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setup.go
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setup.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 (
"crypto/sha256"
"github.com/consensys/gnark-crypto/ecc/bw6-761/fr"
"github.com/consensys/gnark-crypto/ecc/bw6-761/fr/fft"
"github.com/consensys/gnark-crypto/ecc/bw6-761/fr/fri"
cs "github.com/consensys/gnark/constraint/bw6-761"
)
// ProvingKey stores the data needed to generate a proof:
// * the commitment scheme
// * ql, prepended with as many ones as they are public inputs
// * qr, qm, qo prepended with as many zeroes as there are public inputs.
// * qk, prepended with as many zeroes as public inputs, to be completed by the prover
// with the list of public inputs.
// * sigma_1, sigma_2, sigma_3 in both basis
// * the copy constraint permutation
type ProvingKey struct {
// Verifying Key is embedded into the proving key (needed by Prove)
Vk *VerifyingKey
// qr,ql,qm,qo and Qk incomplete (Ls=Lagrange basis big domain, L=Lagrange basis small domain, C=canonical basis)
EvaluationQlDomainBigBitReversed []fr.Element
EvaluationQrDomainBigBitReversed []fr.Element
EvaluationQmDomainBigBitReversed []fr.Element
EvaluationQoDomainBigBitReversed []fr.Element
LQkIncompleteDomainSmall []fr.Element
CQl, CQr, CQm, CQo, CQkIncomplete []fr.Element
// Domains used for the FFTs
// 0 -> "small" domain, used for individual polynomials
// 1 -> "big" domain, used for the computation of the quotient
Domain [2]fft.Domain
// s1, s2, s3 (L=Lagrange basis small domain, C=canonical basis, Ls=Lagrange Shifted big domain)
LId []fr.Element
EvaluationId1BigDomain, EvaluationId2BigDomain, EvaluationId3BigDomain []fr.Element
EvaluationS1BigDomain, EvaluationS2BigDomain, EvaluationS3BigDomain []fr.Element
// position -> permuted position (position in [0,3*sizeSystem-1])
Permutation []int64
}
// VerifyingKey stores the data needed to verify a proof:
// * The commitment scheme
// * Commitments of ql prepended with as many ones as there are public inputs
// * Commitments of qr, qm, qo, qk prepended with as many zeroes as there are public inputs
// * Commitments to S1, S2, S3
type VerifyingKey struct {
// Size circuit, that is the closest power of 2 bounding above
// number of constraints+number of public inputs
Size uint64
SizeInv fr.Element
Generator fr.Element
NbPublicVariables uint64
// cosetShift generator of the coset on the small domain
CosetShift fr.Element
// S commitments to S1, S2, S3
SCanonical [3][]fr.Element
Spp [3]fri.ProofOfProximity
// Id commitments to Id1, Id2, Id3
// Id [3]Commitment
IdCanonical [3][]fr.Element
Idpp [3]fri.ProofOfProximity
// Commitments to ql, qr, qm, qo prepended with as many zeroes (ones for l) as there are public inputs.
// In particular Qk is not complete.
Qpp [5]fri.ProofOfProximity // Ql, Qr, Qm, Qo, Qk
// Iopp scheme (currently one for each size of polynomial)
Iopp fri.Iopp
// generator of the group on which the Iopp works. If i is the opening position,
// the polynomials will be opened at genOpening^{i}.
GenOpening fr.Element
}
// Setup sets proving and verifying keys
func Setup(spr *cs.SparseR1CS) (*ProvingKey, *VerifyingKey, error) {
var pk ProvingKey
var vk VerifyingKey
// The verifying key shares data with the proving key
pk.Vk = &vk
nbConstraints := spr.GetNbConstraints()
// fft domains
sizeSystem := uint64(nbConstraints + len(spr.Public)) // len(spr.Public) is for the placeholder constraints
pk.Domain[0] = *fft.NewDomain(sizeSystem)
// h, the quotient polynomial is of degree 3(n+1)+2, so it's in a 3(n+2) dim vector space,
// the domain is the next power of 2 superior to 3(n+2). 4*domainNum is enough in all cases
// except when n<6.
