00:00 2000 GMT
            Not After : Jan  1 00:00:00 2099 GMT
        Subject: CN=82
        Subject Public Key Info:
            Public Key Algorithm: rsaEncryption
                Public-Key: (4096 bit)
                Modulus:
                    00:ab:78:3c:8c:2d:be:59:f2:74:17:fc:8e:58:69:
                    67:10:ac:c1:59:35:b6:09:24:1d:1a:d3:67:47:ae:
                    5c:03:c9:f4:da:ac:90:56:e2:21:0c:3f:3d:fd:62:
                    31:d8:25:73:64:c0:c0:6f:f5:d2:e4:33:91:11:d8:
                    be:2d:2e:3a:7b:5e:7c:c7:2c:9c:96:2d:5e:48:6e:
                    8f:bd:a3:e4:97:58:87:f9:54:21:8c:e4:de:26:ec:
                    6e:f8:fe:57:4f:3e:92:dd:96:9a:db:42:8f:29:3a:
                    e2:db:72:45:14:9c:11:6b:3e:12:50:99:1c:60:07:
                    e6:f8:ce:fa:0d:8f:ce:b8:a3:e3:c9:a5:5c:26:0a:
                    ca:34:ac:5f:5d:ad:f9:da:5f:38:38:cc:29:87:9a:
                    8e:76:7f:75:e7:fb:65:06:8a:fe:e4:76:ea:89:76:
                    12:65:6a:95:b5:df:5c:2f:c1:54:2c:c9:d2:31:52:
                    3e:3b:a3:7d:a3:34:47:f9:d1:76:ce:7e:5d:5b:ab:
                    6b:28:7a:67:8d:92:cd:13:32:4c:b3:40:3f:ff:ee:
                    b5:74:6b:7d:ca:f3:02:86:57:68:47:af:68:c3:b0:
                    f6:1d:fe:80:df:3b:1a:b3:2e:d1:7e:5e:7a:ff:49:
                    57:6f:77:8f:20:8d:25:29:f9:b3:f7:25:f8:fa:de:
                    ad:9a:a0:86:6b:7a:1b:56:f5:0c:92:ee:a8:58:f3:
                    0d:5a:6f:22:f6:bc:dc:4c:1e:9d:f6:76:c7:fc:bc:
                    18:9f:fa:83:9a:9b:63:3e:ca:47:51:aa:ee:84:ca:
                    fc:16:d2:99:e7:81:8b:37:e2:2f:38:cf:79:8d:e9:
                    03:54:6e:64:96:63:bc:e3:99:65:64:72:2c:54:14:
                    aa:96:ab:c9:ce:04:4f:40:0d:37:5f:62:1e:7f:48:
                    5f:c8:8b:fa:d6:0a:59:9d:9b:a3:c7:aa:6b:f3:61:
                    5a:59:ff:3d:42:cf:3b:17:8c:8e:da:e8:46:ab:e4:
                    54:cf:53:6a:53:d0:54:02:9b:2d:84:77:99:d3:4e:
                    11:f0:71:52:39:c7:3d:67:b8:67:8d:df:de:e2:d9:
                    2a:a8:7f:56:18:3f:b8:26:92:f3:4d:ed:12:68:e0:
                    16:f5:60:be:db:22:a5:a0:ca:6d:9b:fb:e6:bc:6d:
                    68:f8:e1:53:b5:05:a3:f6:83:10:dd:b8:06:dd:3e:
                    e9:b1:f7:27:fa:3f:35:7b:ea:d1:e9:64:e7:ba:d8:
                    d1:53:69:41:24:94:32:d7:7c:4a:de:a4:f9:ef:5e:
                    14:13:6e:53:16:c8:3a:94:0a:89:e3:02:de:8e:c5:
                    4e:20:40:44:cb:4b:1e:5a:75:39:11:cc:f2:ec:db:
                    a3:23:31
                Exponent: 65537 (0x10001)
        X509v3 extensions:
            X509v3 Basic Constraints: critical
                CA:FALSE
            X509v3 Key Usage: critical
                Digital Signature, Non Repudiation
            X509v3 Extended Key Usage: 
                TLS Web Client Authentication, Microsoft Smartcard Login
            S/MIME Capabilities: 
    0:d=0  hl=3 l= 131 cons: SEQUENCE          
    3:d=1  hl=2 l=  11 cons:  SEQUENCE          
    5:d=2  hl=2 l=   9 prim:   OBJECT            :aes-256-cbc
   16:d=1  hl=2 l=  11 cons:  SEQUENCE          
   18:d=2  hl=2 l=   9 prim:   OBJECT            :id-aes256-wrap
   29:d=1  hl=2 l=  11 cons:  SEQUENCE          
   31:d=2  hl=2 l=   9 prim:   OBJECT            :aes-192-cbc
   42:d=1  hl=2 l=  11 cons:  SEQUENCE          
   44:d=2  hl=2 l=   9 prim:   OBJECT            :id-aes192-wrap
   55:d=1  hl=2 l=  11 cons:  SEQUENCE          
   57:d=2  hl=2 l=   9 prim:   OBJECT            :aes-128-cbc
   68:d=1  hl=2 l=  11 cons:  SEQUENCE          
   70:d=2  hl=2 l=   9 prim:   OBJECT            :id-aes128-wrap
   81:d=1  hl=2 l=  10 cons:  SEQUENCE          
   83:d=2  hl=2 l=   8 prim:   OBJECT            :des-ede3-cbc
   93:d=1  hl=2 l=   7 cons:  SEQUENCE          
   95:d=2  hl=2 l=   5 prim:   OBJECT            :des-cbc
  102:d=1  hl=2 l=  14 cons:  SEQUENCE          
  104:d=2  hl=2 l=   8 prim:   OBJECT            :rc2-cbc
  114:d=2  hl=2 l=   2 prim:   INTEGER           :80
  118:d=1  hl=2 l=  14 cons:  SEQUENCE          
  120:d=2  hl=2 l=   8 prim:   OBJECT            :rc4
  130:d=2  hl=2 l=   2 prim:   INTEGER           :0200

