A demo of three-party secure multiplication.
Each of the two players, Alice and Bob, has an non-negative integer that is smaller than a large prime number PRIME, x and y respectively. Alice and Bob want to know the product of x and y, but neither of them want their input known by the other player. To meet this requirement, we introduce a third player, Server, to generate and distribute "masks" u, v, and w to Alice and Bob.
This requirement seems absurd for two numbers' multiplication: if, say, Alice knows x and x * y, she can easily recover y by multiplying x * y by x ^ -1. However, if there are three or more numbers to be multiplied together, none of the players can recover other players' inputs from the product. And the solution in this demo can be easily extended to the occasions where there are three or more numbers to be multiplied.
Both Alice and Bob takes an argument as their input for the multiplication:
javac Bob.java && java Bob 42javac Alice.java && java Alice 27Server doesn't take arguments:
javac Server.java && java ServerNote that you should run Alice after Bob, and Server after Alice; otherwise there would be Sockets issues since these three processes are not multi-threaded.
It is recommended that you run the three processes in three vertically aligned terminals. A screenshot of the running demo is shown below.
- Since this is just a demonstration of the idea, the processes are not programmed using multi-threading and have to be run in a certain sequence, otherwise they will not communicate with each other properly. In a more realistic project this cannot happen.
- Class
AliceandBobcould be deduplicated, since they share very similar codes. - Perhaps I should make the multiplication protocol a separate class which is taken in by the constructors of
Player's, so that thePlayer's would do according to the protocol. This is a way of deduplication, as well as a way of extension to more protocols.
A Pragmatic Introduction to Secure Multi-Party Computation, Section 3.4.