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verify.go
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verify.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 plonkfri
import (
"errors"
"fmt"
"github.com/consensys/gnark-crypto/ecc/bls24-317/fr"
"github.com/consensys/gnark-crypto/ecc/bls24-317/fr/fri"
fiatshamir "github.com/consensys/gnark-crypto/fiat-shamir"
"github.com/consensys/gnark/backend"
"math/big"
)
var ErrInvalidAlgebraicRelation = errors.New("algebraic relation does not hold")
func Verify(proof *Proof, vk *VerifyingKey, publicWitness fr.Vector, opts ...backend.VerifierOption) error {
cfg, err := backend.NewVerifierConfig(opts...)
if err != nil {
return fmt.Errorf("create backend config: %w", err)
}
// 0 - derive the challenges with Fiat Shamir
fs := fiatshamir.NewTranscript(cfg.ChallengeHash, "gamma", "beta", "alpha", "zeta")
dataFiatShamir := make([][fr.Bytes]byte, len(publicWitness)+3)
for i := 0; i < len(publicWitness); i++ {
copy(dataFiatShamir[i][:], publicWitness[i].Marshal())
}
copy(dataFiatShamir[len(publicWitness)][:], proof.LROpp[0].ID)
copy(dataFiatShamir[len(publicWitness)+1][:], proof.LROpp[1].ID)
copy(dataFiatShamir[len(publicWitness)+2][:], proof.LROpp[2].ID)
beta, err := deriveRandomnessFixedSize(fs, "gamma", dataFiatShamir...)
if err != nil {
return err
}
gamma, err := deriveRandomness(fs, "beta", nil)
if err != nil {
return err
}
alpha, err := deriveRandomness(fs, "alpha", proof.Zpp.ID)
if err != nil {
return err
}
// compute the size of the domain of evaluation of the committed polynomial,
// the opening position. The challenge zeta will be g^{i} where i is the opening
// position, and g is the generator of the fri domain.
rho := uint64(fri.GetRho())
friSize := 2 * rho * vk.Size
var bFriSize big.Int
bFriSize.SetInt64(int64(friSize))
frOpeningPosition, err := deriveRandomness(fs, "zeta", proof.Hpp[0].ID, proof.Hpp[1].ID, proof.Hpp[2].ID)
if err != nil {
return err
}
var bOpeningPosition big.Int
bOpeningPosition.SetBytes(frOpeningPosition.Marshal()).Mod(&bOpeningPosition, &bFriSize)
openingPosition := bOpeningPosition.Uint64()
shiftedOpeningPosition := (openingPosition + uint64(2*rho)) % friSize
err = vk.Iopp.VerifyOpening(shiftedOpeningPosition, proof.OpeningsZmp[1], proof.Zpp)
if err != nil {
return err
}
// 1 - verify that the commitments are low degree polynomials
// ql, qr, qm, qo, qkIncomplete
err = vk.Iopp.VerifyProofOfProximity(vk.Qpp[0])
if err != nil {
return err
}
err = vk.Iopp.VerifyProofOfProximity(vk.Qpp[1])
if err != nil {
return err
}
err = vk.Iopp.VerifyProofOfProximity(vk.Qpp[2])
if err != nil {
return err
}
err = vk.Iopp.VerifyProofOfProximity(vk.Qpp[3])
if err != nil {
return err
}
err = vk.Iopp.VerifyProofOfProximity(vk.Qpp[4])
if err != nil {
return err
}
// l, r, o
err = vk.Iopp.VerifyProofOfProximity(proof.LROpp[0])
if err != nil {
return err
}
err = vk.Iopp.VerifyProofOfProximity(proof.LROpp[1])
if err != nil {
return err
}
err = vk.Iopp.VerifyProofOfProximity(proof.LROpp[2])
if err != nil {
return err
}
err = vk.Iopp.VerifyProofOfProximity(proof.Zpp)
if err != nil {
return err
}
// h0, h1, h2
err = vk.Iopp.VerifyProofOfProximity(proof.Hpp[0])
if err != nil {
return err
}
err = vk.Iopp.VerifyProofOfProximity(proof.Hpp[1])
if err != nil {
return err
}
err = vk.Iopp.VerifyProofOfProximity(proof.Hpp[2])
if err != nil {
return err
}
