SPEKE (cryptography) - Description

Description

The protocol consists of little more than a Diffie-Hellman key exchange where the Diffie-Hellman generator g is created from a hash of the password.

Here is one simple form of SPEKE:

1. Alice and Bob agree to use an appropriately large and randomly selected safe prime p.
2. Alice and Bob agree on a shared password π.
3. Alice and Bob both construct g = hash(π)2 mod p. (Squaring makes g a generator of the prime order subgroup of the multiplicative group of integers modulo p.)
4. Alice chooses a secret random integer a, then sends Bob ga mod p.
5. Bob chooses a secret random integer b, then sends Alice gb mod p.
6. Alice and Bob each abort if their received values are not in the range, to prevent small subgroup confinement attack.
7. Alice computes K = (gb mod p)a mod p.
8. Bob computes K = (ga mod p)b mod p.

Both Alice and Bob will arrive at the same value for K if and only if they use the same value for π. Once Alice and Bob compute the shared secret K they can use it in a key confirmation protocol to prove to each other that they know the same password π, and to derive a shared secret encryption key for sending secure and authenticated messages to each other.

Unlike unauthenticated Diffie-Hellman, SPEKE prevents man in the middle attack by the incorporation of the password. An attacker who is able to read and modify all messages between Alice and Bob cannot learn the shared key K and cannot make more than one guess for the password in each interaction with a party that knows it.

In general, SPEKE can use any prime order group that is suitable for public key cryptography, including elliptic curve cryptography.