zkSNARKs Example

An example of how generate zero-knowledge proofs and verify using an Ethereum smart contract.

Tutorial

• Install circom and snarkjs:

  npm install -g circom
  npm install -g snarkjs

  NOTE: for this demo I used [email protected] and [email protected]

  • Circom is a language for writing arithmetic circuits that can be used in zero-knowledge proofs. Circom stands for circuit compiler.
  • Snarkjs is a JavaScript implementation of zkSNARK schemes which is used to generate proofs given circuits generated with circom.

• Create a circuit:

  We'll create a circuit that tries to prove we are able to factor a number.

  • The circuit will have 2 private inputs and 1 output.
  • The output signal c must be the value of signal a times signal b.
  • We instantiate the circuit and assign it to the main component. The component main must always exist.

  circuit.circom

  template Multiplier() {
    signal private input a;
    signal private input b;
    signal output c;
    c <== a*b;
  }
  
  component main = Multiplier();

  Ths only thing the circuit enforces is that c equals a times b with the statement c <== a*b which defines the constraint.

• Compile the circuit with circom:

  circom factor/circuit.circom -o circuit.json

  This will output circuit.json

• Run setup for the circuit:

  Running the setup method will instantiate key files we'll need:

  snarkjs setup --circuit=circuit.json

  The setup will generate a proving key and a verification key, proving_key.json and verification_key.json respectively.

• Calculate a witness:

  We'll create a file containing the input parameters.

  • Provide a file with the inputs and it will execute the circuit.
  • Snarkjs will calculate the intermediate signals and the output.
  • The calculated set of signals is the witness.

  For this example, we'll be proving we can factor 56 without revealing the two factor numbers.

  We'll prove that we know that 7 and 8 multiply to 56:

  input.json

  {
    "a": 7,
    "b": 8
  }

  • The zero knowledge proofs prove that we know a set of signals that match the constraints.
  • These signals are the witness.
  • The witness doesn't reveal any of the signals except the public inputs and the outputs.

  We can calculate the witness now:

  snarkjs calculatewitness --circuit=circuit.json --input=input.json

  This generates witness.json with all the signals.

• Generate proof:

  We'll use the proving key and witness to generate a proof that we the inputs that factor into 56:

  snarkjs proof --witness=witness.json --provingkey=proving_key.json

  This generates proof.json and public.json which is the values of the public inputs and outputs. In this case it's just the output because our inputs were private.

  [
   "56"
  ]

• Verify proof:

  We can verify a proof using snarkjs:

  $ snarkjs verify --proof=proof.json --verificationkey=verification_key.json --public=public.json
  OK

  This will output OK if correct or INVALID if incorrect.

• Smart contract to verify proofs:

  snarkjs provides a method to generate a contract to verify proofs onchain:

  snarkjs generateverifier --verificationkey=verification_key.json

  This outputs verifier.sol

  The contract method we'll be using is verifyProof:

  function verifyProof(
          uint[2] a,
          uint[2] a_p,
          uint[2][2] b,
          uint[2] b_p,
          uint[2] c,
          uint[2] c_p,
          uint[2] h,
          uint[2] k,
          uint[1] input
      ) view public returns (bool r) {
      Proof memory proof;
      proof.A = Pairing.G1Point(a[0], a[1]);
      proof.A_p = Pairing.G1Point(a_p[0], a_p[1]);
      proof.B = Pairing.G2Point([b[0][0], b[0][1]], [b[1][0], b[1][1]]);
      proof.B_p = Pairing.G1Point(b_p[0], b_p[1]);
      proof.C = Pairing.G1Point(c[0], c[1]);
      proof.C_p = Pairing.G1Point(c_p[0], c_p[1]);
      proof.H = Pairing.G1Point(h[0], h[1]);
      proof.K = Pairing.G1Point(k[0], k[1]);
      uint[] memory inputValues = new uint[](input.length);
      for(uint i = 0; i < input.length; i++){
          inputValues[i] = input[i];
      }
      if (verify(inputValues, proof) == 0) {
          return true;
      } else {
          return false;
      }
  }

  As you can see there is a lot going on. Snarkjs conveniently provides a method to generate the transaction input parameters.

  snarkjs generatecall --proof=proof.json --public=public.json

  The output will look similar to this:

  ["0x225074f4c52d6abfbe39070488e9ad4a614c17e954f6dd1f95df298a0eef0a6c", "0x16c7e4b0c01a120fe48c8eb2339a7209e77796328a61e56547b73567016fd75e"],["0x250a2c4eb6c8d434b3fa3c408c1a3ab4a2db6d63c7ba917c9849083c86812832", "0x2f9c617819fec52b3417745eee59319eb56d846b5e428cb81d90a9a1f09beaf4"],[["0x19ab9c29a7e580507cc3054f36f12506d429112faa75e751ddc4c6237344ab1a", "0x099afd70d77234c35b15112b7a9352f6ec2b3030408125b66654631de21c078e"],["0x2d67175e322ab6e6a98921e29c94cdd1ab07db28d62de7e104199361e5092851", "0x0bdc9fd000cdbc79b344fb307c1ea679b2a14f1756a47cbccefe6349265fdd9d"]],["0x2f17a8a96f4f1a37dcf99fceddbb942e94a3a83547b80f4061eaa295d969dccc", "0x086cc7c64c083849eba6161be31f794b359e735e83c25a7ee9475d9943d9b8f5"],["0x26f172ffa1f027799863c43c640ccb632fc664c918138fea026127bdf07c6c0a", "0x0e0dd693317beda6b8bf1ac9024af15a35bee071cc5bdcb2784926df18ba3fb0"],["0x1c23be59028e8095a430b2e5b3768303ec5163a49e2a9b4da7f3a6b30b78a5f1", "0x0318a6a3bd9a7c36e35fc44030fda9dd594965b1cba90c942211028c3f308fb6"],["0x1f84acf96a6d7b112c097feb438dadd8bc56c59f5e466e7d17e33560df87c893", "0x257a236d53fb9a129d5e8239d592bc3173f99ab378df5f5c5a00d4e3fb6983b2"],["0x1c55a602b2237a439ccc899ae6a49e1d08ca66300283500188e5823d246a9321", "0x1c297b898c386684bc32e504317dbfdb09971227d413541f74659fcc2cd8a9a5"],["0x0000000000000000000000000000000000000000000000000000000000000038"]

  The verify function returns true if the public inputs satisfy the proof.

• Compiling verifier contract:

  Head over to the Ethereum Remix IDE and paste in the smart contract.

  • Compile the smart contract using the correct solidity compiler version.
  

• Deploying verifier contract:

  Use the MetaMask extension and connect to a testnet. I chose the Rinkeby testnet for this example.

  • Select Injected Web3 as the environment.
  • Select the Verifier contract and click Deploy.
  

  Deployment transaction: https://rinkeby.etherscan.io/tx/0x6b7c99bc9b6972e11c3a2918d8fe00b40f0036ebf18d28918a20a80b8d306947

• Verify proofs using the deployed contract:

  Use the generatecall helper like we did in a previous step and paste it in to the verifyProof input field under Deployed Contracts:

  

  This is a pure function meaning it doesn't perform any writes. You'll get back a boolean response as you can see in the bottom right below the method input field.

Additional

• To show general statistics of a circuit, you can run:

  snarkjs info --circuit=circuit.json

• Print the constraints of the circuit by running:

  snarkjs printconstraints --circuit=circuit.json

Resources

• zkSNARKs in a Nutshell
• Awesome Zero Knowledge Proofs
• circom and snarkjs tutorial

License

MIT