ECDH Key Exchange - Examples

Now let's implement the ECDH algorithm (Elliptic Curve Diffie–Hellman Key Exchange) in Python.

We shall use the tinyec library for ECC in Python:

pip install tinyec

Now, let's generate two public-private key pairs, exchange the public keys and calculate the shared secret:

from tinyec import registry
import secrets

def compress(pubKey):
    return hex(pubKey.x) + hex(pubKey.y % 2)[2:]

curve = registry.get_curve('brainpoolP256r1')

alicePrivKey = secrets.randbelow(curve.field.n)
alicePubKey = alicePrivKey * curve.g
print("Alice public key:", compress(alicePubKey))

bobPrivKey = secrets.randbelow(curve.field.n)
bobPubKey = bobPrivKey * curve.g
print("Bob public key:", compress(bobPubKey))

print("Now exchange the public keys (e.g. through Internet)")

aliceSharedKey = alicePrivKey * bobPubKey
print("Alice shared key:", compress(aliceSharedKey))

bobSharedKey = bobPrivKey * alicePubKey
print("Bob shared key:", compress(bobSharedKey))

print("Equal shared keys:", aliceSharedKey == bobSharedKey)

Run the above code example: https://repl.it/@nakov/ECDH-Key-Exchange-in-Python.

The elliptic curve used for the ECDH calculations is 256-bit named curve brainpoolP256r1. The private keys are 256-bit (64 hex digits) and are generated randomly. The public keys will be 257 bits (65 hex digits), due to key compression.

The output of the above code looks like this:

Alice public key: 0x66c808e6b5be6d6620934bc6ffa2b8b47f9786c002bfb06d53a0c27535641a5d1
Bob public key: 0x7d15195432d1ac7f38aeb054d07d9b2e1faa913b78ad04d5efdd4a1ee8d9a3191
Now exchange the public keys (e.g. through Internet)
Alice shared key: 0x90f5a1cf2ed1dbb0322178df6bb0dd72c541884618b2989a3e5e663198667a621
Bob shared key: 0x90f5a1cf2ed1dbb0322178df6bb0dd72c541884618b2989a3e5e663198667a621
Equal shared keys: True

Due to randomization, if you run the above code, the keys will be different, but the calculated shared secret for Alice and Bob at the end will always be the same. The generated shared secret is a 257-bit integer (compressed EC point for 256-bit curve, encoded as 65 hex digits).