// s1, s2, s3
err = vk.Iopp.VerifyProofOfProximity(vk.Spp[0])
if err != nil {
return err
}
err = vk.Iopp.VerifyProofOfProximity(vk.Spp[1])
if err != nil {
return err
}
err = vk.Iopp.VerifyProofOfProximity(vk.Spp[2])
if err != nil {
return err
}
// id1, id2, id3
err = vk.Iopp.VerifyProofOfProximity(vk.Idpp[0])
if err != nil {
return err
}
err = vk.Iopp.VerifyProofOfProximity(vk.Idpp[1])
if err != nil {
return err
}
err = vk.Iopp.VerifyProofOfProximity(vk.Idpp[2])
if err != nil {
return err
}
// Z
err = vk.Iopp.VerifyProofOfProximity(proof.Zpp)
if err != nil {
return err
}
// 2 - verify the openings
// ql, qr, qm, qo, qkIncomplete
// openingPosition := uint64(2)
err = vk.Iopp.VerifyOpening(openingPosition, proof.OpeningsQlQrQmQoQkincompletemp[0], vk.Qpp[0])
if err != nil {
return err
}
err = vk.Iopp.VerifyOpening(openingPosition, proof.OpeningsQlQrQmQoQkincompletemp[1], vk.Qpp[1])
if err != nil {
return err
}
err = vk.Iopp.VerifyOpening(openingPosition, proof.OpeningsQlQrQmQoQkincompletemp[2], vk.Qpp[2])
if err != nil {
return err
}
err = vk.Iopp.VerifyOpening(openingPosition, proof.OpeningsQlQrQmQoQkincompletemp[3], vk.Qpp[3])
if err != nil {
return err
}
err = vk.Iopp.VerifyOpening(openingPosition, proof.OpeningsQlQrQmQoQkincompletemp[4], vk.Qpp[4])
if err != nil {
return err
}
// l, r, o
err = vk.Iopp.VerifyOpening(openingPosition, proof.OpeningsLROmp[0], proof.LROpp[0])
if err != nil {
return err
}
err = vk.Iopp.VerifyOpening(openingPosition, proof.OpeningsLROmp[1], proof.LROpp[1])
if err != nil {
return err
}
err = vk.Iopp.VerifyOpening(openingPosition, proof.OpeningsLROmp[2], proof.LROpp[2])
if err != nil {
return err
}
// h0, h1, h2
err = vk.Iopp.VerifyOpening(openingPosition, proof.OpeningsHmp[0], proof.Hpp[0])
if err != nil {
return err
}
err = vk.Iopp.VerifyOpening(openingPosition, proof.OpeningsHmp[1], proof.Hpp[1])
if err != nil {
return err
}
err = vk.Iopp.VerifyOpening(openingPosition, proof.OpeningsHmp[2], proof.Hpp[2])
if err != nil {
return err
}
// s0, s1, s2
err = vk.Iopp.VerifyOpening(openingPosition, proof.OpeningsS1S2S3mp[0], vk.Spp[0])
if err != nil {
return err
}
err = vk.Iopp.VerifyOpening(openingPosition, proof.OpeningsS1S2S3mp[1], vk.Spp[1])
if err != nil {
return err
}
err = vk.Iopp.VerifyOpening(openingPosition, proof.OpeningsS1S2S3mp[2], vk.Spp[2])
if err != nil {
return err
}
// id0, id1, id2
err = vk.Iopp.VerifyOpening(openingPosition, proof.OpeningsId1Id2Id3mp[0], vk.Idpp[0])
if err != nil {
return err
}
err = vk.Iopp.VerifyOpening(openingPosition, proof.OpeningsId1Id2Id3mp[1], vk.Idpp[1])
if err != nil {
return err
}
err = vk.Iopp.VerifyOpening(openingPosition, proof.OpeningsId1Id2Id3mp[2], vk.Idpp[2])
if err != nil {
return err
}
// Z, Zshift
err = vk.Iopp.VerifyOpening(openingPosition, proof.OpeningsZmp[0], proof.Zpp)
if err != nil {
return err
}
// verification of the algebraic relation
var ql, qr, qm, qo, qk fr.Element
ql.Set(&proof.OpeningsQlQrQmQoQkincompletemp[0].ClaimedValue)
qr.Set(&proof.OpeningsQlQrQmQoQkincompletemp[1].ClaimedValue)
qm.Set(&proof.OpeningsQlQrQmQoQkincompletemp[2].ClaimedValue)
qo.Set(&proof.OpeningsQlQrQmQoQkincompletemp[3].ClaimedValue)
qk.Set(&proof.OpeningsQlQrQmQoQkincompletemp[4].ClaimedValue) // -> to be completed
var l, r, o fr.Element
l.Set(&proof.OpeningsLROmp[0].ClaimedValue)
r.Set(&proof.OpeningsLROmp[1].ClaimedValue)
