After we explained in the previous section how the EdDSA signatures work, now it is time to demonstrate them with code examples. First, we shall demonstrated how to use Ed25519 signatures.

Ed25519 Signatures - Example

We shall use the Python library ed25519, which is based on the Bernstein's original optimized highly optimized C implementation of the Ed25519 signature algorithm (EdDSA over the Curve25519 in Edwards form):

pip install ed25519

Next, generate a private + public key pair for the Ed25519 cryptosystem, sign a sample message, and verify the signature:

import ed25519
​
privKey, pubKey = ed25519.create_keypair()
print("Private key (32 bytes):", privKey.to_ascii(encoding='hex'))
print("Public key (32 bytes): ", pubKey.to_ascii(encoding='hex'))
​
msg = b'Message for Ed25519 signing'
signature = privKey.sign(msg, encoding='hex')
print("Signature (64 bytes):", signature)
​
try:
    pubKey.verify(signature, msg, encoding='hex')
    print("The signature is valid.")
except:
    print("Invalid signature!")

Run the above code example: https://repl.it/@nakov/Ed25519-sign-verify-in-Python.

The output from the above sample code looks like this:

Private key (32 bytes): b'1498b5467a63dffa2dc9d9e069caf075d16fc33fdd4c3b01bfadae6433767d93'
Public key (32 bytes):  b'b7a3c12dc0c8c748ab07525b701122b88bd78f600c76342d27f25e5f92444cde'
Signature (64 bytes): b'6dd355667fae4eb43c6e0ab92e870edb2de0a88cae12dbd8591507f584fe4912babff497f1b8edf9567d2483d54ddc6459bea7855281b7a246a609e3001a4e08'
The signature is valid.

The Ed25519 key pair is generated randomly: first a 32-byte random seed is generated, then the private key is derived from the seed, then the public key is derived from the private key. The hash function for key generation is SHA-512.

The private key is encoded as 64 hex digits (32 bytes). The public key is encoded also as 64 hex digits (32 bytes). The EdDSA-Ed25519 signature {R, s} is 32 + 32 bytes (64 bytes, 128 hex digits).

If we try to verify a tampered message, the verification will fail:

try:
    pubKey.verify(signature, "Tampered msg", encoding='hex')
    print("The signature is valid.")
except:
    print("Invalid signature!")

Run the above code example: https://repl.it/@nakov/Ed25519-verify-tampered-message-in-Python.

The output from the above sample code is as expected:

Invalid signature!

Ed448 Signatures - Example

Now, let's demonstrate how to use the Ed448 signature (EdDSA over the Curve448-Goldilocks curve in Edwards form).

We shall use the Python elliptic curve library ECPy, which implements ECC with Weierstrass curves (like secp256k1 and NIST P-256), Montgomery curves (like Curve25519 and Curve448) and twisted Edwards curves (like Ed25519 and Ed448):

pip install ecpy

Next, generate a private + public key pair for the Ed448 cryptosystem:

from ecpy.curves import Curve
from ecpy.keys import ECPrivateKey
from ecpy.eddsa import EDDSA
import secrets, hashlib, binascii
​
curve = Curve.get_curve('Ed448')
signer = EDDSA(hashlib.shake_256, hash_len=114)
privKey = ECPrivateKey(secrets.randbits(57*8), curve)
pubKey = signer.get_public_key(privKey, hashlib.shake_256, hash_len=114)
print("Private key (57 bytes):", privKey)
print("Public key (compressed, 57 bytes): ",
      binascii.hexlify(curve.encode_point(pubKey.W)))
print("Public key (point): ", pubKey)

Run the above code example: https://repl.it/@nakov/Ed448-private-public-keys-in-Python.

The Ed448 key pair is generated randomly. According to RFC 8032 the Ed448 private key is generated from 57-byte random seed, which is transformed to 57-byte public key using the SHAKE256(x, hash_len=114) hash function, along with EC point multiplication and the special key encoding rules for Ed448.

The output from the above sample code may look like this:

Private key (57 bytes): ECPrivateKey:
  d: 625d3edeb5cd69b20b0b6387c3522a21d356ac40b408e34fb2f8442e2c91eee3f877afe583a2fd11770567df69178019d6fbc6357c35eefa3e
Public key (compressed, 57 bytes):  b'261d23911e194ed0cb7f9233568e906d6abcf4d60f73451ca807636d8fa6e4ea5ca12f51d240299a0b86a61ccb2174ce4ed2a8c4f7a8cced00'
Public key (point):  ECPublicKey:
  x: cb5aec366d6b3293354418f8abf67bd5aaf46b49ff9c2154fbc14d9ca22fe93b680954f27c10fed3327ef51c8bce5d2522f41fd554731d88
  y: edcca8f7c4a8d24ece7421cb1ca6860b9a2940d2512fa15ceae4a68f6d6307a81c45730fd6f4bc6a6d908e5633927fcbd04e191e91231d26

The private key is encoded as 114 hex digits (57 bytes). The public key is encoded also as 114 hex digits (57 bytes), in compressed form. In the above example the public key EC point is printed also in uncompressed format (x and y coordinates). The EdDSA-Ed448 signature {R, s} consists of 57 + 57 bytes (114 bytes, 228 hex digits).

Next, sign a sample message using the private key, and verify the signature using the public key after that:

msg = b'Message for Ed448 signing'
signature = signer.sign(msg, privKey)
print("Signature (114 bytes):", binascii.hexlify(signature))
​
valid = signer.verify(msg, signature, pubKey)
print("Valid signature?", valid)

Run the above code example: https://repl.it/@nakov/Ed448-sign-verify-in-Python.

The output from the above code example (for the above Ed448 key pair) is:

Signature (114 bytes): b'5114674f1ce8a2615f2b15138944e5c58511804d72a96260ce8c587e7220daa90b9e65b450ff49563744d7633b43a78b8dc6ec3e3397b50080a15f06ce8005ad817a1681a4e96ee6b4831679ef448d7c283b188ed64d399d6bac420fadf33964b2f2e0f2d1abd401e8eb09ab29e3ff280600'
Valid signature? True

The signature is deterministic: the same message with the same private key produces the same signature.

If we try to verify the same signature with a tampered message, the verification will fail:

valid = signer.verify(b'Tampered msg', signature, pubKey)
print("Valid signature?", valid)

Run the above code example: https://repl.it/@nakov/Ed448-verify-tampered-message-in-Python.

The output from the above sample code is as expected:

Valid signature? False