if sizeSystem < 6 {
pk.Domain[1] = *fft.NewDomain(8 * sizeSystem)
} else {
pk.Domain[1] = *fft.NewDomain(4 * sizeSystem)
}
pk.Vk.CosetShift.Set(&pk.Domain[0].FrMultiplicativeGen)
vk.Size = pk.Domain[0].Cardinality
vk.SizeInv.SetUint64(vk.Size).Inverse(&vk.SizeInv)
vk.Generator.Set(&pk.Domain[0].Generator)
vk.NbPublicVariables = uint64(len(spr.Public))
// IOP schemess
// The +2 is to handle the blinding.
sizeIopp := pk.Domain[0].Cardinality + 2
vk.Iopp = fri.RADIX_2_FRI.New(sizeIopp, sha256.New())
// only there to access the group used in FRI...
rho := uint64(fri.GetRho())
// we multiply by 2 because the IOP is created with size pk.Domain[0].Cardinality + 2 (because
// of the blinding), so the domain will be rho*size_domain where size_domain is the next power
// of 2 after pk.Domain[0].Cardinality + 2, which is 2*rho*pk.Domain[0].Cardinality
tmpDomain := fft.NewDomain(2 * rho * pk.Domain[0].Cardinality)
vk.GenOpening.Set(&tmpDomain.Generator)
// public polynomials corresponding to constraints: [ placholders | constraints | assertions ]
pk.EvaluationQlDomainBigBitReversed = make([]fr.Element, pk.Domain[1].Cardinality)
pk.EvaluationQrDomainBigBitReversed = make([]fr.Element, pk.Domain[1].Cardinality)
pk.EvaluationQmDomainBigBitReversed = make([]fr.Element, pk.Domain[1].Cardinality)
pk.EvaluationQoDomainBigBitReversed = make([]fr.Element, pk.Domain[1].Cardinality)
pk.LQkIncompleteDomainSmall = make([]fr.Element, pk.Domain[0].Cardinality)
pk.CQkIncomplete = make([]fr.Element, pk.Domain[0].Cardinality)
for i := 0; i < len(spr.Public); i++ { // placeholders (-PUB_INPUT_i + qk_i = 0) TODO should return error if size is inconsistent
pk.EvaluationQlDomainBigBitReversed[i].SetOne().Neg(&pk.EvaluationQlDomainBigBitReversed[i])
pk.EvaluationQrDomainBigBitReversed[i].SetZero()
pk.EvaluationQmDomainBigBitReversed[i].SetZero()
pk.EvaluationQoDomainBigBitReversed[i].SetZero()
pk.LQkIncompleteDomainSmall[i].SetZero() // --> to be completed by the prover
pk.CQkIncomplete[i].Set(&pk.LQkIncompleteDomainSmall[i]) // --> to be completed by the prover
}
offset := len(spr.Public)
j := 0
it := spr.GetSparseR1CIterator()
for c := it.Next(); c != nil; c = it.Next() {
pk.EvaluationQlDomainBigBitReversed[offset+j].Set(&spr.Coefficients[c.QL])
pk.EvaluationQrDomainBigBitReversed[offset+j].Set(&spr.Coefficients[c.QR])
pk.EvaluationQmDomainBigBitReversed[offset+j].Set(&spr.Coefficients[c.QM])
pk.EvaluationQoDomainBigBitReversed[offset+j].Set(&spr.Coefficients[c.QO])
pk.LQkIncompleteDomainSmall[offset+j].Set(&spr.Coefficients[c.QC])
pk.CQkIncomplete[offset+j].Set(&pk.LQkIncompleteDomainSmall[offset+j])
j++
}
pk.Domain[0].FFTInverse(pk.EvaluationQlDomainBigBitReversed[:pk.Domain[0].Cardinality], fft.DIF)
pk.Domain[0].FFTInverse(pk.EvaluationQrDomainBigBitReversed[:pk.Domain[0].Cardinality], fft.DIF)
pk.Domain[0].FFTInverse(pk.EvaluationQmDomainBigBitReversed[:pk.Domain[0].Cardinality], fft.DIF)
pk.Domain[0].FFTInverse(pk.EvaluationQoDomainBigBitReversed[:pk.Domain[0].Cardinality], fft.DIF)
pk.Domain[0].FFTInverse(pk.CQkIncomplete, fft.DIF)
fft.BitReverse(pk.EvaluationQlDomainBigBitReversed[:pk.Domain[0].Cardinality])
fft.BitReverse(pk.EvaluationQrDomainBigBitReversed[:pk.Domain[0].Cardinality])
