From 53026fce89ae04f053c1ba729439f8c5f0e3a7c4 Mon Sep 17 00:00:00 2001 From: AlexandreBelling Date: Mon, 4 Dec 2023 13:49:21 +0100 Subject: [PATCH 1/2] add SIS to BLS12-377 --- ecc/bls12-377/fr/sis/sis.go | 409 + ecc/bls12-377/fr/sis/sis.sage | 272 + ecc/bls12-377/fr/sis/sis_fft.go | 494 + ecc/bls12-377/fr/sis/sis_test.go | 439 + ecc/bls12-377/fr/sis/test_cases.json | 117269 ++++++++++++++++++++++++ 5 files changed, 118883 insertions(+) create mode 100644 ecc/bls12-377/fr/sis/sis.go create mode 100644 ecc/bls12-377/fr/sis/sis.sage create mode 100644 ecc/bls12-377/fr/sis/sis_fft.go create mode 100644 ecc/bls12-377/fr/sis/sis_test.go create mode 100644 ecc/bls12-377/fr/sis/test_cases.json diff --git a/ecc/bls12-377/fr/sis/sis.go b/ecc/bls12-377/fr/sis/sis.go new file mode 100644 index 0000000000..164dc1a0e1 --- /dev/null +++ b/ecc/bls12-377/fr/sis/sis.go @@ -0,0 +1,409 @@ +// Copyright 2023 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. + +package sis + +import ( + "bytes" + "encoding/binary" + "errors" + "hash" + "math/big" + "math/bits" + + "github.com/bits-and-blooms/bitset" + "github.com/consensys/gnark-crypto/ecc/bls12-377/fr" + "github.com/consensys/gnark-crypto/ecc/bls12-377/fr/fft" + "github.com/consensys/gnark-crypto/internal/parallel" + "golang.org/x/crypto/blake2b" +) + +var ( + ErrNotAPowerOfTwo = errors.New("d must be a power of 2") +) + +// Ring-SIS instance +type RSis struct { + + // buffer storing the data to hash + buffer bytes.Buffer + + // Vectors in ℤ_{p}/Xⁿ+1 + // A[i] is the i-th polynomial. + // Ag the evaluation form of the polynomials in A on the coset √(g) * + A [][]fr.Element + Ag [][]fr.Element + + // LogTwoBound (Infinity norm) of the vector to hash. It means that each component in m + // is < 2^B, where m is the vector to hash (the hash being A*m). + // cf https://hackmd.io/7OODKWQZRRW9RxM5BaXtIw , B >= 3. + LogTwoBound int + + // domain for the polynomial multiplication + Domain *fft.Domain + twiddleCosets []fr.Element // see fft64 and precomputeTwiddlesCoset + + // d, the degree of X^{d}+1 + Degree int + + // in bytes, represents the maximum number of bytes the .Write(...) will handle; + // ( maximum number of bytes to sum ) + capacity int + maxNbElementsToHash int + + // allocate memory once per instance (used in Sum()) + bufM, bufRes fr.Vector + bufMValues *bitset.BitSet +} + +// NewRSis creates an instance of RSis. +// seed: seed for the randomness for generating A. +// logTwoDegree: if d := logTwoDegree, the ring will be ℤ_{p}[X]/Xᵈ-1, where X^{2ᵈ} is the 2ᵈ⁺¹-th cyclotomic polynomial +// logTwoBound: the bound of the vector to hash (using the infinity norm). +// maxNbElementsToHash: maximum number of field elements the instance handles +// used to derived n, the number of polynomials in A, and max size of instance's internal buffer. +func NewRSis(seed int64, logTwoDegree, logTwoBound, maxNbElementsToHash int) (*RSis, error) { + + if logTwoBound > 64 { + return nil, errors.New("logTwoBound too large") + } + if bits.UintSize == 32 { + return nil, errors.New("unsupported architecture; need 64bit target") + } + + degree := 1 << logTwoDegree + capacity := maxNbElementsToHash * fr.Bytes + + // n: number of polynomials in A + // len(m) == degree * n + // with each element in m being logTwoBounds bits from the instance buffer. + // that is, to fill m, we need [degree * n * logTwoBound] bits of data + // capacity == [degree * n * logTwoBound] / 8 + // n == (capacity*8)/(degree*logTwoBound) + + // First n <- #limbs to represent a single field element + n := (fr.Bytes * 8) / logTwoBound + if n*logTwoBound < fr.Bytes*8 { + n++ + } + + // Then multiply by the number of field elements + n *= maxNbElementsToHash + + // And divide (+ ceil) to get the number of polynomials + if n%degree == 0 { + n /= degree + } else { + n /= degree // number of polynomials + n++ + } + + // domains (shift is √{gen} ) + var shift fr.Element + shift.SetString("8065159656716812877374967518403273466521432693661810619979959746626482506078") // -> 2^47-th root of unity of bls12377 + e := int64(1 << (47 - (logTwoDegree + 1))) + shift.Exp(shift, big.NewInt(e)) + + r := &RSis{ + LogTwoBound: logTwoBound, + capacity: capacity, + Degree: degree, + Domain: fft.NewDomain(uint64(degree), shift), + A: make([][]fr.Element, n), + Ag: make([][]fr.Element, n), + bufM: make(fr.Vector, degree*n), + bufRes: make(fr.Vector, degree), + bufMValues: bitset.New(uint(n)), + maxNbElementsToHash: maxNbElementsToHash, + } + if r.LogTwoBound == 8 && r.Degree == 64 { + // TODO @gbotrel fixme, that's dirty. + r.twiddleCosets = precomputeTwiddlesCoset(r.Domain.Twiddles, r.Domain.FrMultiplicativeGen) + } + + // filling A + a := make([]fr.Element, n*r.Degree) + ag := make([]fr.Element, n*r.Degree) + + parallel.Execute(n, func(start, end int) { + var buf bytes.Buffer + for i := start; i < end; i++ { + rstart, rend := i*r.Degree, (i+1)*r.Degree + r.A[i] = a[rstart:rend:rend] + r.Ag[i] = ag[rstart:rend:rend] + for j := 0; j < r.Degree; j++ { + r.A[i][j] = genRandom(seed, int64(i), int64(j), &buf) + } + + // fill Ag the evaluation form of the polynomials in A on the coset √(g) * + copy(r.Ag[i], r.A[i]) + r.Domain.FFT(r.Ag[i], fft.DIF, fft.OnCoset()) + } + }) + + return r, nil +} + +func (r *RSis) Write(p []byte) (n int, err error) { + r.buffer.Write(p) + return len(p), nil +} + +// Sum appends the current hash to b and returns the resulting slice. +// It does not change the underlying hash state. +// The instance buffer is interpreted as a sequence of coefficients of size r.Bound bits long. +// The function returns the hash of the polynomial as a a sequence []fr.Elements, interpreted as []bytes, +// corresponding to sum_i A[i]*m Mod X^{d}+1 +func (r *RSis) Sum(b []byte) []byte { + buf := r.buffer.Bytes() + if len(buf) > r.capacity { + panic("buffer too large") + } + + fastPath := r.LogTwoBound == 8 && r.Degree == 64 + + // clear the buffers of the instance. + defer r.cleanupBuffers() + + m := r.bufM + mValues := r.bufMValues + + if fastPath { + // fast path. + limbDecomposeBytes8_64(buf, m, mValues) + } else { + limbDecomposeBytes(buf, m, r.LogTwoBound, r.Degree, mValues) + } + + // we can hash now. + res := r.bufRes + + // method 1: fft + for i := 0; i < len(r.Ag); i++ { + if !mValues.Test(uint(i)) { + // means m[i*r.Degree : (i+1)*r.Degree] == [0...0] + // we can skip this, FFT(0) = 0 + continue + } + k := m[i*r.Degree : (i+1)*r.Degree] + if fastPath { + // fast path. + fft64(k, r.twiddleCosets) + } else { + r.Domain.FFT(k, fft.DIF, fft.OnCoset(), fft.WithNbTasks(1)) + } + mulModAcc(res, r.Ag[i], k) + } + r.Domain.FFTInverse(res, fft.DIT, fft.OnCoset(), fft.WithNbTasks(1)) // -> reduces mod Xᵈ+1 + + resBytes, err := res.MarshalBinary() + if err != nil { + panic(err) + } + + return append(b, resBytes[4:]...) // first 4 bytes are uint32(len(res)) +} + +// Reset resets the Hash to its initial state. +func (r *RSis) Reset() { + r.buffer.Reset() +} + +// Size returns the number of bytes Sum will return. +func (r *RSis) Size() int { + + // The size in bits is the size in bits of a polynomial in A. + degree := len(r.A[0]) + totalSize := degree * fr.Modulus().BitLen() / 8 + + return totalSize +} + +// BlockSize returns the hash's underlying block size. +// The Write method must be able to accept any amount +// of data, but it may operate more efficiently if all writes +// are a multiple of the block size. +func (r *RSis) BlockSize() int { + return 0 +} + +// Construct a hasher generator. It takes as input the same parameters +// as `NewRingSIS` and outputs a function which returns fresh hasher +// everytime it is called +func NewRingSISMaker(seed int64, logTwoDegree, logTwoBound, maxNbElementsToHash int) (func() hash.Hash, error) { + return func() hash.Hash { + h, err := NewRSis(seed, logTwoDegree, logTwoBound, maxNbElementsToHash) + if err != nil { + panic(err) + } + return h + }, nil + +} + +func genRandom(seed, i, j int64, buf *bytes.Buffer) fr.Element { + + buf.Reset() + buf.WriteString("SIS") + binary.Write(buf, binary.BigEndian, seed) + binary.Write(buf, binary.BigEndian, i) + binary.Write(buf, binary.BigEndian, j) + + digest := blake2b.Sum256(buf.Bytes()) + + var res fr.Element + res.SetBytes(digest[:]) + + return res +} + +// mulMod computes p * q in ℤ_{p}[X]/Xᵈ+1. +// Is assumed that pLagrangeShifted and qLagrangeShifted are of the correct sizes +// and that they are in evaluation form on √(g) * +// The result is not FFTinversed. The fft inverse is done once every +// multiplications are done. +func mulMod(pLagrangeCosetBitReversed, qLagrangeCosetBitReversed []fr.Element) []fr.Element { + + res := make([]fr.Element, len(pLagrangeCosetBitReversed)) + for i := 0; i < len(pLagrangeCosetBitReversed); i++ { + res[i].Mul(&pLagrangeCosetBitReversed[i], &qLagrangeCosetBitReversed[i]) + } + + // NOT fft inv for now, wait until every part of the keys have been multiplied + // r.Domain.FFTInverse(res, fft.DIT, true) + + return res + +} + +// mulMod + accumulate in res. +func mulModAcc(res []fr.Element, pLagrangeCosetBitReversed, qLagrangeCosetBitReversed []fr.Element) { + var t fr.Element + for i := 0; i < len(pLagrangeCosetBitReversed); i++ { + t.Mul(&pLagrangeCosetBitReversed[i], &qLagrangeCosetBitReversed[i]) + res[i].Add(&res[i], &t) + } +} + +// Returns a clone of the RSis parameters with a fresh and empty buffer. Does not +// mutate the current instance. The keys and the public parameters of the SIS +// instance are not deep-copied. It is useful when we want to hash in parallel. +// Otherwise, we would have to generate an entire RSis for each thread. +func (r *RSis) CopyWithFreshBuffer() RSis { + res := *r + res.buffer = bytes.Buffer{} + res.bufM = make(fr.Vector, len(r.bufM)) + res.bufMValues = bitset.New(r.bufMValues.Len()) + res.bufRes = make(fr.Vector, len(r.bufRes)) + return res +} + +// Cleanup the buffers of the RSis instance +func (r *RSis) cleanupBuffers() { + r.bufMValues.ClearAll() + for i := 0; i < len(r.bufM); i++ { + r.bufM[i].SetZero() + } + for i := 0; i < len(r.bufRes); i++ { + r.bufRes[i].SetZero() + } +} + +// Split an slice of bytes representing an array of serialized field element in +// big-endian form into an array of limbs representing the same field elements +// in little-endian form. Namely, if our field is represented with 64 bits and we +// have the following field element 0x0123456789abcdef (0 being the most significant +// character and and f being the least significant one) and our log norm bound is +// 16 (so 1 hex character = 1 limb). The function assigns the values of m to [f, e, +// d, c, b, a, ..., 3, 2, 1, 0]. m should be preallocated and zeroized. Additionally, +// we have the guarantee that 2 bits contributing to different field elements cannot +// be part of the same limb. +func LimbDecomposeBytes(buf []byte, m fr.Vector, logTwoBound int) { + limbDecomposeBytes(buf, m, logTwoBound, 0, nil) +} + +// Split an slice of bytes representing an array of serialized field element in +// big-endian form into an array of limbs representing the same field elements +// in little-endian form. Namely, if our field is represented with 64 bits and we +// have the following field element 0x0123456789abcdef (0 being the most significant +// character and and f being the least significant one) and our log norm bound is +// 16 (so 1 hex character = 1 limb). The function assigns the values of m to [f, e, +// d, c, b, a, ..., 3, 2, 1, 0]. m should be preallocated and zeroized. mValues is +// an optional bitSet. If provided, it must be empty. The function will set bit "i" +// to indicate the that i-th SIS input polynomial should be non-zero. Recall, that a +// SIS polynomial corresponds to a chunk of limbs of size `degree`. Additionally, +// we have the guarantee that 2 bits contributing to different field elements cannot +// be part of the same limb. +func limbDecomposeBytes(buf []byte, m fr.Vector, logTwoBound, degree int, mValues *bitset.BitSet) { + + // bitwise decomposition of the buffer, in order to build m (the vector to hash) + // as a list of polynomials, whose coefficients are less than r.B bits long. + // Say buf=[0xbe,0x0f]. As a stream of bits it is interpreted like this: + // 10111110 00001111. BitAt(0)=1 (=leftmost bit), bitAt(1)=0 (=second leftmost bit), etc. + nbBits := len(buf) * 8 + bitAt := func(i int) uint8 { + k := i / 8 + if k >= len(buf) { + return 0 + } + b := buf[k] + j := i % 8 + return b >> (7 - j) & 1 + } + + // we process the input buffer by blocks of r.LogTwoBound bits + // each of these block (<< 64bits) are interpreted as a coefficient + mPos := 0 + for fieldStart := 0; fieldStart < nbBits; { + for bitInField := 0; bitInField < fr.Bytes*8; { + + j := bitInField % logTwoBound + + // r.LogTwoBound < 64; we just use the first word of our element here, + // and set the bits from LSB to MSB. + at := fieldStart + fr.Bytes*8 - bitInField - 1 + + m[mPos][0] |= uint64(bitAt(at) << j) + bitInField++ + + // Check if mPos is zero and mark as non-zero in the bitset if not + if m[mPos][0] != 0 && mValues != nil { + mValues.Set(uint(mPos / degree)) + } + + if j == logTwoBound-1 || bitInField == fr.Bytes*8 { + mPos++ + } + } + fieldStart += fr.Bytes * 8 + } +} + +// see limbDecomposeBytes; this function is optimized for the case where +// logTwoBound == 8 and degree == 64 +func limbDecomposeBytes8_64(buf []byte, m fr.Vector, mValues *bitset.BitSet) { + // with logTwoBound == 8, we can actually advance byte per byte. + const degree = 64 + j := 0 + + for startPos := fr.Bytes - 1; startPos < len(buf); startPos += fr.Bytes { + for i := startPos; i >= startPos-fr.Bytes+1; i-- { + m[j][0] = uint64(buf[i]) + if m[j][0] != 0 { + mValues.Set(uint(j / degree)) + } + j++ + } + } +} diff --git a/ecc/bls12-377/fr/sis/sis.sage b/ecc/bls12-377/fr/sis/sis.sage new file mode 100644 index 0000000000..eeecc4d3ce --- /dev/null +++ b/ecc/bls12-377/fr/sis/sis.sage @@ -0,0 +1,272 @@ +## "sage sis.sage" will generate test_cases.json +## tested with a fresh sage install on macOS (Feb 2023) + +import json + +# bls12377 Fr +r = 8444461749428370424248824938781546531375899335154063827935233455917409239041 +frByteSize = 32 +countToDeath = int(5) +gfr = GF(r) +Fr = GF(r) +Fr. = Fr[] +rz = IntegerRing() + +# Montgomery constant +rr = Fr(2**256) + +# utils + + +def buildPoly(a): + """ Builds a poly from the array a + + Args: + a an array + + Returns: + a[0]+a[1]*X + .. + a[n]*X**n + """ + + res = Fr(0) + for i, v in enumerate(a): + res += Fr(v)*x**i + return res + + +def bitAt(i, b): + """ + Args: + i: index of the bit to retrieve + b: array of bytes + + Returns: + the i-th bit of b, when it is written b[0] || b[1] || ... + """ + k = i//8 + if k >= len(b): + return 0 + j = i % 8 + return (b[k] >> (7-j)) & 1 + + +def toBytes(m, s): + """ + + Args: + m: a bit int + s: the expected number of bytes of the result. If s is bigger than the + number of bytes in m, the remaining bytes are set to zero. + + Returns: + the byte representation of m as a byte array, as + in gnark-crypto. + """ + _m = rz(m) + res = s*[0] + mask = 255 + for i in range(s): + res[s-1-i] = _m & 255 + _m = _m >> 8 + return res + + +def splitCoeffs(b, logTwoBound): + """ + Args: + b: an array of bytes + logTwoBound: number of bits of the bound + + Returns: + an array of coeffs, each coeff being the i-th chunk of logTwoBounds bits of b. + The coeffs are formed as follow. The input byte string is implicitly parsed as + a slice of field elements of 32 bytes each in bigendian-natural form. the outputs + are in a little-endian form. That is, each chunk of size 256 / logTwoBounds of the + output can be seen as a polynomial, such that, when evaluated at 2 we get the original + field element. + """ + nbBits = len(b)*8 + res = [] + i = 0 + + if len(b) % frByteSize != 0: + exit("the length of b should divide the field size") + + # The number of fields that we are parsing. In case we have that + # logTwoBound does not divide the number of bits to represent a + # field element, we do not merge them. + nbField = len(b) / 32 + nbBitsInField = int(frByteSize * 8) + + for fieldID in range(nbField): + fieldStart = fieldID * 256 + e = 0 + for bitInField in range(nbBitsInField): + j = bitInField % logTwoBound + at = fieldStart + nbBitsInField - 1 - bitInField + e |= bitAt(at, b) << j + # Switch to a new limb + if j == logTwoBound - 1 or bitInField == frByteSize * 8 - 1: + res.append(e) + e = 0 + + # careful Montgomery constant... + return [Fr(e)*rr**-1 for e in res] + + +def polyRand(seed, n): + """ Generates a pseudo random polynomial of size n from seed. + + Args: + seed: seed for the pseudo random gen + n: degree of the polynomial + """ + seed = gfr(seed) + a = n*[0] + for i in range(n): + a[i] = seed**2 + seed = a[i] + return buildPoly(a) + + +# SIS +class SIS: + def __init__(self, seed, logTwoDegree, logTwoBound, maxNbElementsToHash): + """ + Args: + seed + logTwoDegree: + logTwoBound: bound of SIS + maxNbElementsToHash + """ + capacity = maxNbElementsToHash * frByteSize + degree = 1 << logTwoDegree + + n = capacity * 8 / logTwoBound # number of coefficients + if n % degree == 0: # check how sage / python rounds the int div. + n = n / degree + else: + n = n / degree + n = n + 1 + + n = int(n) + + self.logTwoBound = logTwoBound + self.degree = degree + self.size = n + self.key = n * [0] + for i in range(n): + self.key[i] = polyRand(seed, self.degree) + seed += 1 + + def hash(self, inputs): + """ + Args: + inputs is a vector of Fr elements + + Returns: + the sis hash of m. + """ + b = [] + for i in inputs: + b.extend(toBytes(i, 32)) + + return self.hash_bytes(b) + + def hash_bytes(self, b): + """ + Args: + b is a list of bytes to hash + + Returns: + the sis hash of m. + """ + # step 1: build the polynomials from m + c = splitCoeffs(b, self.logTwoBound) + mp = [buildPoly(c[self.degree*i:self.degree*(i+1)]) + for i in range(self.size)] + + # step 2: compute sum_i mp[i]*key[i] mod X^n+1 + modulo = x**self.degree+1 + res = 0 + for i in range(self.size): + res += self.key[i]*mp[i] + res = res % modulo + return res + + +def vectorToString(v): + # v is a vector of field elements + # we return a list of strings in base10 + r = [] + for e in v: + r.append("0x"+rz(e).hex()) + return r + + +def SISParams(seed, logTwoDegree, logTwoBound, maxNbElementsToHash): + p = {} + p['seed'] = int(seed) + p['logTwoDegree'] = int(logTwoDegree) + p['logTwoBound'] = int(logTwoBound) + p['maxNbElementsToHash'] = int(maxNbElementsToHash) + return p + +params = [ + SISParams(5, 2, 3, 10), + SISParams(5, 4, 3, 10), + SISParams(5, 4, 4, 10), + SISParams(5, 5, 4, 10), + SISParams(5, 6, 5, 10), + # SISParams(5, 8, 6, 10), + SISParams(5, 10, 6, 10), + SISParams(5, 11, 7, 10), + SISParams(5, 12, 7, 10), +] + +inputs = [ + [Fr(21888242871839275222246405745257275088548364400416034343698204186575808495614)], + [Fr(1)], + [Fr(42),Fr(8000)], + [Fr(1),Fr(2), Fr(0),Fr(21888242871839275222246405745257275088548364400416034343698204186575808495616)], + [Fr(1), Fr(0)], + [Fr(0), Fr(1)], + [Fr(0)], + [Fr(0),Fr(0),Fr(0),Fr(0)], + [Fr(0),Fr(0),Fr(8000),Fr(0)], +] + +# sprinkle some random elements +for i in range(10): + line = [] + for j in range(i): + line.append(gfr.random_element()) + inputs.append(line) + +testCases = {} +testCases['inputs'] = [] +testCases['entries'] = [] + + +for i, v in enumerate(inputs): + testCases['inputs'].append(vectorToString(v)) + + +for p in params: + entry = {} + entry['params'] = p + entry['expected'] = [] + + print("generating test cases with SIS params " + json.dumps(p)) + instance = SIS(p['seed'], p['logTwoDegree'], p['logTwoBound'], p['maxNbElementsToHash']) + for i, v in enumerate(inputs): + # hash the vector + hResult = instance.hash(v) + entry['expected'].append(vectorToString(hResult)) + + testCases['entries'].append(entry) + + +testCases_json = json.dumps(testCases, indent=4) +with open("test_cases.json", "w") as outfile: + outfile.write(testCases_json) diff --git a/ecc/bls12-377/fr/sis/sis_fft.go b/ecc/bls12-377/fr/sis/sis_fft.go new file mode 100644 index 0000000000..891b7e677b --- /dev/null +++ b/ecc/bls12-377/fr/sis/sis_fft.go @@ -0,0 +1,494 @@ +// 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 consensys/gnark-crypto DO NOT EDIT + +package sis + +import ( + "github.com/consensys/gnark-crypto/ecc/bls12-377/fr" +) + +// fft64 is generated by gnark-crypto and contains the unrolled code for FFT (DIF) on 64 elements +// equivalent code: r.Domain.FFT(k, fft.DIF, fft.OnCoset(), fft.WithNbTasks(1)) +// twiddlesCoset must be pre-computed from twiddles and coset table, see precomputeTwiddlesCoset +func fft64(a []fr.Element, twiddlesCoset []fr.Element) { + + a[32].Mul(&a[32], &twiddlesCoset[0]) + a[33].Mul(&a[33], &twiddlesCoset[0]) + a[34].Mul(&a[34], &twiddlesCoset[0]) + a[35].Mul(&a[35], &twiddlesCoset[0]) + a[36].Mul(&a[36], &twiddlesCoset[0]) + a[37].Mul(&a[37], &twiddlesCoset[0]) + a[38].Mul(&a[38], &twiddlesCoset[0]) + a[39].Mul(&a[39], &twiddlesCoset[0]) + a[40].Mul(&a[40], &twiddlesCoset[0]) + a[41].Mul(&a[41], &twiddlesCoset[0]) + a[42].Mul(&a[42], &twiddlesCoset[0]) + a[43].Mul(&a[43], &twiddlesCoset[0]) + a[44].Mul(&a[44], &twiddlesCoset[0]) + a[45].Mul(&a[45], &twiddlesCoset[0]) + a[46].Mul(&a[46], &twiddlesCoset[0]) + a[47].Mul(&a[47], &twiddlesCoset[0]) + a[48].Mul(&a[48], &twiddlesCoset[0]) + a[49].Mul(&a[49], &twiddlesCoset[0]) + a[50].Mul(&a[50], &twiddlesCoset[0]) + a[51].Mul(&a[51], &twiddlesCoset[0]) + a[52].Mul(&a[52], &twiddlesCoset[0]) + a[53].Mul(&a[53], &twiddlesCoset[0]) + a[54].Mul(&a[54], &twiddlesCoset[0]) + a[55].Mul(&a[55], &twiddlesCoset[0]) + a[56].Mul(&a[56], &twiddlesCoset[0]) + a[57].Mul(&a[57], &twiddlesCoset[0]) + a[58].Mul(&a[58], &twiddlesCoset[0]) + a[59].Mul(&a[59], &twiddlesCoset[0]) + a[60].Mul(&a[60], &twiddlesCoset[0]) + a[61].Mul(&a[61], &twiddlesCoset[0]) + a[62].Mul(&a[62], &twiddlesCoset[0]) + a[63].Mul(&a[63], &twiddlesCoset[0]) + fr.Butterfly(&a[0], &a[32]) + fr.Butterfly(&a[1], &a[33]) + fr.Butterfly(&a[2], &a[34]) + fr.Butterfly(&a[3], &a[35]) + fr.Butterfly(&a[4], &a[36]) + fr.Butterfly(&a[5], &a[37]) + fr.Butterfly(&a[6], &a[38]) + fr.Butterfly(&a[7], &a[39]) + fr.Butterfly(&a[8], &a[40]) + fr.Butterfly(&a[9], &a[41]) + fr.Butterfly(&a[10], &a[42]) + fr.Butterfly(&a[11], &a[43]) + fr.Butterfly(&a[12], &a[44]) + fr.Butterfly(&a[13], &a[45]) + fr.Butterfly(&a[14], &a[46]) + fr.Butterfly(&a[15], &a[47]) + fr.Butterfly(&a[16], &a[48]) + fr.Butterfly(&a[17], &a[49]) + fr.Butterfly(&a[18], &a[50]) + fr.Butterfly(&a[19], &a[51]) + fr.Butterfly(&a[20], &a[52]) + fr.Butterfly(&a[21], &a[53]) + fr.Butterfly(&a[22], &a[54]) + fr.Butterfly(&a[23], &a[55]) + fr.Butterfly(&a[24], &a[56]) + fr.Butterfly(&a[25], &a[57]) + fr.Butterfly(&a[26], &a[58]) + fr.Butterfly(&a[27], &a[59]) + fr.Butterfly(&a[28], &a[60]) + fr.Butterfly(&a[29], &a[61]) + fr.Butterfly(&a[30], &a[62]) + fr.Butterfly(&a[31], &a[63]) + a[16].Mul(&a[16], &twiddlesCoset[1]) + a[17].Mul(&a[17], &twiddlesCoset[1]) + a[18].Mul(&a[18], &twiddlesCoset[1]) + a[19].Mul(&a[19], &twiddlesCoset[1]) + a[20].Mul(&a[20], &twiddlesCoset[1]) + a[21].Mul(&a[21], &twiddlesCoset[1]) + a[22].Mul(&a[22], &twiddlesCoset[1]) + a[23].Mul(&a[23], &twiddlesCoset[1]) + a[24].Mul(&a[24], &twiddlesCoset[1]) + a[25].Mul(&a[25], &twiddlesCoset[1]) + a[26].Mul(&a[26], &twiddlesCoset[1]) + a[27].Mul(&a[27], &twiddlesCoset[1]) + a[28].Mul(&a[28], &twiddlesCoset[1]) + a[29].Mul(&a[29], &twiddlesCoset[1]) + a[30].Mul(&a[30], &twiddlesCoset[1]) + a[31].Mul(&a[31], &twiddlesCoset[1]) + a[48].Mul(&a[48], &twiddlesCoset[2]) + a[49].Mul(&a[49], &twiddlesCoset[2]) + a[50].Mul(&a[50], &twiddlesCoset[2]) + a[51].Mul(&a[51], &twiddlesCoset[2]) + a[52].Mul(&a[52], &twiddlesCoset[2]) + a[53].Mul(&a[53], &twiddlesCoset[2]) + a[54].Mul(&a[54], &twiddlesCoset[2]) + a[55].Mul(&a[55], &twiddlesCoset[2]) + a[56].Mul(&a[56], &twiddlesCoset[2]) + a[57].Mul(&a[57], &twiddlesCoset[2]) + a[58].Mul(&a[58], &twiddlesCoset[2]) + a[59].Mul(&a[59], &twiddlesCoset[2]) + a[60].Mul(&a[60], &twiddlesCoset[2]) + a[61].Mul(&a[61], &twiddlesCoset[2]) + a[62].Mul(&a[62], &twiddlesCoset[2]) + a[63].Mul(&a[63], &twiddlesCoset[2]) + fr.Butterfly(&a[0], &a[16]) + fr.Butterfly(&a[1], &a[17]) + fr.Butterfly(&a[2], &a[18]) + fr.Butterfly(&a[3], &a[19]) + fr.Butterfly(&a[4], &a[20]) + fr.Butterfly(&a[5], &a[21]) + fr.Butterfly(&a[6], &a[22]) + fr.Butterfly(&a[7], &a[23]) + fr.Butterfly(&a[8], &a[24]) + fr.Butterfly(&a[9], &a[25]) + fr.Butterfly(&a[10], &a[26]) + fr.Butterfly(&a[11], &a[27]) + fr.Butterfly(&a[12], &a[28]) + fr.Butterfly(&a[13], &a[29]) + fr.Butterfly(&a[14], &a[30]) + fr.Butterfly(&a[15], &a[31]) + fr.Butterfly(&a[32], &a[48]) + fr.Butterfly(&a[33], &a[49]) + fr.Butterfly(&a[34], &a[50]) + fr.Butterfly(&a[35], &a[51]) + fr.Butterfly(&a[36], &a[52]) + fr.Butterfly(&a[37], &a[53]) + fr.Butterfly(&a[38], &a[54]) + fr.Butterfly(&a[39], &a[55]) + fr.Butterfly(&a[40], &a[56]) + fr.Butterfly(&a[41], &a[57]) + fr.Butterfly(&a[42], &a[58]) + fr.Butterfly(&a[43], &a[59]) + fr.Butterfly(&a[44], &a[60]) + fr.Butterfly(&a[45], &a[61]) + fr.Butterfly(&a[46], &a[62]) + fr.Butterfly(&a[47], &a[63]) + a[8].Mul(&a[8], &twiddlesCoset[3]) + a[9].Mul(&a[9], &twiddlesCoset[3]) + a[10].Mul(&a[10], &twiddlesCoset[3]) + a[11].Mul(&a[11], &twiddlesCoset[3]) + a[12].Mul(&a[12], &twiddlesCoset[3]) + a[13].Mul(&a[13], &twiddlesCoset[3]) + a[14].Mul(&a[14], &twiddlesCoset[3]) + a[15].Mul(&a[15], &twiddlesCoset[3]) + a[24].Mul(&a[24], &twiddlesCoset[4]) + a[25].Mul(&a[25], &twiddlesCoset[4]) + a[26].Mul(&a[26], &twiddlesCoset[4]) + a[27].Mul(&a[27], &twiddlesCoset[4]) + a[28].Mul(&a[28], &twiddlesCoset[4]) + a[29].Mul(&a[29], &twiddlesCoset[4]) + a[30].Mul(&a[30], &twiddlesCoset[4]) + a[31].Mul(&a[31], &twiddlesCoset[4]) + a[40].Mul(&a[40], &twiddlesCoset[5]) + a[41].Mul(&a[41], &twiddlesCoset[5]) + a[42].Mul(&a[42], &twiddlesCoset[5]) + a[43].Mul(&a[43], &twiddlesCoset[5]) + a[44].Mul(&a[44], &twiddlesCoset[5]) + a[45].Mul(&a[45], &twiddlesCoset[5]) + a[46].Mul(&a[46], &twiddlesCoset[5]) + a[47].Mul(&a[47], &twiddlesCoset[5]) + a[56].Mul(&a[56], &twiddlesCoset[6]) + a[57].Mul(&a[57], &twiddlesCoset[6]) + a[58].Mul(&a[58], &twiddlesCoset[6]) + a[59].Mul(&a[59], &twiddlesCoset[6]) + a[60].Mul(&a[60], &twiddlesCoset[6]) + a[61].Mul(&a[61], &twiddlesCoset[6]) + a[62].Mul(&a[62], &twiddlesCoset[6]) + a[63].Mul(&a[63], &twiddlesCoset[6]) + fr.Butterfly(&a[0], &a[8]) + fr.Butterfly(&a[1], &a[9]) + fr.Butterfly(&a[2], &a[10]) + fr.Butterfly(&a[3], &a[11]) + fr.Butterfly(&a[4], &a[12]) + fr.Butterfly(&a[5], &a[13]) + fr.Butterfly(&a[6], &a[14]) + fr.Butterfly(&a[7], &a[15]) + fr.Butterfly(&a[16], &a[24]) + fr.Butterfly(&a[17], &a[25]) + fr.Butterfly(&a[18], &a[26]) + fr.Butterfly(&a[19], &a[27]) + fr.Butterfly(&a[20], &a[28]) + fr.Butterfly(&a[21], &a[29]) + fr.Butterfly(&a[22], &a[30]) + fr.Butterfly(&a[23], &a[31]) + fr.Butterfly(&a[32], &a[40]) + fr.Butterfly(&a[33], &a[41]) + fr.Butterfly(&a[34], &a[42]) + fr.Butterfly(&a[35], &a[43]) + fr.Butterfly(&a[36], &a[44]) + fr.Butterfly(&a[37], &a[45]) + fr.Butterfly(&a[38], &a[46]) + fr.Butterfly(&a[39], &a[47]) + fr.Butterfly(&a[48], &a[56]) + fr.Butterfly(&a[49], &a[57]) + fr.Butterfly(&a[50], &a[58]) + fr.Butterfly(&a[51], &a[59]) + fr.Butterfly(&a[52], &a[60]) + fr.Butterfly(&a[53], &a[61]) + fr.Butterfly(&a[54], &a[62]) + fr.Butterfly(&a[55], &a[63]) + a[4].Mul(&a[4], &twiddlesCoset[7]) + a[5].Mul(&a[5], &twiddlesCoset[7]) + a[6].Mul(&a[6], &twiddlesCoset[7]) + a[7].Mul(&a[7], &twiddlesCoset[7]) + a[12].Mul(&a[12], &twiddlesCoset[8]) + a[13].Mul(&a[13], &twiddlesCoset[8]) + a[14].Mul(&a[14], &twiddlesCoset[8]) + a[15].Mul(&a[15], &twiddlesCoset[8]) + a[20].Mul(&a[20], &twiddlesCoset[9]) + a[21].Mul(&a[21], &twiddlesCoset[9]) + a[22].Mul(&a[22], &twiddlesCoset[9]) + a[23].Mul(&a[23], &twiddlesCoset[9]) + a[28].Mul(&a[28], &twiddlesCoset[10]) + a[29].Mul(&a[29], &twiddlesCoset[10]) + a[30].Mul(&a[30], &twiddlesCoset[10]) + a[31].Mul(&a[31], &twiddlesCoset[10]) + a[36].Mul(&a[36], &twiddlesCoset[11]) + a[37].Mul(&a[37], &twiddlesCoset[11]) + a[38].Mul(&a[38], &twiddlesCoset[11]) + a[39].Mul(&a[39], &twiddlesCoset[11