Inputs

Given a sudoku puzzle as an example, where the verifier needs to check if the solution honours the rules of sudoku. The proof would be an exmaple of how the board could be filled

• x -> puzzle (obfuscated info: public info)

• w -> solution (witness: secret info)

• phi -> constraints (predicate)

The predicate is the set of constraints that must be honoured. In this case, the rules of sudoku. In other cases, its your r1CS.

The witness is the secret info that should not be shared. It is represented by the x via an obfuscating homomorphism.