o.Set(&proof.OpeningsLROmp[2].ClaimedValue)
var h1, h2, h3 fr.Element
h1.Set(&proof.OpeningsHmp[0].ClaimedValue)
h2.Set(&proof.OpeningsHmp[1].ClaimedValue)
h3.Set(&proof.OpeningsHmp[2].ClaimedValue)
var s1, s2, s3 fr.Element
s1.Set(&proof.OpeningsS1S2S3mp[0].ClaimedValue)
s2.Set(&proof.OpeningsS1S2S3mp[1].ClaimedValue)
s3.Set(&proof.OpeningsS1S2S3mp[2].ClaimedValue)
var id1, id2, id3 fr.Element
id1.Set(&proof.OpeningsId1Id2Id3mp[0].ClaimedValue)
id2.Set(&proof.OpeningsId1Id2Id3mp[1].ClaimedValue)
id3.Set(&proof.OpeningsId1Id2Id3mp[2].ClaimedValue)
var z, zshift fr.Element
z.Set(&proof.OpeningsZmp[0].ClaimedValue)
zshift.Set(&proof.OpeningsZmp[1].ClaimedValue)
// 2 - compute the LHS: (ql*l+..+qk)+ α*(z(μx)*(l+β*s₁+γ)*..-z*(l+β*id1+γ))+α²*z*(l1-1)
var zeta fr.Element
zeta.Exp(vk.GenOpening, &bOpeningPosition)
var lhs, t1, t2, t3, tmp, tmp2 fr.Element
// 2.1 (ql*l+..+qk)
t1.Mul(&l, &ql)
tmp.Mul(&r, &qr)
t1.Add(&t1, &tmp)
tmp.Mul(&qm, &l).Mul(&tmp, &r)
t1.Add(&t1, &tmp)
tmp.Mul(&o, &qo)
t1.Add(&tmp, &t1)
tmp = completeQk(publicWitness, vk, zeta)
tmp.Add(&qk, &tmp)
t1.Add(&tmp, &t1)
// 2.2 (z(ux)*(l+β*s1+γ)*..-z*(l+β*id1+γ))
t2.Mul(&beta, &s1).Add(&t2, &l).Add(&t2, &gamma)
tmp.Mul(&beta, &s2).Add(&tmp, &r).Add(&tmp, &gamma)
t2.Mul(&tmp, &t2)
tmp.Mul(&beta, &s3).Add(&tmp, &o).Add(&tmp, &gamma)
t2.Mul(&tmp, &t2).Mul(&t2, &zshift)
tmp.Mul(&beta, &id1).Add(&tmp, &l).Add(&tmp, &gamma)
tmp2.Mul(&beta, &id2).Add(&tmp2, &r).Add(&tmp2, &gamma)
tmp.Mul(&tmp, &tmp2)
tmp2.Mul(&beta, &id3).Add(&tmp2, &o).Add(&tmp2, &gamma)
tmp.Mul(&tmp2, &tmp).Mul(&tmp, &z)
t2.Sub(&t2, &tmp)
// 2.3 (z-1)*l1
var one fr.Element
one.SetOne()
t3.Exp(zeta, big.NewInt(int64(vk.Size))).Sub(&t3, &one)
tmp.Sub(&zeta, &one).Inverse(&tmp).Mul(&tmp, &vk.SizeInv)
t3.Mul(&tmp, &t3)
tmp.Sub(&z, &one)
t3.Mul(&tmp, &t3)
// 2.4 (ql*l+s+qk) + α*(z(ux)*(l+β*s1+γ)*...-z*(l+β*id1+γ)..)+ α²*z*(l1-1)
lhs.Set(&t3).Mul(&lhs, &alpha).Add(&lhs, &t2).Mul(&lhs, &alpha).Add(&lhs, &t1)
// 3 - compute the RHS
var rhs fr.Element
tmp.Exp(zeta, big.NewInt(int64(vk.Size+2)))
rhs.Mul(&h3, &tmp).
Add(&rhs, &h2).
Mul(&rhs, &tmp).
Add(&rhs, &h1)
tmp.Exp(zeta, big.NewInt(int64(vk.Size))).Sub(&tmp, &one)
rhs.Mul(&rhs, &tmp)
// 4 - verify the relation LHS==RHS
if !rhs.Equal(&lhs) {
return ErrInvalidAlgebraicRelation
}
return nil
}
// completeQk returns ∑_{i<nb_public_inputs}w_i*L_i
func completeQk(publicWitness []fr.Element, vk *VerifyingKey, zeta fr.Element) fr.Element {
var res fr.Element
// compute l1(zeta). Exceptional case: if zeta=1, then l1(zeta)=1,
// we need to manually initialise l to this value otherwise there
// is a denominator equal to zero in the formula.
var l, tmp, acc, one fr.Element
one.SetOne()
acc.SetOne()
l.Sub(&zeta, &one)
if l.IsZero() {
l.SetOne()
} else {
l.Inverse(&l).Mul(&l, &vk.SizeInv)
tmp.Exp(zeta, big.NewInt(int64(vk.Size))).Sub(&tmp, &one)
l.Mul(&l, &tmp)
}
// use L_i+1 = w*Li*(X-z**i)/(X-z**i+1)
for i := 0; i < len(publicWitness); i++ {
tmp.Mul(&l, &publicWitness[i])
res.Add(&res, &tmp)
tmp.Sub(&zeta, &acc)
l.Mul(&l, &tmp).Mul(&l, &vk.Generator)
acc.Mul(&acc, &vk.Generator)
tmp.Sub(&zeta, &acc)
// if tmp==0, then zeta=vk.Generator**i, so l_i(zeta)=1. We need
// to manually set the value to 1, exacty as in the case l_0 before
// the loop, otherwise the generic formula leads to a division by zero.
if tmp.IsZero() {
l.SetOne()
} else {
l.Div(&l, &tmp)
}
}
return res
}