fft.BitReverse(pk.EvaluationQmDomainBigBitReversed[:pk.Domain[0].Cardinality])
fft.BitReverse(pk.EvaluationQoDomainBigBitReversed[:pk.Domain[0].Cardinality])
fft.BitReverse(pk.CQkIncomplete)
// Commit to the polynomials to set up the verifying key
pk.CQl = make([]fr.Element, pk.Domain[0].Cardinality)
pk.CQr = make([]fr.Element, pk.Domain[0].Cardinality)
pk.CQm = make([]fr.Element, pk.Domain[0].Cardinality)
pk.CQo = make([]fr.Element, pk.Domain[0].Cardinality)
copy(pk.CQl, pk.EvaluationQlDomainBigBitReversed)
copy(pk.CQr, pk.EvaluationQrDomainBigBitReversed)
copy(pk.CQm, pk.EvaluationQmDomainBigBitReversed)
copy(pk.CQo, pk.EvaluationQoDomainBigBitReversed)
var err error
vk.Qpp[0], err = vk.Iopp.BuildProofOfProximity(pk.CQl)
if err != nil {
return &pk, &vk, err
}
vk.Qpp[1], err = vk.Iopp.BuildProofOfProximity(pk.CQr)
if err != nil {
return &pk, &vk, err
}
vk.Qpp[2], err = vk.Iopp.BuildProofOfProximity(pk.CQm)
if err != nil {
return &pk, &vk, err
}
vk.Qpp[3], err = vk.Iopp.BuildProofOfProximity(pk.CQo)
if err != nil {
return &pk, &vk, err
}
vk.Qpp[4], err = vk.Iopp.BuildProofOfProximity(pk.CQkIncomplete)
if err != nil {
return &pk, &vk, err
}
pk.Domain[1].FFT(pk.EvaluationQlDomainBigBitReversed, fft.DIF, fft.OnCoset())
pk.Domain[1].FFT(pk.EvaluationQrDomainBigBitReversed, fft.DIF, fft.OnCoset())
pk.Domain[1].FFT(pk.EvaluationQmDomainBigBitReversed, fft.DIF, fft.OnCoset())
pk.Domain[1].FFT(pk.EvaluationQoDomainBigBitReversed, fft.DIF, fft.OnCoset())
// build permutation. Note: at this stage, the permutation takes in account the placeholders
buildPermutation(spr, &pk)
// set s1, s2, s3
err = computePermutationPolynomials(&pk, &vk)
if err != nil {
return &pk, &vk, err
}
return &pk, &vk, nil
}
// buildPermutation builds the Permutation associated with a circuit.
//
// The permutation s is composed of cycles of maximum length such that
//
// s. (l||r||o) = (l||r||o)
//
// , where l||r||o is the concatenation of the indices of l, r, o in
// ql.l+qr.r+qm.l.r+qo.O+k = 0.
//
// The permutation is encoded as a slice s of size 3*size(l), where the
// i-th entry of l||r||o is sent to the s[i]-th entry, so it acts on a tab
// like this: for i in tab: tab[i] = tab[permutation[i]]
func buildPermutation(spr *cs.SparseR1CS, pk *ProvingKey) {
nbVariables := spr.NbInternalVariables + len(spr.Public) + len(spr.Secret)
sizeSolution := int(pk.Domain[0].Cardinality)
// init permutation
pk.Permutation = make([]int64, 3*sizeSolution)
for i := 0; i < len(pk.Permutation); i++ {
pk.Permutation[i] = -1
}
// init LRO position -> variable_ID
lro := make([]int, 3*sizeSolution) // position -> variable_ID
for i := 0; i < len(spr.Public); i++ {
lro[i] = i // IDs of LRO associated to placeholders (only L needs to be taken care of)
}
offset := len(spr.Public)
j := 0
it := spr.GetSparseR1CIterator()
for c := it.Next(); c != nil; c = it.Next() {
lro[offset+j] = int(c.XA)
lro[sizeSolution+offset+j] = int(c.XB)
lro[2*sizeSolution+offset+j] = int(c.XC)
j++
}
// init cycle:
// map ID -> last position the ID was seen
cycle := make([]int64, nbVariables)
for i := 0; i < len(cycle); i++ {
cycle[i] = -1
}
for i := 0; i < len(lro); i++ {
if cycle[lro[i]] != -1 {
// if != -1, it means we already encountered this value
// so we need to set the corresponding permutation index.
