Examples of flattening code to create an R1CS

Question

When preparing logic for use in a zkSnark, one needs to first "flatten" the code so it can be written as a series of constraints.

I'm finding it hard to find examples of doing this. For instance, how would I do convert the following logic into a series of constraints:

if ((input_1 && input_2) || input_3) {
  result = input_1 + input_2
} else {
  result = input_3
}

How would you go about converting this into an arithmetic statement that can then be then re-written as a series of constraints? Or does there exist any examples of this sort of process that someone could learn from?

Answer 1

This sort of programming logic for the ZK SNARK systems can be developed into Arithmetic Circuits using Zokrates, a toolbox for zkSNARKs on Ethereum. It helps you use verifiable computation in your Decentralised Applications, from the specification of your program in a high-level language to generating proofs of computation to verifying those proofs in Solidity, the Smart Contract Langauge for Ethereum Blockchain. Please find a sample programming logic written for Zokrates below.

Once you compile the code, you can proceed to the circuit setup. It creates a prover key and verification key. These keys are derived from a source of randomness, commonly referred to as “toxic waste”. Once it is generated, you can proceed to generate a Solidity contract which contains the generated verification key and a public function to verify a solution to the compiled program. Then you can compute a witness for the compiled program. A witness is a valid assignment of the variables, which include the results of the computation.

def main(field a, field b, field c) -> (field):
    field result = 0
    result = if a + b > c  then a + b else 1 fi
    result = if a + b < c  then c else 1 fi
  return result