Introduction to Cryptography with Coding Theory, 3rd Edition

22.3 Tripartite Diffie-Hellman

Alice, Bob, and Carlos want to agree on a common key (for a symmetric cryptosystem). All communications among them are public. If there were only two people, Diffie-Hellman could be used. A slight extension of this procedure works for three people:

1. Alice, Bob, and Carlos agree on a large prime $p$ and a primitive root $\alpha$.

2. Alice chooses a secret integer $a\text{,}$ Bob chooses a secret integer $b\text{,}$ and Carlos chooses a secret integer $c$.

3. Alice computes $A\equiv {\alpha }^a(\text{mod}p)\text{,}$ Bob computes $B\equiv {\alpha }^b(\text{mod}p)\text{,}$ and Carlos computes $C\equiv {\alpha }^c(\text{mod}p)$.

4. Alice sends $A$ to Bob, Bob sends $B$ to Carlos, and Carlos sends $C$ to Alice.

5. Alice computes $A^{\prime }\equiv C^a\text{,}$ Bob computes $B^{\prime }\equiv A^b\text{,}$ and Carlos computes $C^{\prime }\equiv B^c\text{.}$

6. Alice sends $A^{\prime }$ to Bob, Bob sends $B^{\prime }$ to Carlos, and Carlos ...