]) + a[44].Mul(&a[44], &twiddlesCoset[12]) + a[45].Mul(&a[45], &twiddlesCoset[12]) + a[46].Mul(&a[46], &twiddlesCoset[12]) + a[47].Mul(&a[47], &twiddlesCoset[12]) + a[52].Mul(&a[52], &twiddlesCoset[13]) + a[53].Mul(&a[53], &twiddlesCoset[13]) + a[54].Mul(&a[54], &twiddlesCoset[13]) + a[55].Mul(&a[55], &twiddlesCoset[13]) + a[60].Mul(&a[60], &twiddlesCoset[14]) + a[61].Mul(&a[61], &twiddlesCoset[14]) + a[62].Mul(&a[62], &twiddlesCoset[14]) + a[63].Mul(&a[63], &twiddlesCoset[14]) + fr.Butterfly(&a[0], &a[4]) + fr.Butterfly(&a[1], &a[5]) + fr.Butterfly(&a[2], &a[6]) + fr.Butterfly(&a[3], &a[7]) + fr.Butterfly(&a[8], &a[12]) + fr.Butterfly(&a[9], &a[13]) + fr.Butterfly(&a[10], &a[14]) + fr.Butterfly(&a[11], &a[15]) + fr.Butterfly(&a[16], &a[20]) + fr.Butterfly(&a[17], &a[21]) + fr.Butterfly(&a[18], &a[22]) + fr.Butterfly(&a[19], &a[23]) + fr.Butterfly(&a[24], &a[28]) + fr.Butterfly(&a[25], &a[29]) + fr.Butterfly(&a[26], &a[30]) + fr.Butterfly(&a[27], &a[31]) + fr.Butterfly(&a[32], &a[36]) + fr.Butterfly(&a[33], &a[37]) + fr.Butterfly(&a[34], &a[38]) + fr.Butterfly(&a[35], &a[39]) + fr.Butterfly(&a[40], &a[44]) + fr.Butterfly(&a[41], &a[45]) + fr.Butterfly(&a[42], &a[46]) + fr.Butterfly(&a[43], &a[47]) + fr.Butterfly(&a[48], &a[52]) + fr.Butterfly(&a[49], &a[53]) + fr.Butterfly(&a[50], &a[54]) + fr.Butterfly(&a[51], &a[55]) + fr.Butterfly(&a[56], &a[60]) + fr.Butterfly(&a[57], &a[61]) + fr.Butterfly(&a[58], &a[62]) + fr.Butterfly(&a[59], &a[63]) + a[2].Mul(&a[2], &twiddlesCoset[15]) + a[3].Mul(&a[3], &twiddlesCoset[15]) + a[6].Mul(&a[6], &twiddlesCoset[16]) + a[7].Mul(&a[7], &twiddlesCoset[16]) + a[10].Mul(&a[10], &twiddlesCoset[17]) + a[11].Mul(&a[11], &twiddlesCoset[17]) + a[14].Mul(&a[14], &twiddlesCoset[18]) + a[15].Mul(&a[15], &twiddlesCoset[18]) + a[18].Mul(&a[18], &twiddlesCoset[19]) + a[19].Mul(&a[19], &twiddlesCoset[19]) + a[22].Mul(&a[22], &twiddlesCoset[20]) + a[23].Mul(&a[23], &twiddlesCoset[20]) + a[26].Mul(&a[26], &twiddlesCoset[21]) + a[27].Mul(&a[27], &twiddlesCoset[21]) + a[30].Mul(&a[30], &twiddlesCoset[22]) + a[31].Mul(&a[31], &twiddlesCoset[22]) + a[34].Mul(&a[34], &twiddlesCoset[23]) + a[35].Mul(&a[35], &twiddlesCoset[23]) + a[38].Mul(&a[38], &twiddlesCoset[24]) + a[39].Mul(&a[39], &twiddlesCoset[24]) + a[42].Mul(&a[42], &twiddlesCoset[25]) + a[43].Mul(&a[43], &twiddlesCoset[25]) + a[46].Mul(&a[46], &twiddlesCoset[26]) + a[47].Mul(&a[47], &twiddlesCoset[26]) + a[50].Mul(&a[50], &twiddlesCoset[27]) + a[51].Mul(&a[51], &twiddlesCoset[27]) + a[54].Mul(&a[54], &twiddlesCoset[28]) + a[55].Mul(&a[55], &twiddlesCoset[28]) + a[58].Mul(&a[58], &twiddlesCoset[29]) + a[59].Mul(&a[59], &twiddlesCoset[29]) + a[62].Mul(&a[62], &twiddlesCoset[30]) + a[63].Mul(&a[63], &twiddlesCoset[30]) + fr.Butterfly(&a[0], &a[2]) + fr.Butterfly(&a[1], &a[3]) + fr.Butterfly(&a[4], &a[6]) + fr.Butterfly(&a[5], &a[7]) + fr.Butterfly(&a[8], &a[10]) + fr.Butterfly(&a[9], &a[11]) + fr.Butterfly(&a[12], &a[14]) + fr.Butterfly(&a[13], &a[15]) + fr.Butterfly(&a[16], &a[18]) + fr.Butterfly(&a[17], &a[19]) + fr.Butterfly(&a[20], &a[22]) + fr.Butterfly(&a[21], &a[23]) + fr.Butterfly(&a[24], &a[26]) + fr.Butterfly(&a[25], &a[27]) + fr.Butterfly(&a[28], &a[30]) + fr.Butterfly(&a[29], &a[31]) + fr.Butterfly(&a[32], &a[34]) + fr.Butterfly(&a[33], &a[35]) + fr.Butterfly(&a[36], &a[38]) + fr.Butterfly(&a[37], &a[39]) + fr.Butterfly(&a[40], &a[42]) + fr.Butterfly(&a[41], &a[43]) + fr.Butterfly(&a[44], &a[46]) + fr.Butterfly(&a[45], &a[47]) + fr.Butterfly(&a[48], &a[50]) + fr.Butterfly(&a[49], &a[51]) + fr.Butterfly(&a[52], &a[54]) + fr.Butterfly(&a[53], &a[55]) + fr.Butterfly(&a[56], &a[58]) + fr.Butterfly(&a[57], &a[59]) + fr.Butterfly(&a[60], &a[62]) + fr.Butterfly(&a[61], &a[63]) + a[1].Mul(&a[1], &twiddlesCoset[31]) + a[3].Mul(&a[3], &twiddlesCoset[32]) + a[5].Mul(&a[5], &twiddlesCoset[33]) + a[7].Mul(&a[7], &twiddlesCoset[34]) + a[9].Mul(&a[9], &twiddlesCoset[35]) + a[11].Mul(&a[11], &twiddlesCoset[36]) + a[13].Mul(&a[13], &twiddlesCoset[37]) + a[15].Mul(&a[15], &twiddlesCoset[38]) + a[17].Mul(&a[17], &twiddlesCoset[39]) + a[19].Mul(&a[19], &twiddlesCoset[40]) + a[21].Mul(&a[21], &twiddlesCoset[41]) + a[23].Mul(&a[23], &twiddlesCoset[42]) + a[25].Mul(&a[25], &twiddlesCoset[43]) + a[27].Mul(&a[27], &twiddlesCoset[44]) + a[29].Mul(&a[29], &twiddlesCoset[45]) + a[31].Mul(&a[31], &twiddlesCoset[46]) + a[33].Mul(&a[33], &twiddlesCoset[47]) + a[35].Mul(&a[35], &twiddlesCoset[48]) + a[37].Mul(&a[37], &twiddlesCoset[49]) + a[39].Mul(&a[39], &twiddlesCoset[50]) + a[41].Mul(&a[41], &twiddlesCoset[51]) + a[43].Mul(&a[43], &twiddlesCoset[52]) + a[45].Mul(&a[45], &twiddlesCoset[53]) + a[47].Mul(&a[47], &twiddlesCoset[54]) + a[49].Mul(&a[49], &twiddlesCoset[55]) + a[51].Mul(&a[51], &twiddlesCoset[56]) + a[53].Mul(&a[53], &twiddlesCoset[57]) + a[55].Mul(&a[55], &twiddlesCoset[58]) + a[57].Mul(&a[57], &twiddlesCoset[59]) + a[59].Mul(&a[59], &twiddlesCoset[60]) + a[61].Mul(&a[61], &twiddlesCoset[61]) + a[63].Mul(&a[63], &twiddlesCoset[62]) + fr.Butterfly(&a[0], &a[1]) + fr.Butterfly(&a[2], &a[3]) + fr.Butterfly(&a[4], &a[5]) + fr.Butterfly(&a[6], &a[7]) + fr.Butterfly(&a[8], &a[9]) + fr.Butterfly(&a[10], &a[11]) + fr.Butterfly(&a[12], &a[13]) + fr.Butterfly(&a[14], &a[15]) + fr.Butterfly(&a[16], &a[17]) + fr.Butterfly(&a[18], &a[19]) + fr.Butterfly(&a[20], &a[21]) + fr.Butterfly(&a[22], &a[23]) + fr.Butterfly(&a[24], &a[25]) + fr.Butterfly(&a[26], &a[27]) + fr.Butterfly(&a[28], &a[29]) + fr.Butterfly(&a[30], &a[31]) + fr.Butterfly(&a[32], &a[33]) + fr.Butterfly(&a[34], &a[35]) + fr.Butterfly(&a[36], &a[37]) + fr.Butterfly(&a[38], &a[39]) + fr.Butterfly(&a[40], &a[41]) + fr.Butterfly(&a[42], &a[43]) + fr.Butterfly(&a[44], &a[45]) + fr.Butterfly(&a[46], &a[47]) + fr.Butterfly(&a[48], &a[49]) + fr.Butterfly(&a[50], &a[51]) + fr.Butterfly(&a[52], &a[53]) + fr.Butterfly(&a[54], &a[55]) + fr.Butterfly(&a[56], &a[57]) + fr.Butterfly(&a[58], &a[59]) + fr.Butterfly(&a[60], &a[61]) + fr.Butterfly(&a[62], &a[63]) +} + +// precomputeTwiddlesCoset precomputes twiddlesCoset from twiddles and coset table +// it then return all elements in the correct order for the unrolled FFT. +func precomputeTwiddlesCoset(twiddles [][]fr.Element, shifter fr.Element) []fr.Element { + r := make([][]fr.Element, len(twiddles)) + for i := 0; i < len(twiddles); i++ { + r[i] = make([]fr.Element, len(twiddles[i])) + s := shifter + for k := 0; k < i; k++ { + s.Mul(&s, &s) + } + for j := 0; j < len(twiddles[i]); j++ { + r[i][j].Mul(&twiddles[i][j], &s) + } + } + toReturn := make([]fr.Element, 0, 63) + + toReturn = append(toReturn, r[5][0]) + toReturn = append(toReturn, r[4][0]) + toReturn = append(toReturn, r[4][1]) + toReturn = append(toReturn, r[3][0]) + toReturn = append(toReturn, r[3][2]) + toReturn = append(toReturn, r[3][1]) + toReturn = append(toReturn, r[3][3]) + toReturn = append(toReturn, r[2][0]) + toReturn = append(toReturn, r[2][4]) + toReturn = append(toReturn, r[2][2]) + toReturn = append(toReturn, r[2][6]) + toReturn = append(toReturn, r[2][1]) + toReturn = append(toReturn, r[2][5]) + toReturn = append(toReturn, r[2][3]) + toReturn = append(toReturn, r[2][7]) + toReturn = append(toReturn, r[1][0]) + toReturn = append(toReturn, r[1][8]) + toReturn = append(toReturn, r[1][4]) + toReturn = append(toReturn, r[1][12]) + toReturn = append(toReturn, r[1][2]) + toReturn = append(toReturn, r[1][10]) + toReturn = append(toReturn, r[1][6]) + toReturn = append(toReturn, r[1][14]) + toReturn = append(toReturn, r[1][1]) + toReturn = append(toReturn, r[1][9]) + toReturn = append(toReturn, r[1][5]) + toReturn = append(toReturn, r[1][13]) + toReturn = append(toReturn, r[1][3]) + toReturn = append(toReturn, r[1][11]) + toReturn = append(toReturn, r[1][7]) + toReturn = append(toReturn, r[1][15]) + toReturn = append(toReturn, r[0][0]) + toReturn = append(toReturn, r[0][16]) + toReturn = append(toReturn, r[0][8]) + toReturn = append(toReturn, r[0][24]) + toReturn = append(toReturn, r[0][4]) + toReturn = append(toReturn, r[0][20]) + toReturn = append(toReturn, r[0][12]) + toReturn = append(toReturn, r[0][28]) + toReturn = append(toReturn, r[0][2]) + toReturn = append(toReturn, r[0][18]) + toReturn = append(toReturn, r[0][10]) + toReturn = append(toReturn, r[0][26]) + toReturn = append(toReturn, r[0][6]) + toReturn = append(toReturn, r[0][22]) + toReturn = append(toReturn, r[0][14]) + toReturn = append(toReturn, r[0][30]) + toReturn = append(toReturn, r[0][1]) + toReturn = append(toReturn, r[0][17]) + toReturn = append(toReturn, r[0][9]) + toReturn = append(toReturn, r[0][25]) + toReturn = append(toReturn, r[0][5]) + toReturn = append(toReturn, r[0][21]) + toReturn = append(toReturn, r[0][13]) + toReturn = append(toReturn, r[0][29]) + toReturn = append(toReturn, r[0][3]) + toReturn = append(toReturn, r[0][19]) + toReturn = append(toReturn, r[0][11]) + toReturn = append(toReturn, r[0][27]) + toReturn = append(toReturn, r[0][7]) + toReturn = append(toReturn, r[0][23]) + toReturn = append(toReturn, r[0][15]) + toReturn = append(toReturn, r[0][31]) + return toReturn +} diff --git a/ecc/bls12-377/fr/sis/sis_test.go b/ecc/bls12-377/fr/sis/sis_test.go new file mode 100644 index 0000000000..ddccf9222d --- /dev/null +++ b/ecc/bls12-377/fr/sis/sis_test.go @@ -0,0 +1,439 @@ +// Copyright 2023 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. + +package sis + +import ( + "bytes" + "encoding/binary" + "encoding/json" + "fmt" + "io" + "io/ioutil" + "math/big" + "math/bits" + "math/rand" + "testing" + "time" + + "github.com/bits-and-blooms/bitset" + "github.com/consensys/gnark-crypto/ecc/bls12-377/fr" + "github.com/consensys/gnark-crypto/ecc/bls12-377/fr/fft" + "github.com/stretchr/testify/assert" + "github.com/stretchr/testify/require" +) + +type sisParams struct { + logTwoBound, logTwoDegree int +} + +var params128Bits []sisParams = []sisParams{ + {logTwoBound: 2, logTwoDegree: 3}, + {logTwoBound: 4, logTwoDegree: 4}, + {logTwoBound: 6, logTwoDegree: 5}, + {logTwoBound: 8, logTwoDegree: 6}, + {logTwoBound: 10, logTwoDegree: 6}, + {logTwoBound: 16, logTwoDegree: 7}, + {logTwoBound: 32, logTwoDegree: 8}, +} + +type TestCases struct { + Inputs [][]fr.Element `json:"inputs"` + Entries []struct { + Params struct { + Seed int64 `json:"seed"` + LogTwoDegree int `json:"logTwoDegree"` + LogTwoBound int `json:"logTwoBound"` + MaxNbElementsToHash int `json:"maxNbElementsToHash"` + } `json:"params"` + Expected [][]fr.Element `json:"expected"` + } `json:"entries"` +} + +func TestReference(t *testing.T) { + if bits.UintSize == 32 { + t.Skip("skipping this test in 32bit.") + } + assert := require.New(t) + + // read the test case file + var testCases TestCases + data, err := ioutil.ReadFile("test_cases.json") + assert.NoError(err, "reading test cases failed") + err = json.Unmarshal(data, &testCases) + assert.NoError(err, "reading test cases failed") + + for testCaseID, testCase := range testCases.Entries { + // create the SIS instance + sis, err := NewRSis(testCase.Params.Seed, testCase.Params.LogTwoDegree, testCase.Params.LogTwoBound, testCase.Params.MaxNbElementsToHash) + assert.NoError(err) + + // key generation same than in sage + makeKeyDeterministic(t, sis, testCase.Params.Seed) + + for i, in := range testCases.Inputs { + sis.Reset() + + // hash test case entry input and compare with expected (computed by sage) + got, err := sis.Hash(in) + assert.NoError(err) + if len(testCase.Expected[i]) == 0 { + for _, e := range got { + assert.True(e.IsZero(), "mismatch between reference test and computed value") + } + } else { + assert.EqualValues( + testCase.Expected[i], got, + "mismatch between reference test and computed value (testcase %v - input n° %v)", + testCaseID, i, + ) + } + + // ensure max nb elements to hash has no incidence on result. + if len(in) < testCase.Params.MaxNbElementsToHash { + sis2, err := NewRSis(testCase.Params.Seed, testCase.Params.LogTwoDegree, testCase.Params.LogTwoBound, len(in)) + assert.NoError(err) + makeKeyDeterministic(t, sis2, testCase.Params.Seed) + + got2, err := sis2.Hash(in) + assert.NoError(err) + if len(testCase.Expected[i]) == 0 { + for _, e := range got2 { + assert.True(e.IsZero(), "mismatch between reference test and computed value") + } + } else { + assert.EqualValues(got, got2, "max nb elements to hash change SIS result") + } + } + + } + } + +} + +func TestMulMod(t *testing.T) { + + size := 4 + + p := make([]fr.Element, size) + p[0].SetString("2389") + p[1].SetString("987192") + p[2].SetString("623") + p[3].SetString("91") + + q := make([]fr.Element, size) + q[0].SetString("76755") + q[1].SetString("232893720") + q[2].SetString("989273") + q[3].SetString("675273") + + // creation of the domain. Note that the value of the shift is purely arbitrary + // and random. + var shift fr.Element + shift.SetString("19540430494807482326159819597004422086093766032135589407132600596362845576832") + domain := fft.NewDomain(uint64(size), shift) + + // mul mod + domain.FFT(p, fft.DIF, fft.OnCoset()) + domain.FFT(q, fft.DIF, fft.OnCoset()) + r := mulMod(p, q) + domain.FFTInverse(r, fft.DIT, fft.OnCoset()) + + // expected result + expectedr := make([]fr.Element, 4) + expectedr[0].SetString("1612335717510792699655803640368030375030102334758014597273992900671209760644") + expectedr[1].SetString("7801939531701554412773487946871330804032103116849274522170062191886789772982") + expectedr[2].SetString("3958508915483304256780311126107405810447277056055916093890488600778971951103") + expectedr[3].SetString("1123315390878") + + for i := 0; i < 4; i++ { + assert.Equal(t, expectedr[i].String(), r[i].String()) + } +} + +// Test the fact that the limb decomposition allows obtaining the original +// field element by evaluating the polynomial whose the coeffiients are the +// limbs. +func TestLimbDecomposition(t *testing.T) { + + // Skipping the test for 32 bits + if bits.UintSize == 32 { + t.Skip("skipping this test in 32bit.") + } + + sis, _ := NewRSis(0, 4, 4, 3) + + testcases := []fr.Vector{ + {fr.One()}, + {fr.NewElement(2)}, + {fr.NewElement(1 << 32), fr.NewElement(2), fr.NewElement(1)}, + } + + for _, testcase := range testcases { + + // clean the sis hasher + sis.bufMValues.ClearAll() + for i := 0; i < len(sis.bufM); i++ { + sis.bufM[i].SetZero() + } + for i := 0; i < len(sis.bufRes); i++ { + sis.bufRes[i].SetZero() + } + + buf := bytes.Buffer{} + for _, x := range testcase { + xBytes := x.Bytes() + buf.Write(xBytes[:]) + } + limbDecomposeBytes(buf.Bytes(), sis.bufM, sis.LogTwoBound, sis.Degree, sis.bufMValues) + + // Just to test, this does not return panic + dummyBuffer := make(fr.Vector, 192) + LimbDecomposeBytes(buf.Bytes(), dummyBuffer, sis.LogTwoBound) + + // b is a field element representing the max norm bound + // used for limb splitting the input field elements. + b := fr.NewElement(1 << sis.LogTwoBound) + numLimbsPerField := fr.Bytes * 8 / sis.LogTwoBound + + // Compute r (corresponds to the Montgommery constant) + var r fr.Element + r.SetString("6014086494747379908336260804527802945383293308637734276299549080986809532403") + + // Attempt to recompose the entry #i in the test-case + for i := range testcase { + // allegedly corresponds to the limbs of the entry i + subRes := sis.bufM[i*numLimbsPerField : (i+1)*numLimbsPerField] + + // performs a Horner evaluation of subres by b + var y fr.Element + for j := numLimbsPerField - 1; j >= 0; j-- { + y.Mul(&y, &b) + y.Add(&y, &subRes[j]) + } + + fmt.Printf("subres: %v\n", subRes) + + y.Mul(&y, &r) + require.Equal(t, testcase[i].String(), y.String(), "the subRes was %v", subRes) + } + } +} + +func makeKeyDeterministic(t *testing.T, sis *RSis, _seed int64) { + t.Helper() + // generate the key deterministically, the same way + // we do in sage to generate the test vectors. + + polyRand := func(seed fr.Element, deg int) []fr.Element { + res := make([]fr.Element, deg) + for i := 0; i < deg; i++ { + res[i].Square(&seed) + seed.Set(&res[i]) + } + return res + } + + var seed, one fr.Element + one.SetOne() + seed.SetInt64(_seed) + for i := 0; i < len(sis.A); i++ { + sis.A[i] = polyRand(seed, sis.Degree) + copy(sis.Ag[i], sis.A[i]) + sis.Domain.FFT(sis.Ag[i], fft.DIF, fft.OnCoset()) + seed.Add(&seed, &one) + } +} + +const ( + LATENCY_MUL_FIELD_NS int = 18 + LATENCY_ADD_FIELD_NS int = 4 +) + +// Estimate the theoretical performances that are achievable using ring-SIS +// operations. The time is obtained by counting the number of additions and +// multiplications occurring in the computation. This does not account for the +// possibilities to use SIMD instructions or for cache-locality issues. Thus, it +// does not represents a maximum even though it returns a good idea of what is +// achievable . This returns performances in term of ns/field. This also does not +// account for the time taken for "limb-splitting" the input. +func estimateSisTheory(p sisParams) float64 { + + // Since the FFT occurs over a coset, we need to multiply all the coefficients + // of the input by some coset factors (for an entire polynomial) + timeCosetShift := (1 << p.logTwoDegree) * LATENCY_MUL_FIELD_NS + + // The two additions are from the butterfly, and the multiplication represents + // the one by the twiddle. (for an entire polynomial) + timeFFT := (1 << p.logTwoDegree) * p.logTwoDegree * (2*LATENCY_ADD_FIELD_NS + LATENCY_MUL_FIELD_NS) + + // Time taken to multiply by the key and accumulate (for an entire polynomial) + timeMulAddKey := (1 << p.logTwoDegree) * (LATENCY_MUL_FIELD_NS + LATENCY_ADD_FIELD_NS) + + // Total computation time for an entire polynomial + totalTimePoly := timeCosetShift + timeFFT + timeMulAddKey + + // Convert this into a time per input field + r := totalTimePoly * fr.Bits / p.logTwoBound / (1 << p.logTwoDegree) + return float64(r) +} + +func BenchmarkSIS(b *testing.B) { + + // max nb field elements to hash + const nbInputs = 1 << 16 + + // Assign the input with random bytes. In practice, theses bytes encodes + // a string of field element. It would be more meaningful to take a slice + // of field element directly because otherwise the conversion time is not + // accounted for in the benchmark. + inputs := make(fr.Vector, nbInputs) + for i := 0; i < len(inputs); i++ { + inputs[i].SetRandom() + } + + for _, param := range params128Bits { + for n := 1 << 10; n <= nbInputs; n <<= 1 { + in := inputs[:n] + benchmarkSIS(b, in, false, param.logTwoBound, param.logTwoDegree, estimateSisTheory(param)) + } + + } +} + +func benchmarkSIS(b *testing.B, input []fr.Element, sparse bool, logTwoBound, logTwoDegree int, theoretical float64) { + b.Helper() + + n := len(input) + + benchName := "ring-sis/" + if sparse { + benchName += "sparse/" + } + benchName += fmt.Sprintf("inputs=%v/log2-bound=%v/log2-degree=%v", n, logTwoBound, logTwoDegree) + + b.Run(benchName, func(b *testing.B) { + instance, err := NewRSis(0, logTwoDegree, logTwoBound, n) + if err != nil { + b.Fatal(err) + } + + // We introduce a custom metric which is the time per field element + // Since the benchmark object allows to report extra meta but does + // not allow accessing them. We measure the time ourself. + + startTime := time.Now() + b.ResetTimer() + for i := 0; i < b.N; i++ { + _, err = instance.Hash(input) + if err != nil { + b.Fatal(err) + } + } + b.StopTimer() + + totalDuration := time.Since(startTime) + nsPerField := totalDuration.Nanoseconds() / int64(b.N) / int64(n) + + b.ReportMetric(float64(nsPerField), "ns/field") + + b.ReportMetric(theoretical, "ns/field(theory)") + + }) +} + +// Hash interprets the input vector as a sequence of coefficients of size r.LogTwoBound bits long, +// and return the hash of the polynomial corresponding to the sum sum_i A[i]*m Mod X^{d}+1 +// +// It is equivalent to calling r.Write(element.Marshal()); outBytes = r.Sum(nil); +// ! note @gbotrel: this is a place holder, may not make sense +func (r *RSis) Hash(v []fr.Element) ([]fr.Element, error) { + if len(v) > r.maxNbElementsToHash { + return nil, fmt.Errorf("can't hash more than %d elements with params provided in constructor", r.maxNbElementsToHash) + } + + r.Reset() + for _, e := range v { + r.Write(e.Marshal()) + } + sum := r.Sum(nil) + var rlen [4]byte + binary.BigEndian.PutUint32(rlen[:], uint32(len(sum)/fr.Bytes)) + reader := io.MultiReader(bytes.NewReader(rlen[:]), bytes.NewReader(sum)) + var result fr.Vector + _, err := result.ReadFrom(reader) + if err != nil { + return nil, err + } + return result, nil +} + +func TestLimbDecompositionFastPath(t *testing.T) { + assert := require.New(t) + + for size := fr.Bytes; size < 5*fr.Bytes; size += fr.Bytes { + // Test the fast path of limbDecomposeBytes8_64 + buf := make([]byte, size) + m := make([]fr.Element, size) + mValues := bitset.New(uint(size)) + n := make([]fr.Element, size) + nValues := bitset.New(uint(size)) + + // Generate a random buffer + rand.Seed(time.Now().UnixNano()) //#nosec G404 weak rng is fine here + _, err := rand.Read(buf) //#nosec G404 weak rng is fine here + assert.NoError(err) + + limbDecomposeBytes8_64(buf, m, mValues) + limbDecomposeBytes(buf, n, 8, 64, nValues) + + for i := 0; i < size; i++ { + assert.Equal(mValues.Test(uint(i)), nValues.Test(uint(i))) + assert.True(m[i].Equal(&n[i])) + } + } + +} + +func TestUnrolledFFT(t *testing.T) { + + var shift fr.Element + shift.SetString("8065159656716812877374967518403273466521432693661810619979959746626482506078") // -> 2^47-th root of unity of bls12377 + e := int64(1 << (47 - (6 + 1))) + shift.Exp(shift, big.NewInt(e)) + + const size = 64 + assert := require.New(t) + domain := fft.NewDomain(size, shift) + + k1 := make([]fr.Element, size) + for i := 0; i < size; i++ { + k1[i].SetRandom() + } + k2 := make([]fr.Element, size) + copy(k2, k1) + + // default FFT + domain.FFT(k1, fft.DIF, fft.OnCoset(), fft.WithNbTasks(1)) + + // unrolled FFT + twiddlesCoset := precomputeTwiddlesCoset(domain.Twiddles, domain.FrMultiplicativeGen) + fft64(k2, twiddlesCoset) + + // compare results + for i := 0; i < size; i++ { + // fmt.Printf("i = %d, k1 = %v, k2 = %v\n", i, k1[i].String(), k2[i].String()) + assert.True(k1[i].Equal(&k2[i]), "i = %d", i) + } +} diff --git a/ecc/bls12-377/fr/sis/test_cases.json b/ecc/bls12-377/fr/sis/test_cases.json new file mode 100644 index 0000000000..4633004f1b --- /dev/null +++ b/ecc/bls12-377/fr/sis/test_cases.json @@ -0,0 +1,117269 @@ +{ + "inputs": [ + [ + "0xb0d83b5acd8557cf6e7ab79c911f85a74defa4ad9b9708f2fbef593effffffc" + ], + [ + "0x1" + ], + [ + "0x2a", + "0x1f40" + ], + [ + "0x1", + "0x2", + "0x0", + "0xb0d83b5acd8557cf6e7ab79c911f85a74defa4ad9b9708f2fbef593effffffe" + ], + [ + "0x1", + "0x0" + ], + [ + "0x0", + "0x1" + ], + [ + "0x0" + ], + [ + "0x0", + "0x0", + "0x0", + "0x0" + ], + [ + "0x0", + "0x0", + "0x1f40", + "0x0" + ], + [], + [ + "0xb9379e134c45b017065a67b369cac3ebef7850de00d365afdd6ac9481f9e730" + ], + [ + "0x26349d648892b5e2e1bd74237151588f6c117cf991cda6797e5297c84975a22", + "0xde84b530873db8172c9b4c71933323b8908b20210b4ebee2da42afe5eb8c23e" + ], + [ + "0x10d0a4cbfa5ff5943b6fa7199e21730221ed0ccd331380f07480c58f020ce401", + 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"0xc75dbff63f4b4b92c76052ed8d851d0254d7c9ef3e02f22ae91f4617092f220", + "0x1217521b740d7c2923de5eab9e0b2618886b25dfa452b94484ae2ee70fc3cd18", + "0x376484fcebc29cb93910bc91be14633bb9875dcf430ebbef70ab45412bf0e28", + "0x86e37e82b1f9b0ecc54ea8e56b1ca217e86e445ff787e8c95d420d2f80ded3e", + "0x97fc5c0617f3229dbdd3f187772294eb885a3ee988e3206ac87118420030087", + "0x23f584a31e3acd83db9c7177864c4024bc77a9c4f077843e79f05343507d475", + "0x1046c8e00fa9e3f5d086e9eedcdab27fbb0c1384a651b4517a1cad33538ce620", + "0xd54356b58e084a59e01192de3382678f5cca7f96c737f860c08449a6e775113", + "0xa0e2dd7a23b244d5fb810f6543aa89e8fe621adbd233eb98035fda2b462f4e5", + "0x52c28d775905d846c808c6157ef8d2638a2465b3ff7845b855d688c992ed6ab", + "0x89e607f273ffde31926370d4efce60497651a87397cec1a548c198194288a63", + "0xbc0e5e73a7cff5a5634d65547377f65d504486653d536fdfd70e8ab3ff64fb3", + "0xfb3e6dedde6024560e638c805e04ff6ee254a7f32ad97bd099e018141b5b228", + "0x5674485864593112530d821e2d78f5d68a1e1d829765288b9844347c3cd16f9" + ] + ] + } + ] +} \ No newline at end of file From 58826d8f3cb2b1d815acd20f7e64add7db31296e Mon Sep 17 00:00:00 2001 From: AlexandreBelling Date: Mon, 4 Dec 2023 15:07:52 +0100 Subject: [PATCH 2/2] update the test-vectors to contain the right values --- ecc/bls12-377/fr/sis/sis.sage | 4 +- ecc/bls12-377/fr/sis/test_cases.json | 160694 ++++++++++++------------ 2 files changed, 80349 insertions(+), 80349 deletions(-) diff --git a/ecc/bls12-377/fr/sis/sis.sage b/ecc/bls12-377/fr/sis/sis.sage index eeecc4d3ce..2de4689be3 100644 --- a/ecc/bls12-377/fr/sis/sis.sage +++ b/ecc/bls12-377/fr/sis/sis.sage @@ -225,10 +225,10 @@ params = [ ] inputs = [ - [Fr(21888242871839275222246405745257275088548364400416034343698204186575808495614)], + [Fr(8444461749428370424248824938781546531375899335154063827935233455917409239037)], [Fr(1)], [Fr(42),Fr(8000)], - [Fr(1),Fr(2), Fr(0),Fr(21888242871839275222246405745257275088548364400416034343698204186575808495616)], + [Fr(1),Fr(2), Fr(0),Fr(8444461749428370424248824938781546531375899335154063827935233455917409239040)], [Fr(1), Fr(0)], [Fr(0), Fr(1)], [Fr(0)], diff --git a/ecc/bls12-377/fr/sis/test_cases.json b/ecc/bls12-377/fr/sis/test_cases.json index 4633004f1b..4d2a45dca6 100644 --- a/ecc/bls12-377/fr/sis/test_cases.json +++ b/ecc/bls12-377/fr/sis/test_cases.json @@ -1,7 +1,7 @@ { "inputs": [ [ - "0xb0d83b5acd8557cf6e7ab79c911f85a74defa4ad9b9708f2fbef593effffffc" + "0x12ab655e9a2ca55660b44d1e5c37b00159aa76fed00000010a117ffffffffffd" ], [ "0x1" @@ -14,7 +14,7 @@ "0x1", "0x2", "0x0", - "0xb0d83b5acd8557cf6e7ab79c911f85a74defa4ad9b9708f2fbef593effffffe" + "0x12ab655e9a2ca55660b44d1e5c37b00159aa76fed00000010a11800000000000" ], [ "0x1", @@ -41,67 +41,67 @@ ], [], [ - "0xb9379e134c45b017065a67b369cac3ebef7850de00d365afdd6ac9481f9e730" + "0xffce5e50681376dae465b351bffd139699af26a3d8a64b41a23f4d1a5e026e8" ], [ - "0x26349d648892b5e2e1bd74237151588f6c117cf991cda6797e5297c84975a22", - 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"0x935735485749453a781f8d825cfd9824373373f5b372c7a70f717259fad3302", + "0x126e2f109a930f024194111b74caccaad73e7ff23e3a98932129a2f1eb7bad88", + "0x4e9c4dcf01e0099821bb6e5195c585f03447ca5f5bffce2d366dcbe1a55eee5", + "0xe87c5f1086f21f6a21c2a050d42a8ad4628ce37c0a7bbcc80ff010894a82c2b", + "0xa48d46dead84343c64cdfb869c74bf17d25a9d5b1c5ee883cfb9dad95b741f8", + "0xab433390aeb2f9951323951e94b3b3921d7ea210fb50ba14480519d049f695b", + "0xd9d170b136a3b7db6fd8966a76e314a30602d4843065767ec7430bb76ecdb15", + "0x6647e3858e361fddbfe5cbd6aef6d3c39ad5d101b66fcd9b6870da8a87c2903", + "0x6bfac249ba2915efb1c3154d5544db551c499a4d9dcce645b3ac07dbb630a80", + "0xeaa6afd27a6e176e48a55dce956e342d619df6799ac0536c52090a8ca372ac0", + "0xaff749f16632cb24eb133bb6d33eb8cb5a0af7124ded1d3ca0d2a15a6888f09", + "0x99ec86011d6aa23ca1a52e2b1a42b9070e67982d0b08ce7c1e3cd408e7818e1", + "0xc99c3db973d8bd135fd9a8238cd5e2064ac21aeaca51349db73f1b3841240c", + "0x11c86afbac1b4621366cb175404bc20a6751ff7591b7780037e55f1fe7af2775", + 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"0x2c6e3dceb94eb71dbb7a6aa5e25de69685ff78abc980da00a23cc52483082cf" ] ] }, @@ -51693,4102 +51693,4102 @@ }, "expected": [ [ - "0x1247d128549cbd28225d2a8ef1a12e205d5f1bbe6f26938c8aea336d5dd6acd6", - "0x1028e3c86008543a32b01b3886933ea107f4ddc1199e1f4af415439231ae7fe", - "0x129e82f9619a65f85a1459e40ec6a4524d948d498b479611f7892ae33c3552d3", - "0xaf4562b669955ee597c2840947fb6ec49fb8fae032576471be1432e1db11db4", - "0xb9276f7a5d9ce8ff95869709ecd4725bdf34d43a67452091d129e794d829966", - "0x74313f4abda07fb1a2a7c7f612fabee9a11c676dc4cf2be1df68a6e11e0f2cc", - "0x129d7c40091a5ff4d4fe901d6e905b8567906fda79c58983f1c37b039e08b876", - "0x113156db5615ac0389f81e17c8f412078ea1463dc9f903834c54f9024e25fe05", - "0xe6155918d88a9643a4fe53bd2047be187b79c2dba597a14351ca50343a0af71", - "0x32510fed34d90f07b66de3f9a3610ab87316f2c1934038f4d46288ec7068be8", - "0xb45662638c1c0ad3d83a8a562afe7878ced0a595d7fd88521e3b279e3900686", - "0xbc7a240ce68fcabe91c586c21c55123f1a7da0d4cc5356ef4cb52fa8c24941a", - 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