What are zk-SNARK Circuits ?

In this section, we will explore what zk-SNARK circuits are, their role in zero-knowledge proofs, and how they are used to define computations that can be proven without revealing sensitive data.

zk-SNARK circuits are mathematical models used to prove computations without revealing data. In Poseidon, these circuits are written in Circom and saved as .circom files.

Key Components of zk-SNARK Circuits:

1. Inputs:

   • Public: Visible to both the prover and verifier (e.g., a public key).

   • Private: Known only to the prover (e.g., a secret password).

   Example: Proving that you know a secret number without revealing it.

2. Constraints:

   • Logical conditions that ensure the computation is correct.

   • These are the rules that must be satisfied for the proof to be valid.

   Example: Verifying that a sum of two numbers equals a known result without revealing the numbers.

3. Outputs:

   • The result of the computation that needs to be proven.

   • This shows that the prover knows the valid solution, without disclosing how it was derived.

   Example: Proving that you know a solution to a cryptographic puzzle.

Process:

1. Write Circuit: Define inputs, constraints, and outputs using the Circom language in a .circom file. This represents the logic you want to prove.

2. Compile Circuit: Convert the written circuit into an R1CS (Rank-1 Constraint System), along with a .wasm file and witness generator for proof generation.

3. Trusted Setup (Powers of Tau): Perform a one-time cryptographic setup to generate secure parameters (e.g., .tau files). This phase ensures the integrity and trustworthiness of the zk-SNARK system.

4. Key Generation: Use the R1CS and setup data to generate:

5. A proving key (e.g., circuit_final.zkey) used to create zk-proofs.

6. A verification key used to verify proofs.

7. Generate Proof: Provide valid inputs and use the proving key and compiled circuit to generate a zk-proof (.proof and .wtns files).

8. Verify Proof: Use the verification key to confirm the validity of the proof without learning the private inputs.

Example Workflow:

• Circuit Definition: Prove you know two numbers x and y such that x + y = 10.

  • Inputs: x, y (private)

  • Constraint: x + y = 10 (logic)

  • Output: Prove the sum without revealing x or y.

Once compiled, the circuit generates an R1CS, which is used to create a zk-proof that can be verified by anyone without knowing the values of x and y.