pk.Permutation[i] = cycle[lro[i]]
}
cycle[lro[i]] = int64(i)
}
// complete the Permutation by filling the first IDs encountered
for i := 0; i < len(pk.Permutation); i++ {
if pk.Permutation[i] == -1 {
pk.Permutation[i] = cycle[lro[i]]
}
}
}
// computePermutationPolynomials computes the LDE (Lagrange basis) of the permutations
// s1, s2, s3.
//
// 0 1 .. n-1 | n n+1 .. 2*n-1 | 2n 2n+1 .. 3n-1 |
//
// |
// | Permutation
//
// s00 s01 .. s0n-1 s10 s11 .. s1n-1 s20 s21 .. s2n-1 v
// \---------------/ \--------------------/ \------------------------/
//
// s1 (LDE) s2 (LDE) s3 (LDE)
func computePermutationPolynomials(pk *ProvingKey, vk *VerifyingKey) error {
nbElmt := int(pk.Domain[0].Cardinality)
// sID = [1,..,g^{n-1},s,..,s*g^{n-1},s^2,..,s^2*g^{n-1}]
pk.LId = getIDSmallDomain(&pk.Domain[0])
// canonical form of S1, S2, S3
pk.EvaluationS1BigDomain = make([]fr.Element, pk.Domain[1].Cardinality)
pk.EvaluationS2BigDomain = make([]fr.Element, pk.Domain[1].Cardinality)
pk.EvaluationS3BigDomain = make([]fr.Element, pk.Domain[1].Cardinality)
for i := 0; i < nbElmt; i++ {
pk.EvaluationS1BigDomain[i].Set(&pk.LId[pk.Permutation[i]])
pk.EvaluationS2BigDomain[i].Set(&pk.LId[pk.Permutation[nbElmt+i]])
pk.EvaluationS3BigDomain[i].Set(&pk.LId[pk.Permutation[2*nbElmt+i]])
}
// Evaluations of Sid1, Sid2, Sid3 on cosets of Domain[1]
pk.EvaluationId1BigDomain = make([]fr.Element, pk.Domain[1].Cardinality)
pk.EvaluationId2BigDomain = make([]fr.Element, pk.Domain[1].Cardinality)
pk.EvaluationId3BigDomain = make([]fr.Element, pk.Domain[1].Cardinality)
copy(pk.EvaluationId1BigDomain, pk.LId[:nbElmt])
copy(pk.EvaluationId2BigDomain, pk.LId[nbElmt:2*nbElmt])
copy(pk.EvaluationId3BigDomain, pk.LId[2*nbElmt:])
pk.Domain[0].FFTInverse(pk.EvaluationId1BigDomain[:pk.Domain[0].Cardinality], fft.DIF)
pk.Domain[0].FFTInverse(pk.EvaluationId2BigDomain[:pk.Domain[0].Cardinality], fft.DIF)
pk.Domain[0].FFTInverse(pk.EvaluationId3BigDomain[:pk.Domain[0].Cardinality], fft.DIF)
fft.BitReverse(pk.EvaluationId1BigDomain[:pk.Domain[0].Cardinality])
fft.BitReverse(pk.EvaluationId2BigDomain[:pk.Domain[0].Cardinality])
fft.BitReverse(pk.EvaluationId3BigDomain[:pk.Domain[0].Cardinality])
vk.IdCanonical[0] = make([]fr.Element, pk.Domain[0].Cardinality)
vk.IdCanonical[1] = make([]fr.Element, pk.Domain[0].Cardinality)
vk.IdCanonical[2] = make([]fr.Element, pk.Domain[0].Cardinality)
copy(vk.IdCanonical[0], pk.EvaluationId1BigDomain)
copy(vk.IdCanonical[1], pk.EvaluationId2BigDomain)
copy(vk.IdCanonical[2], pk.EvaluationId3BigDomain)
var err error
vk.Idpp[0], err = vk.Iopp.BuildProofOfProximity(pk.EvaluationId1BigDomain)
if err != nil {
return err
}
