go-snark/README.md
README.mdRaw
1# go-snark [](https://goreportcard.com/report/github.com/arnaucube/go-snark)
2
3Not finished, work in progress (doing this in my free time, so I don't have much time).
4
5
6
7#### Test
8```
9go test ./... -v
10```
11
12## R1CS to Quadratic Arithmetic Program
13- `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
14- Vitalik Buterin blog post about QAP https://medium.com/@VitalikButerin/quadratic-arithmetic-programs-from-zero-to-hero-f6d558cea649
15- Ariel Gabizon in Zcash blog https://z.cash/blog/snark-explain5
16- Lagrange polynomial Wikipedia article https://en.wikipedia.org/wiki/Lagrange_polynomial
17
18#### Usage
19- R1CS to QAP
20```go
21b0 := big.NewFloat(float64(0))
22b1 := big.NewFloat(float64(1))
23b5 := big.NewFloat(float64(5))
24a := [][]*big.Float{
25 []*big.Float{b0, b1, b0, b0, b0, b0},
26 []*big.Float{b0, b0, b0, b1, b0, b0},
27 []*big.Float{b0, b1, b0, b0, b1, b0},
28 []*big.Float{b5, b0, b0, b0, b0, b1},
29}
30b := [][]*big.Float{
31 []*big.Float{b0, b1, b0, b0, b0, b0},
32 []*big.Float{b0, b1, b0, b0, b0, b0},
33 []*big.Float{b1, b0, b0, b0, b0, b0},
34 []*big.Float{b1, b0, b0, b0, b0, b0},
35}
36c := [][]*big.Float{
37 []*big.Float{b0, b0, b0, b1, b0, b0},
38 []*big.Float{b0, b0, b0, b0, b1, b0},
39 []*big.Float{b0, b0, b0, b0, b0, b1},
40 []*big.Float{b0, b0, b1, b0, b0, b0},
41}
42alpha, beta, gamma, z := R1CSToQAP(a, b, c)
43fmt.Println(alpha)
44fmt.Println(beta)
45fmt.Println(gamma)
46fmt.Println(z)
47/*
48out:
49alpha: [[-5 9.166666666666666 -5 0.8333333333333334] [8 -11.333333333333332 5 -0.6666666666666666] [0 0 0 0] [-6 9.5 -4 0.5] [4 -7 3.5 -0.5] [-1 1.8333333333333333 -1 0.16666666666666666]]
50beta: [[3 -5.166666666666667 2.5 -0.33333333333333337] [-2 5.166666666666667 -2.5 0.33333333333333337] [0 0 0 0] [0 0 0 0] [0 0 0 0] [0 0 0 0]]
51gamma: [[0 0 0 0] [0 0 0 0] [-1 1.8333333333333333 -1 0.16666666666666666] [4 -4.333333333333333 1.5 -0.16666666666666666] [-6 9.5 -4 0.5] [4 -7 3.5 -0.5]]
52z: [24 -50 35 -10 1]
53*/
54```
55
56## Bn128
57Implementation of the bn128 pairing.
58
59
60Implementation followng the information and the implementations from:
61- `Multiplication and Squaring on Pairing-Friendly
62Fields`, Augusto Jun Devegili, Colm Ó hÉigeartaigh, Michael Scott, and Ricardo Dahab https://pdfs.semanticscholar.org/3e01/de88d7428076b2547b60072088507d881bf1.pdf
63- `Optimal Pairings`, Frederik Vercauteren https://www.cosic.esat.kuleuven.be/bcrypt/optimal.pdf , https://eprint.iacr.org/2008/096.pdf
64- `Double-and-Add with Relative Jacobian
65Coordinates`, Björn Fay https://eprint.iacr.org/2014/1014.pdf
66- `Fast and Regular Algorithms for Scalar Multiplication
67over Elliptic Curves`, Matthieu Rivain https://eprint.iacr.org/2011/338.pdf
68- `High-Speed Software Implementation of the Optimal Ate Pairing over Barreto–Naehrig Curves`, Jean-Luc Beuchat, Jorge E. González-Díaz, Shigeo Mitsunari, Eiji Okamoto, Francisco Rodríguez-Henríquez, and Tadanori Teruya https://eprint.iacr.org/2010/354.pdf
69- `New software speed records for cryptographic pairings`, Michael Naehrig, Ruben Niederhagen, Peter Schwabe https://cryptojedi.org/papers/dclxvi-20100714.pdf
70- `Implementing Cryptographic Pairings over Barreto-Naehrig Curves`, Augusto Jun Devegili, Michael Scott, Ricardo Dahab https://eprint.iacr.org/2007/390.pdf
71- https://github.com/zcash/zcash/tree/master/src/snark
72- https://github.com/iden3/snarkjs
73- https://github.com/ethereum/py_ecc/tree/master/py_ecc/bn128
74
75
76#### Usage
77
78- Pairing
79```go
80bn128, err := NewBn128()
81assert.Nil(t, err)
82
83big25 := big.NewInt(int64(25))
84big30 := big.NewInt(int64(30))
85
86g1a := bn128.G1.MulScalar(bn128.G1.G, big25)
87g2a := bn128.G2.MulScalar(bn128.G2.G, big30)
88
89g1b := bn128.G1.MulScalar(bn128.G1.G, big30)
90g2b := bn128.G2.MulScalar(bn128.G2.G, big25)
91
92pA, err := bn128.Pairing(g1a, g2a)
93assert.Nil(t, err)
94pB, err := bn128.Pairing(g1b, g2b)
95assert.Nil(t, err)
96assert.True(t, bn128.Fq12.Equal(pA, pB))
97```