    Signature Algorithm: sha256WithRSAEncryption
    Signature Value:
        66:7a:af:a2:f5:31:07:e1:77:36:ba:6c:86:cb:8c:5f:57:45:
        1e:7d:3a:7b:8f:3c:e0:d8:27:38:4e:98:96:df:41:61:1f:f7:
        3c:dd:89:be:c0:12:13:3d:cb:48:29:df:ac:01:e5:09:90:2a:
        83:b1:4b:7e:b7:8b:6b:fe:2c:75:02:ba:41:2a:60:0b:c5:1d:
        88:19:18:d0:a4:8d:14:30:5d:c3:15:a9:43:27:a5:4e:c5:94:
        f2:d8:01:a7:c7:59:96:5d:4b:63:4f:5b:ad:bc:75:63:fa:04:
        7a:63:d9:29:f3:ff:9b:4b:cb:27:41:91:0d:d1:30:54:29:dc:
        85:83:9b:31:49:64:ae:39:50:37:b1:a9:b0:b1:51:8b:b0:6e:
        48:24:04:19:c7:17:d3:99:22:e1:cc:44:b0:39:94:1d:db:7d:
        77:38:a9:06:00:9f:de:ce:7f:8f:e7:03:7d:ad:49:e1:74:62:
        4b:c8:a5:37:ed:5a:12:84:53:44:75:0a:e5:91:86:78:44:31:
        b6:67:34:67:ae:47:5e:db:fe:3b:94:1e:d8:3d:12:ed:00:ae:
        ce:e3:0f:40:1c:23:54:cc:96:29:a6:e8:fe:bf:8f:39:66:2e:
        fe:b1:e9:6a:26:98:5c:1a:81:1a:05:c5:7e:49:6a:e2:1d:63:
        3d:13:ee:b3:b6:71:1c:69:67:9e:8d:79:81:87:9b:fa:fe:b9:
        9e:fb:0c:7d:8c:a8:52:a5:f8:b2:50:1a:a7:78:00:7f:71:5e:
        4b:2a:04:5e:2b:18:3c:d8:a7:11:62:2f:1b:43:8d:70:3e:5a:
        86:95:df:59:c5:14:fa:94:24:60:fb:f1:5b:e1:c4:7b:f9:a6:
        4d:de:31:21:e3:d0:61:9f:40:97:b8:62:17:ec:37:02:3b:eb:
        44:9b:16:32:97:ae:31:7a:10:8b:19:87:a7:13:7a:78:8a:80:
        3a:eb:ae:33:88:7c:6a:bb:50:c5:50:66:12:2b:65:b3:f6:5e:
        21:08:8b:13:8e:87:c4:0a:c9:9d:41:23:c5:4c:5b:aa:60:61:
        68:0a:6b:f3:f0:52:74:4b:d5:24:41:21:f7:95:02:23:98:ea:
        73:09:00:45:17:85:e9:38:45:54:f6:a9:4e:de:99:ba:76:98:
        f5:81:5a:d3:28:dc:f6:aa:ee:d0:d3:4f:d5:55:1d:54:b5:4c:
        e7:6e:1b:2e:6f:54:eb:4b:4d:a2:5f:e8:b5:26:93:1f:1f:d8:
        a8:b0:8a:21:ef:53:48:62:9f:55:31:5e:15:a8:c2:66:12:97:
        d6:ac:7e:e1:96:3f:dc:06:49:75:00:51:da:f2:c4:8c:57:81:
        97:f6:a0:5f:d2:bd:73:03

maybe you can release some stub driver like yubico to expose full rsa4096? the piv firmware is clearly capable of performing it - it's just not exposed in a convenient way (altough with raw APDU it's likely possible)

Uh oh!

PIV: Support all algorithms the NK3 support #700

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