ECDH.md

tags	aliases	sources
security	Elliptic Curve Diffie–Hellman Elliptic Curve Diffie–Hellman Key Exchange

Anonymous [[key establishment|key exchange]] scheme

Based on the following property of EC points:

$$ (a * G) * b = (b * G) * a $$ Where

• a, b - secrets
• G - ECC elliptic curve with generator point

Algorithm

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

1. Alice generates a random ECC key pair: {alicePrivKey, alicePubKey = alicePrivKey * G}
2. Bob generates a random ECC key pair: {bobPrivKey, bobPubKey = bobPrivKey * G}
3. Alice and Bob exchange their public keys through the insecure channel
4. Alice calculates sharedKey = bobPubKey * alicePrivKey
5. Bob calculates sharedKey = alicePubKey * bobPrivKey
6. Now both Alice and Bob have the same sharedKey == bobPubKey * alicePrivKey == alicePubKey * bobPrivKey