This is a simple example of how to create a private multiplication application. The objective is to create a circuit in multiple languages and DSL and compare the experience.
This is a particular simple circuit, but it is a good starting point for more complex circuits.
- The circuit gets two private inputs (witness) and multiplies them. The result is then revealed by the prover (public input).
- The circuit checks that the two inputs are smaller than the multiplication result, which itself is less than 2^255. This removes trivial solutions, such as
1 * n = n, as well as solutions that exploit modular arithmetics, such asa * b = n = -a * -b. - The circuit checks that the first input is smaller or equal to the second input. This removes trivial solution permutations, such as
a * b = n = b * a.
This circuit prompts the user to give any factorization of C. This can be used to build a game where users are prompted to submit factorizations, only new factorizations are accepted, and each subsequent factorization, as it is harder to find, is worth more points.