1package kzg
  2
  3import (
  4	"fmt"
  5	"math/big"
  6
  7	bn256 "github.com/ethereum/go-ethereum/crypto/bn256/cloudflare"
  8)
  9
 10// TrustedSetup also named Reference String
 11type TrustedSetup struct {
 12	Tau1 []*bn256.G1
 13	Tau2 []*bn256.G2
 14}
 15
 16// NewTrustedSetup returns a new trusted setup. This step should be done in a
 17// secure & distributed way
 18func NewTrustedSetup(p []*big.Int) (*TrustedSetup, error) {
 19	// compute random s
 20	s, err := randBigInt()
 21	if err != nil {
 22		return nil, err
 23	}
 24
 25	// Notation: [x]₁=xG ∈ 𝔾₁, [x]₂=xH ∈ 𝔾₂
 26	// τ₁: [x₀]₁, [x₁]₁, [x₂]₁, ..., [x n₋₁]₁
 27	// τ₂: [x₀]₂, [x₁]₂, [x₂]₂, ..., [x n₋₁]₂
 28
 29	// sPow := make([]*big.Int, len(p))
 30	tauG1 := make([]*bn256.G1, len(p))
 31	tauG2 := make([]*bn256.G2, len(p))
 32	for i := 0; i < len(p); i++ {
 33		sPow := fExp(s, big.NewInt(int64(i)))
 34		tauG1[i] = new(bn256.G1).ScalarBaseMult(sPow)
 35		tauG2[i] = new(bn256.G2).ScalarBaseMult(sPow)
 36	}
 37
 38	return &TrustedSetup{tauG1, tauG2}, nil
 39}
 40
 41// Commit generates the commitment to the polynomial p(x)
 42func Commit(ts *TrustedSetup, p []*big.Int) *bn256.G1 {
 43	c := evaluateG1(ts, p)
 44	return c
 45}
 46
 47func evaluateG1(ts *TrustedSetup, p []*big.Int) *bn256.G1 {
 48	c := new(bn256.G1).ScalarMult(ts.Tau1[0], p[0])
 49	for i := 1; i < len(p); i++ {
 50		sp := new(bn256.G1).ScalarMult(ts.Tau1[i], p[i])
 51		c = new(bn256.G1).Add(c, sp)
 52	}
 53	return c
 54}
 55
 56//nolint:deadcode,unused
 57func evaluateG2(ts *TrustedSetup, p []*big.Int) *bn256.G2 {
 58	c := new(bn256.G2).ScalarMult(ts.Tau2[0], p[0])
 59	for i := 1; i < len(p); i++ {
 60		sp := new(bn256.G2).ScalarMult(ts.Tau2[i], p[i])
 61		c = new(bn256.G2).Add(c, sp)
 62	}
 63	return c
 64}
 65
 66// EvaluationProof generates the evaluation proof
 67func EvaluationProof(ts *TrustedSetup, p []*big.Int, z, y *big.Int) (*bn256.G1, error) {
 68	n := polynomialSub(p, []*big.Int{y})    // p-y
 69	d := []*big.Int{fNeg(z), big.NewInt(1)} // x-z
 70	q, rem := polynomialDiv(n, d)
 71	if compareBigIntArray(rem, arrayOfZeroes(len(rem))) {
 72		return nil,
 73			fmt.Errorf("remainder should be 0, instead is %d", rem)
 74	}
 75	fmt.Println("q(x):", polynomialToString(q)) // TMP DBG
 76
 77	// proof: e = [q(s)]₁
 78	e := evaluateG1(ts, q)
 79	return e, nil
 80}
 81
 82// Verify computes the KZG commitment verification
 83func Verify(ts *TrustedSetup, c, proof *bn256.G1, z, y *big.Int) bool {
 84	s2 := ts.Tau2[1] // [s]₂ = sG ∈ 𝔾₂ = Tau2[1]
 85	zG2Neg := new(bn256.G2).Neg(
 86		new(bn256.G2).ScalarBaseMult(z)) // [z]₂ = zG ∈ 𝔾₂
 87	// [s]₂ - [z]₂
 88	sz := new(bn256.G2).Add(s2, zG2Neg)
 89
 90	yG1Neg := new(bn256.G1).Neg(
 91		new(bn256.G1).ScalarBaseMult(y)) // [y]₁ = yG ∈ 𝔾₁
 92	// c - [y]₁
 93	cy := new(bn256.G1).Add(c, yG1Neg)
 94
 95	h := new(bn256.G2).ScalarBaseMult(big.NewInt(1)) // H ∈ 𝔾₂
 96
 97	// e(proof, [s]₂ - [z]₂) == e(c - [y]₁, H)
 98	e1 := bn256.Pair(proof, sz)
 99	e2 := bn256.Pair(cy, h)
100	return e1.String() == e2.String()
101}