7.3 The Diffie-Hellman key-exchange protocol

Alice and Bob communicate over an insecure channel. They can establish a shared secret K using the following protocol steps [49]:

1. Alice and Bob publicly agree on a cyclic group 𝔾 and a corresponding generator g. Very often, this step is performed out of band long before the actual key agreement. For example, 𝔾 and g might be specified in a public document.

2. Alice chooses a natural number α, where 1 < α < N, where N is the order of 𝔾. α is Alice’s private key SK_Alice. She must not disclose this number to any other party.

3. Bob does the same as Alice: he independently chooses a number 1 < β < N as his private key SK_Bob.

4. Alice computes A = g^α in G and sends A to Bob. The number A (together with G and g) can be seen as Alice’s public key: PK_Alice = (g,G,A).

5. Bob computes B = g^β in G and sends B to Alice. The number B (together with G and g) can be seen...