Tiny ECDH in Python

This is a Python implementation of the Tiny ECDH in C

It's a small and portable implementation of the Elliptic-Curve Diffie-Hellman key agreement algorithm written in Python.

Description from Wikipedia:

Elliptic-curve Diffie–Hellman (ECDH) is an anonymous key agreement protocol that allows two parties, each having an elliptic-curve public–private key pair, to establish a shared secret over an insecure channel. This shared secret may be directly used as a key, or to derive another key. The key, or the derived key, can then be used to encrypt subsequent communications using a symmetric-key cipher. It is a variant of the Diffie–Hellman protocol using elliptic-curve cryptography. ` This repository was developed just by replicating the C version in Python, and can be improved to a more pythonic alternative. It's still very slow when compared to the C version.

Usage:

The ECDH algorithm (Elliptic Curve Diffie–Hellman Key Exchange) is trivial:

1. Alice generates a random ECC key pair: {alicePrivKey, alicePubKey = alicePrivKey * G}

# Assumes private key is filled with random data before calling, and generates public key
alicePrivKey, alicePubKey = ecdh_generate_keys(alicePrivKey, alicePubKey)

2. Bob generates a random ECC key pair: {bobPrivKey, bobPubKey = bobPrivKey * G}

# Assumes private key is filled with random data before calling, and generates public key
bobPrivKey, bobPubKey = ecdh_generate_keys(bobPrivKey, bobPubKey)

3. Alice and Bob exchange their public keys through the insecure channel (e.g. over Bluetooth)

4. Alice calculates sharedKey = bobPubKey * alicePrivKey

# own private key + Bob's public key will generate a shared secret key
aliceSharedKey = ecdh_shared_secret(alicePrivKey, bobPubKey)

5. Bob calculates sharedKey = alicePubKey * bobPrivKey

# own private key + Alice's public key will generate a shared secret key
bobSharedKey = ecdh_shared_secret(bobPrivKey, alicePubKey)

6. Now both Alice and Bob have the same sharedKey == bobPubKey * alicePrivKey == alicePubKey * bobPrivKey

assert aliceSharedKey == bobSharedKey

TODO:

• Add more NIST curves
• Create a more pythonic alternative