Bob and Alice Play Mental Poker In a World Where They Trust No-one
We have a major competition … it’s Bob playing Alice in the greatest game of poker ever created. But neither Bob nor Alice trusts each other to deal, as they think the other one will cheat, and they don’t trust anyone else, as each of the dealers selected has some bias towards Bob or Alice.
So how do we deal five cards to each of them so that there are no doubles in their hands, and that Bob and Alice cannot determine what is in each other’s hand? For this we need the SRA (Shamir, Rivest and Adleman) algorithm for commutative encryption, and where we can encrypt in any order and decrypt in any order:
Enc(K2,Enc(K1,message) = Enc(K1,Enc(K2,message)
So let’s deal
First Alice and Bob share the 52 cards (M1, M2, …, M52) and a modulus value of N=pq, p, and q (where p and q are the two prime numbers selected). Alice uses her key pair of [e1,d1] and Bob has a key of [e2,d2].
Now we perform the following:
- Alice encrypts all the cards M1, M2, …, M52 with her key, using:
