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phase1.go
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phase1.go
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// Copyright 2020 ConsenSys Software Inc.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
// Code generated by gnark DO NOT EDIT
package mpcsetup
import (
"crypto/sha256"
"errors"
curve "github.com/consensys/gnark-crypto/ecc/bw6-633"
"github.com/consensys/gnark-crypto/ecc/bw6-633/fr"
"math"
"math/big"
)
// Phase1 represents the Phase1 of the MPC described in
// https://eprint.iacr.org/2017/1050.pdf
//
// Also known as "Powers of Tau"
type Phase1 struct {
Parameters struct {
G1 struct {
Tau []curve.G1Affine // {[τ⁰]₁, [τ¹]₁, [τ²]₁, …, [τ²ⁿ⁻²]₁}
AlphaTau []curve.G1Affine // {α[τ⁰]₁, α[τ¹]₁, α[τ²]₁, …, α[τⁿ⁻¹]₁}
BetaTau []curve.G1Affine // {β[τ⁰]₁, β[τ¹]₁, β[τ²]₁, …, β[τⁿ⁻¹]₁}
}
G2 struct {
Tau []curve.G2Affine // {[τ⁰]₂, [τ¹]₂, [τ²]₂, …, [τⁿ⁻¹]₂}
Beta curve.G2Affine // [β]₂
}
}
PublicKeys struct {
Tau, Alpha, Beta PublicKey
}
Hash []byte // sha256 hash
}
// InitPhase1 initialize phase 1 of the MPC. This is called once by the coordinator before
// any randomness contribution is made (see Contribute()).
func InitPhase1(power int) (phase1 Phase1) {
N := int(math.Pow(2, float64(power)))
// Generate key pairs
var tau, alpha, beta fr.Element
tau.SetOne()
alpha.SetOne()
beta.SetOne()
phase1.PublicKeys.Tau = newPublicKey(tau, nil, 1)
phase1.PublicKeys.Alpha = newPublicKey(alpha, nil, 2)
phase1.PublicKeys.Beta = newPublicKey(beta, nil, 3)
// First contribution use generators
_, _, g1, g2 := curve.Generators()
phase1.Parameters.G2.Beta.Set(&g2)
phase1.Parameters.G1.Tau = make([]curve.G1Affine, 2*N-1)
phase1.Parameters.G2.Tau = make([]curve.G2Affine, N)
phase1.Parameters.G1.AlphaTau = make([]curve.G1Affine, N)
phase1.Parameters.G1.BetaTau = make([]curve.G1Affine, N)
for i := 0; i < len(phase1.Parameters.G1.Tau); i++ {
phase1.Parameters.G1.Tau[i].Set(&g1)
}
for i := 0; i < len(phase1.Parameters.G2.Tau); i++ {
phase1.Parameters.G2.Tau[i].Set(&g2)
phase1.Parameters.G1.AlphaTau[i].Set(&g1)
phase1.Parameters.G1.BetaTau[i].Set(&g1)
}
phase1.Parameters.G2.Beta.Set(&g2)
// Compute hash of Contribution
phase1.Hash = phase1.hash()
return
}
// Contribute contributes randomness to the phase1 object. This mutates phase1.
func (phase1 *Phase1) Contribute() {
N := len(phase1.Parameters.G2.Tau)
// Generate key pairs
var tau, alpha, beta fr.Element
tau.SetRandom()
alpha.SetRandom()
beta.SetRandom()
phase1.PublicKeys.Tau = newPublicKey(tau, phase1.Hash[:], 1)
phase1.PublicKeys.Alpha = newPublicKey(alpha, phase1.Hash[:], 2)
phase1.PublicKeys.Beta = newPublicKey(beta, phase1.Hash[:], 3)
// Compute powers of τ, ατ, and βτ
taus := powers(tau, 2*N-1)
alphaTau := make([]fr.Element, N)
betaTau := make([]fr.Element, N)
for i := 0; i < N; i++ {
alphaTau[i].Mul(&taus[i], &alpha)
betaTau[i].Mul(&taus[i], &beta)
}
// Update using previous parameters
// TODO @gbotrel working with jacobian points here will help with perf.
scaleG1InPlace(phase1.Parameters.G1.Tau, taus)
scaleG2InPlace(phase1.Parameters.G2.Tau, taus[0:N])
scaleG1InPlace(phase1.Parameters.G1.AlphaTau, alphaTau)
scaleG1InPlace(phase1.Parameters.G1.BetaTau, betaTau)
var betaBI big.Int
beta.BigInt(&betaBI)
phase1.Parameters.G2.Beta.ScalarMultiplication(&phase1.Parameters.G2.Beta, &betaBI)
// Compute hash of Contribution
phase1.Hash = phase1.hash()
}
func VerifyPhase1(c0, c1 *Phase1, c ...*Phase1) error {
contribs := append([]*Phase1{c0, c1}, c...)
