1package prover
  2
  3import (
  4	"crypto/rand"
  5	"math"
  6	"math/big"
  7
  8	bn256 "github.com/ethereum/go-ethereum/crypto/bn256/cloudflare"
  9	"github.com/iden3/go-circom-prover-verifier/types"
 10	"github.com/iden3/go-iden3-crypto/ff"
 11	"github.com/iden3/go-iden3-crypto/utils"
 12)
 13
 14// Proof is the data structure of the Groth16 zkSNARK proof
 15type Proof struct {
 16	A *bn256.G1
 17	B *bn256.G2
 18	C *bn256.G1
 19}
 20
 21// Pk holds the data structure of the ProvingKey
 22type Pk struct {
 23	A          []*bn256.G1
 24	B2         []*bn256.G2
 25	B1         []*bn256.G1
 26	C          []*bn256.G1
 27	NVars      int
 28	NPublic    int
 29	VkAlpha1   *bn256.G1
 30	VkDelta1   *bn256.G1
 31	VkBeta1    *bn256.G1
 32	VkBeta2    *bn256.G2
 33	VkDelta2   *bn256.G2
 34	HExps      []*bn256.G1
 35	DomainSize int
 36	PolsA      []map[int]*big.Int
 37	PolsB      []map[int]*big.Int
 38	PolsC      []map[int]*big.Int
 39}
 40
 41// Witness contains the witness
 42type Witness []*big.Int
 43
 44func randBigInt() (*big.Int, error) {
 45	maxbits := types.R.BitLen()
 46	b := make([]byte, (maxbits/8)-1)
 47	_, err := rand.Read(b)
 48	if err != nil {
 49		return nil, err
 50	}
 51	r := new(big.Int).SetBytes(b)
 52	rq := new(big.Int).Mod(r, types.R)
 53
 54	return rq, nil
 55}
 56
 57// GenerateProof generates the Groth16 zkSNARK proof
 58func GenerateProof(pk *types.Pk, w types.Witness) (*types.Proof, []*big.Int, error) {
 59	var proof types.Proof
 60
 61	r, err := randBigInt()
 62	if err != nil {
 63		return nil, nil, err
 64	}
 65	s, err := randBigInt()
 66	if err != nil {
 67		return nil, nil, err
 68	}
 69
 70	proof.A = new(bn256.G1).ScalarBaseMult(big.NewInt(0))
 71	proof.B = new(bn256.G2).ScalarBaseMult(big.NewInt(0))
 72	proof.C = new(bn256.G1).ScalarBaseMult(big.NewInt(0))
 73	proofBG1 := new(bn256.G1).ScalarBaseMult(big.NewInt(0))
 74
 75	for i := 0; i < pk.NVars; i++ {
 76		proof.A = new(bn256.G1).Add(proof.A, new(bn256.G1).ScalarMult(pk.A[i], w[i]))
 77		proof.B = new(bn256.G2).Add(proof.B, new(bn256.G2).ScalarMult(pk.B2[i], w[i]))
 78		proofBG1 = new(bn256.G1).Add(proofBG1, new(bn256.G1).ScalarMult(pk.B1[i], w[i]))
 79	}
 80
 81	for i := pk.NPublic + 1; i < pk.NVars; i++ {
 82		proof.C = new(bn256.G1).Add(proof.C, new(bn256.G1).ScalarMult(pk.C[i], w[i]))
 83	}
 84
 85	proof.A = new(bn256.G1).Add(proof.A, pk.VkAlpha1)
 86	proof.A = new(bn256.G1).Add(proof.A, new(bn256.G1).ScalarMult(pk.VkDelta1, r))
 87
 88	proof.B = new(bn256.G2).Add(proof.B, pk.VkBeta2)
 89	proof.B = new(bn256.G2).Add(proof.B, new(bn256.G2).ScalarMult(pk.VkDelta2, s))
 90
 91	proofBG1 = new(bn256.G1).Add(proofBG1, pk.VkBeta1)
 92	proofBG1 = new(bn256.G1).Add(proofBG1, new(bn256.G1).ScalarMult(pk.VkDelta1, s))
 93
 94	h := calculateH(pk, w)
 95
 96	for i := 0; i < len(h); i++ {
 97		proof.C = new(bn256.G1).Add(proof.C, new(bn256.G1).ScalarMult(pk.HExps[i], h[i]))
 98	}
 99	proof.C = new(bn256.G1).Add(proof.C, new(bn256.G1).ScalarMult(proof.A, s))
100	proof.C = new(bn256.G1).Add(proof.C, new(bn256.G1).ScalarMult(proofBG1, r))
101	rsneg := new(big.Int).Mod(new(big.Int).Neg(new(big.Int).Mul(r, s)), types.R) // fAdd & fMul
102	proof.C = new(bn256.G1).Add(proof.C, new(bn256.G1).ScalarMult(pk.VkDelta1, rsneg))
103
104	pubSignals := w[1 : pk.NPublic+1]
105
106	return &proof, pubSignals, nil
107}
108
109func calculateH(pk *types.Pk, w types.Witness) []*big.Int {
110	m := pk.DomainSize
111	polAT := arrayOfZeroes(m)
112	polBT := arrayOfZeroes(m)
113
114	for i := 0; i < pk.NVars; i++ {
115		for j := range pk.PolsA[i] {
116			polAT[j] = fAdd(polAT[j], fMul(w[i], pk.PolsA[i][j]))
117		}
118		for j := range pk.PolsB[i] {
119			polBT[j] = fAdd(polBT[j], fMul(w[i], pk.PolsB[i][j]))
120		}
121	}
122	polATe := utils.BigIntArrayToElementArray(polAT)
123	polBTe := utils.BigIntArrayToElementArray(polBT)
124
125	polASe := ifft(polATe)
126	polBSe := ifft(polBTe)
127
128	r := int(math.Log2(float64(m))) + 1
129	roots := newRootsT()
130	roots.setRoots(r)
131	for i := 0; i < len(polASe); i++ {
132		polASe[i] = ff.NewElement().Mul(polASe[i], roots.roots[r][i])
133		polBSe[i] = ff.NewElement().Mul(polBSe[i], roots.roots[r][i])
134	}
135
136	polATodd := fft(polASe)
137	polBTodd := fft(polBSe)
138
139	polABT := arrayOfZeroesE(len(polASe) * 2)
140	for i := 0; i < len(polASe); i++ {
141		polABT[2*i] = ff.NewElement().Mul(polATe[i], polBTe[i])
142		polABT[2*i+1] = ff.NewElement().Mul(polATodd[i], polBTodd[i])
143	}
144
145	hSeFull := ifft(polABT)
146
147	hSe := hSeFull[m:]
148	return utils.ElementArrayToBigIntArray(hSe)
149}