vk.Idpp[1], err = vk.Iopp.BuildProofOfProximity(pk.EvaluationId2BigDomain)
if err != nil {
return err
}
vk.Idpp[2], err = vk.Iopp.BuildProofOfProximity(pk.EvaluationId3BigDomain)
if err != nil {
return err
}
pk.Domain[1].FFT(pk.EvaluationId1BigDomain, fft.DIF, fft.OnCoset())
pk.Domain[1].FFT(pk.EvaluationId2BigDomain, fft.DIF, fft.OnCoset())
pk.Domain[1].FFT(pk.EvaluationId3BigDomain, fft.DIF, fft.OnCoset())
pk.Domain[0].FFTInverse(pk.EvaluationS1BigDomain[:pk.Domain[0].Cardinality], fft.DIF)
pk.Domain[0].FFTInverse(pk.EvaluationS2BigDomain[:pk.Domain[0].Cardinality], fft.DIF)
pk.Domain[0].FFTInverse(pk.EvaluationS3BigDomain[:pk.Domain[0].Cardinality], fft.DIF)
fft.BitReverse(pk.EvaluationS1BigDomain[:pk.Domain[0].Cardinality])
fft.BitReverse(pk.EvaluationS2BigDomain[:pk.Domain[0].Cardinality])
fft.BitReverse(pk.EvaluationS3BigDomain[:pk.Domain[0].Cardinality])
// commit S1, S2, S3
vk.SCanonical[0] = make([]fr.Element, pk.Domain[0].Cardinality)
vk.SCanonical[1] = make([]fr.Element, pk.Domain[0].Cardinality)
vk.SCanonical[2] = make([]fr.Element, pk.Domain[0].Cardinality)
copy(vk.SCanonical[0], pk.EvaluationS1BigDomain[:pk.Domain[0].Cardinality])
copy(vk.SCanonical[1], pk.EvaluationS2BigDomain[:pk.Domain[0].Cardinality])
copy(vk.SCanonical[2], pk.EvaluationS3BigDomain[:pk.Domain[0].Cardinality])
vk.Spp[0], err = vk.Iopp.BuildProofOfProximity(vk.SCanonical[0])
if err != nil {
return err
}
vk.Spp[1], err = vk.Iopp.BuildProofOfProximity(vk.SCanonical[1])
if err != nil {
return err
}
vk.Spp[2], err = vk.Iopp.BuildProofOfProximity(vk.SCanonical[2])
if err != nil {
return err
}
pk.Domain[1].FFT(pk.EvaluationS1BigDomain, fft.DIF, fft.OnCoset())
pk.Domain[1].FFT(pk.EvaluationS2BigDomain, fft.DIF, fft.OnCoset())
pk.Domain[1].FFT(pk.EvaluationS3BigDomain, fft.DIF, fft.OnCoset())
return nil
}
// getIDSmallDomain returns the Lagrange form of ID on the small domain
func getIDSmallDomain(domain *fft.Domain) []fr.Element {
res := make([]fr.Element, 3*domain.Cardinality)
res[0].SetOne()
res[domain.Cardinality].Set(&domain.FrMultiplicativeGen)
res[2*domain.Cardinality].Square(&domain.FrMultiplicativeGen)
for i := uint64(1); i < domain.Cardinality; i++ {
res[i].Mul(&res[i-1], &domain.Generator)
res[domain.Cardinality+i].Mul(&res[domain.Cardinality+i-1], &domain.Generator)
res[2*domain.Cardinality+i].Mul(&res[2*domain.Cardinality+i-1], &domain.Generator)
}
return res
}
// NbPublicWitness returns the expected public witness size (number of field elements)
func (vk *VerifyingKey) NbPublicWitness() int {
return int(vk.NbPublicVariables)
}
// VerifyingKey returns pk.Vk
func (pk *ProvingKey) VerifyingKey() interface{} {
return pk.Vk
}