for i := 0; i < len(contribs)-1; i++ {
if err := verifyPhase1(contribs[i], contribs[i+1]); err != nil {
return err
}
}
return nil
}
// verifyPhase1 checks that a contribution is based on a known previous Phase1 state.
func verifyPhase1(current, contribution *Phase1) error {
// Compute R for τ, α, β
tauR := genR(contribution.PublicKeys.Tau.SG, contribution.PublicKeys.Tau.SXG, current.Hash[:], 1)
alphaR := genR(contribution.PublicKeys.Alpha.SG, contribution.PublicKeys.Alpha.SXG, current.Hash[:], 2)
betaR := genR(contribution.PublicKeys.Beta.SG, contribution.PublicKeys.Beta.SXG, current.Hash[:], 3)
// Check for knowledge of toxic parameters
if !sameRatio(contribution.PublicKeys.Tau.SG, contribution.PublicKeys.Tau.SXG, contribution.PublicKeys.Tau.XR, tauR) {
return errors.New("couldn't verify public key of τ")
}
if !sameRatio(contribution.PublicKeys.Alpha.SG, contribution.PublicKeys.Alpha.SXG, contribution.PublicKeys.Alpha.XR, alphaR) {
return errors.New("couldn't verify public key of α")
}
if !sameRatio(contribution.PublicKeys.Beta.SG, contribution.PublicKeys.Beta.SXG, contribution.PublicKeys.Beta.XR, betaR) {
return errors.New("couldn't verify public key of β")
}
// Check for valid updates using previous parameters
if !sameRatio(contribution.Parameters.G1.Tau[1], current.Parameters.G1.Tau[1], tauR, contribution.PublicKeys.Tau.XR) {
return errors.New("couldn't verify that [τ]₁ is based on previous contribution")
}
if !sameRatio(contribution.Parameters.G1.AlphaTau[0], current.Parameters.G1.AlphaTau[0], alphaR, contribution.PublicKeys.Alpha.XR) {
return errors.New("couldn't verify that [α]₁ is based on previous contribution")
}
if !sameRatio(contribution.Parameters.G1.BetaTau[0], current.Parameters.G1.BetaTau[0], betaR, contribution.PublicKeys.Beta.XR) {
return errors.New("couldn't verify that [β]₁ is based on previous contribution")
}
if !sameRatio(contribution.PublicKeys.Tau.SG, contribution.PublicKeys.Tau.SXG, contribution.Parameters.G2.Tau[1], current.Parameters.G2.Tau[1]) {
return errors.New("couldn't verify that [τ]₂ is based on previous contribution")
}
if !sameRatio(contribution.PublicKeys.Beta.SG, contribution.PublicKeys.Beta.SXG, contribution.Parameters.G2.Beta, current.Parameters.G2.Beta) {
return errors.New("couldn't verify that [β]₂ is based on previous contribution")
}
// Check for valid updates using powers of τ
_, _, g1, g2 := curve.Generators()
tauL1, tauL2 := linearCombinationG1(contribution.Parameters.G1.Tau)
if !sameRatio(tauL1, tauL2, contribution.Parameters.G2.Tau[1], g2) {
return errors.New("couldn't verify valid powers of τ in G₁")
}
alphaL1, alphaL2 := linearCombinationG1(contribution.Parameters.G1.AlphaTau)
if !sameRatio(alphaL1, alphaL2, contribution.Parameters.G2.Tau[1], g2) {
return errors.New("couldn't verify valid powers of α(τ) in G₁")
}
betaL1, betaL2 := linearCombinationG1(contribution.Parameters.G1.BetaTau)
if !sameRatio(betaL1, betaL2, contribution.Parameters.G2.Tau[1], g2) {
return errors.New("couldn't verify valid powers of α(τ) in G₁")
}
tau2L1, tau2L2 := linearCombinationG2(contribution.Parameters.G2.Tau)
if !sameRatio(contribution.Parameters.G1.Tau[1], g1, tau2L1, tau2L2) {
return errors.New("couldn't verify valid powers of τ in G₂")
}
// Check hash of the contribution
h := contribution.hash()
for i := 0; i < len(h); i++ {
if h[i] != contribution.Hash[i] {
return errors.New("couldn't verify hash of contribution")
}
}
return nil
}
func (phase1 *Phase1) hash() []byte {
sha := sha256.New()
phase1.writeTo(sha)
return sha.Sum(nil)
}