go-snark

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.pdf
• Pinocchio: Nearly practical verifiable computation, Bryan Parno, Craig Gentry, Jon Howell, Mariana Raykova https://eprint.iacr.org/2013/279.pdf

Caution

Implementation of the zkSNARK Pinocchio protocol from scratch in Go to understand the concepts. Do not use in production.

Not finished, implementing this in my free time to understand it better, so I don't have much time.

Current implementation status:

• Finite Fields (1, 2, 6, 12) operations
• G1 and G2 curve operations
• BN128 Pairing
• circuit code compiler
  • code to flat code (improve circuit compiler)
  • flat code compiler
  • private & public inputs. fix circuit compiler
• circuit to R1CS
• polynomial operations
• R1CS to QAP
• generate trusted setup
• generate proofs
• verify proofs with BN128 pairing
  • fix 4th pairing proofs generation & verification: ê(Vkx+piA, piB) == ê(piH, Vkz) * ê(piC, G2)
• move witness calculation outside the setup phase

Usage

• zkSnark
• bn128 (more details: https://github.com/arnaucube/go-snark/tree/master/bn128)
• Finite Fields operations
• R1CS to QAP (more details: https://github.com/arnaucube/go-snark/tree/master/r1csqap)
• Circuit Compiler

Library usage

Warning: not finished.

Example:

// compile circuit and get the R1CS
flatCode := `
func test(x):
	aux = x*x
	y = aux*x
	z = x + y
	out = z + 5
`

// parse the code
parser := circuitcompiler.NewParser(strings.NewReader(flatCode))
circuit, err := parser.Parse()
assert.Nil(t, err)
fmt.Println(circuit)

// witness
b3 := big.NewInt(int64(3))
inputs := []*big.Int{b3}
w := circuit.CalculateWitness(inputs)
fmt.Println("\nwitness", w)
/*
now we have the witness:
w = [1 3 35 9 27 30]
*/

// 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 1 0 0 0 0] [0 0 0 1 0 0] [0 1 0 0 1 0] [5 0 0 0 0 1]]
b == [[0 1 0 0 0 0] [0 1 0 0 0 0] [1 0 0 0 0 0] [1 0 0 0 0 0]]
c == [[0 0 0 1 0 0] [0 0 0 0 1 0] [0 0 0 0 0 1] [0 0 1 0 0 0]]
*/


alphas, betas, gammas, zx := snark.Utils.PF.R1CSToQAP(a, b, c)


ax, bx, cx, px := snark.Utils.PF.CombinePolynomials(w, alphas, betas, gammas)

hx := snark.Utils.PF.DivisorPolinomial(px, zx)

// hx==px/zx so px==hx*zx
assert.Equal(t, px, snark.Utils.PF.Mul(hx, zx))

// p(x) = a(x) * b(x) - c(x) == h(x) * z(x)
abc := snark.Utils.PF.Sub(pf.Mul(ax, bx), cx)
assert.Equal(t, abc, px)
hz := snark.Utils.PF.Mul(hx, zx)
assert.Equal(t, abc, hz)
	
div, rem := snark.Utils.PF.Div(px, zx)
assert.Equal(t, hx, div)
assert.Equal(t, rem, r1csqap.ArrayOfBigZeros(4))

// calculate trusted setup
setup, err := snark.GenerateTrustedSetup(len(w), circuit, alphas, betas, gammas, zx)
assert.Nil(t, err)
fmt.Println("t", setup.Toxic.T)

// piA = g1 * A(t), piB = g2 * B(t), piC = g1 * C(t), piH = g1 * H(t)
proof, err := snark.GenerateProofs(circuit, setup, hx, w)
assert.Nil(t, err)

assert.True(t, snark.VerifyProof(circuit, setup, proof))

CLI usage

Compile circuit

Having a circuit file test.circuit:

func test(x):
	aux = x*x
	y = aux*x
	z = x + y
	out = z + 5

And a inputs file inputs.json

[
	3
]

In the command line, execute:

> go-snark-cli compile test.circuit

This will output the compiledcircuit.json file.

Trusted Setup

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.

Generate Proofs

Assumming that we have the compiledcircuit.json and the trustedsetup.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.

Verify Proofs

Having the proofs.json, compiledcircuit.json, trustedsetup.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.

Test

go test ./... -v

---

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.