Implementation of the zkSNARK Pinocchio protocol and Groth16 protocol from scratch in Go done in my free time to understand the concepts. Do not use in production.
If you want to generate proofs & verify them from Go, you can try https://github.com/vocdoni/go-snark, which is implemented using the bn256 for the Pairing curve operations for the Groth16 zkSNARK, and it is compatible with circom.
zkSNARK library implementation in Go
Succinct Non-Interactive Zero Knowledge for a von Neumann Architecture, Eli Ben-Sasson, Alessandro Chiesa, Eran Tromer, Madars Virza https://eprint.iacr.org/2013/879.pdfPinocchio: Nearly practical verifiable computation, Bryan Parno, Craig Gentry, Jon Howell, Mariana Raykova https://eprint.iacr.org/2013/279.pdfOn the Size of Pairing-based Non-interactive Arguments, Jens Groth https://eprint.iacr.org/2016/260.pdf
Currently allows to do the complete path with Pinocchio protocol and Groth16 protocol :
- write circuit
- compile circuit
- generate trusted setup
- calculate witness
- generate proofs
- verify proofs
Minimal complete flow implementation:
- Finite Fields (1, 2, 6, 12) operations
- G1 and G2 curve operations
- BN128 Pairing
- circuit flat code compiler
- circuit to R1CS
- polynomial operations
- R1CS to QAP
- generate trusted setup
- generate proofs
- verify proofs with BN128 pairing
Experimentation with go-snark-study compiled to wasm: https://github.com/arnaucube/go-snark-study/tree/master/wasm
zkSnark
zkSnark Groth16
bn128 (more details: https://github.com/arnaucube/go-snark-study/tree/master/bn128)
Finite Fields operations
R1CS to QAP (more details: https://github.com/arnaucube/go-snark-study/tree/master/r1csqap)
Circuit Compiler
The cli still needs some improvements, such as seting input files, etc.
In this example we will follow the equation example from Vitalik's article: y = x^3 + x + 5, where y==35 and x==3. So we want to prove that we know a secret x such as the result of the equation is 35.
Having a circuit file test.circuit:
func exp3(private a):
b = a * a
c = a * b
return c
func main(private s0, public s1):
s3 = exp3(s0)
s4 = s3 + s0
s5 = s4 + 5
equals(s1, s5)
out = 1 * 1
And a private inputs file privateInputs.json
[
3
]
And a public inputs file publicInputs.json
[
35
]
In the command line, execute:
> ./go-snark-cli compile test.circuit
If you want to have the wasm input ready also, add the flag wasm
> ./go-snark-cli compile test.circuit wasm
This will output the compiledcircuit.json file.
Having the compiledcircuit.json, now we can generate the TrustedSetup:
> ./go-snark-cli trustedsetup
This will create the file trustedsetup.json with the TrustedSetup data, and also a toxic.json file, with the parameters to delete from the Trusted Setup.
If you want to have the wasm input ready also, add the flag wasm
> ./go-snark-cli trustedsetup wasm
Assumming that we have the compiledcircuit.json, trustedsetup.json, privateInputs.json and the publicInputs.json we can now generate the Proofs with the following command:
> ./go-snark-cli genproofs
This will store the file proofs.json, that contains all the SNARK proofs.
Having the proofs.json, compiledcircuit.json, trustedsetup.json publicInputs.json files, we can now verify the Pairings of the proofs, in order to verify the proofs.
> ./go-snark-cli verify
This will return a true if the proofs are verified, or a false if the proofs are not verified.
All this process can be done using Groth16 protocol protocol:
> ./go-snark-cli compile test.circuit
> ./go-snark-cli groth16 trustedsetup
> ./go-snark-cli groth16 genproofs
> ./go-snark-cli verify
Example:
// compile circuit and get the R1CS
flatCode := `
func exp3(private a):
b = a * a
c = a * b
return c
func main(private s0, public s1):
s3 = exp3(s0)
s4 = s3 + s0
s5 = s4 + 5
equals(s1, s5)
out = 1 * 1
`
// parse the code
parser := circuitcompiler.NewParser(strings.NewReader(flatCode))
circuit, err := parser.Parse()
assert.Nil(t, err)
fmt.Println(circuit)
b3 := big.NewInt(int64(3))
privateInputs := []*big.Int{b3}
b35 := big.NewInt(int64(35))
publicSignals := []*big.Int{b35}
// witness
w, err := circuit.CalculateWitness(privateInputs, publicSignals)
assert.Nil(t, err)
fmt.Println("witness", w)
// now we have the witness:
// w = [1 35 3 9 27 30 35 1]
// flat code to R1CS
fmt.Println("generating R1CS from flat code")
a, b, c := circuit.GenerateR1CS()
/*
now we have the R1CS from the circuit:
a: [[0 0 1 0 0 0 0 0] [0 0 1 0 0 0 0 0] [0 0 1 0 1 0 0 0] [5 0 0 0 0 1 0 0] [0 0 0 0 0 0 1 0] [0 1 0 0 0 0 0 0] [1 0 0 0 0 0 0 0]]
b: [[0 0 1 0 0 0 0 0] [0 0 0 1 0 0 0 0] [1 0 0 0 0 0 0 0] [1 0 0 0 0 0 0 0] [1 0 0 0 0 0 0 0] [1 0 0 0 0 0 0 0] [1 0 0 0 0 0 0 0]]
c: [[0 0 0 1 0 0 0 0] [0 0 0 0 1 0 0 0] [0 0 0 0 0 1 0 0] [0 0 0 0 0 0 1 0] [0 1 0 0 0 0 0 0] [0 0 0 0 0 0 1 0] [0 0 0 0 0 0 0 1]]
*/
alphas, betas, gammas, _ := snark.Utils.PF.R1CSToQAP(a, b, c)
ax, bx, cx, px := Utils.PF.CombinePolynomials(w, alphas, betas, gammas)
// calculate trusted setup
setup, err := GenerateTrustedSetup(len(w), *circuit, alphas, betas, gammas)
hx := Utils.PF.DivisorPolynomial(px, setup.Pk.Z)
proof, err := GenerateProofs(*circuit, setup, w, px)
b35Verif := big.NewInt(int64(35))
publicSignalsVerif := []*big.Int{b35Verif}
assert.True(t, VerifyProof(*circuit, setup, proof, publicSignalsVerif, true))Verify Proof generated from snarkjs
Is possible with go-snark-study to verify proofs generated by snarkjs
Example:
verified, err := VerifyFromCircom("circom-test/verification_key.json", "circom-test/proof.json", "circom-test/public.json")
assert.Nil(t, err)
assert.True(t, verified)History of versions & tags of this project:
- v0.0.1: zkSnark complete flow working with Pinocchio protocol
- v0.0.2: circuit language improved (allow function calls and file imports)
- v0.0.3: Groth16 zkSnark protocol added
go test ./... -v
For more details and installation instructions see https://github.com/arnaucube/go-snark-study/tree/master/vim-syntax
Thanks to @jbaylina, @bellesmarta, @adriamb for their explanations that helped to understand this a little bit. Also thanks to @vbuterin for all the published articles explaining the zkSNARKs.