From 7ef61c9ebb8a40c86e8cb16bedbc3054e43930e3 Mon Sep 17 00:00:00 2001
From: Gautam Botrel <gautam.botrel@gmail.com>
Date: Fri, 15 Dec 2023 13:24:13 -0600
Subject: [PATCH] fix: sis doesn't use twiddles directly no more

---
 ecc/bls12-377/fr/sis/sis.go                 |   4 +-
 ecc/bls12-377/fr/sis/sis_fft.go             | 225 +++++++++++++-------
 ecc/bls12-377/fr/sis/sis_test.go            |   6 +-
 ecc/bn254/fr/sis/sis.go                     |   2 +-
 ecc/bn254/fr/sis/sis_fft.go                 | 225 +++++++++++++-------
 ecc/bn254/fr/sis/sis_test.go                |   2 +-
 internal/generator/main.go                  |   2 +-
 internal/generator/sis/template/fft.go.tmpl |  36 ++--
 8 files changed, 326 insertions(+), 176 deletions(-)

diff --git a/ecc/bls12-377/fr/sis/sis.go b/ecc/bls12-377/fr/sis/sis.go
index 164dc1a0e1..1279c8145b 100644
--- a/ecc/bls12-377/fr/sis/sis.go
+++ b/ecc/bls12-377/fr/sis/sis.go
@@ -119,7 +119,7 @@ func NewRSis(seed int64, logTwoDegree, logTwoBound, maxNbElementsToHash int) (*R
 		LogTwoBound:         logTwoBound,
 		capacity:            capacity,
 		Degree:              degree,
-		Domain:              fft.NewDomain(uint64(degree), shift),
+		Domain:              fft.NewDomain(uint64(degree), fft.WithShift(shift)),
 		A:                   make([][]fr.Element, n),
 		Ag:                  make([][]fr.Element, n),
 		bufM:                make(fr.Vector, degree*n),
@@ -129,7 +129,7 @@ func NewRSis(seed int64, logTwoDegree, logTwoBound, maxNbElementsToHash int) (*R
 	}
 	if r.LogTwoBound == 8 && r.Degree == 64 {
 		// TODO @gbotrel fixme, that's dirty.
-		r.twiddleCosets = precomputeTwiddlesCoset(r.Domain.Twiddles, r.Domain.FrMultiplicativeGen)
+		r.twiddleCosets = precomputeTwiddlesCoset(r.Domain.Generator, r.Domain.FrMultiplicativeGen)
 	}
 
 	// filling A
diff --git a/ecc/bls12-377/fr/sis/sis_fft.go b/ecc/bls12-377/fr/sis/sis_fft.go
index 891b7e677b..ae351d5ec1 100644
--- a/ecc/bls12-377/fr/sis/sis_fft.go
+++ b/ecc/bls12-377/fr/sis/sis_fft.go
@@ -18,6 +18,7 @@ package sis
 
 import (
 	"github.com/consensys/gnark-crypto/ecc/bls12-377/fr"
+	"math/big"
 )
 
 // fft64 is generated by gnark-crypto and contains the unrolled code for FFT (DIF) on 64 elements
@@ -413,82 +414,154 @@ func fft64(a []fr.Element, twiddlesCoset []fr.Element) {
 
 // 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)
+func precomputeTwiddlesCoset(generator, shifter fr.Element) []fr.Element {
+	toReturn := make([]fr.Element, 63)
+	var r, s fr.Element
+	e := new(big.Int)
 
-	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])
+	s = shifter
+	for k := 0; k < 5; k++ {
+		s.Square(&s)
+	}
+	toReturn[0] = s
+	s = shifter
+	for k := 0; k < 4; k++ {
+		s.Square(&s)
+	}
+	toReturn[1] = s
+	r.Exp(generator, e.SetUint64(uint64(1<<4*1)))
+	toReturn[2].Mul(&r, &s)
+	s = shifter
+	for k := 0; k < 3; k++ {
+		s.Square(&s)
+	}
+	toReturn[3] = s
+	r.Exp(generator, e.SetUint64(uint64(1<<3*2)))
+	toReturn[4].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<3*1)))
+	toReturn[5].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<3*3)))
+	toReturn[6].Mul(&r, &s)
+	s = shifter
+	for k := 0; k < 2; k++ {
+		s.Square(&s)
+	}
+	toReturn[7] = s
+	r.Exp(generator, e.SetUint64(uint64(1<<2*4)))
+	toReturn[8].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<2*2)))
+	toReturn[9].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<2*6)))
+	toReturn[10].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<2*1)))
+	toReturn[11].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<2*5)))
+	toReturn[12].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<2*3)))
+	toReturn[13].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<2*7)))
+	toReturn[14].Mul(&r, &s)
+	s = shifter
+	for k := 0; k < 1; k++ {
+		s.Square(&s)
+	}
+	toReturn[15] = s
+	r.Exp(generator, e.SetUint64(uint64(1<<1*8)))
+	toReturn[16].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<1*4)))
+	toReturn[17].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<1*12)))
+	toReturn[18].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<1*2)))
+	toReturn[19].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<1*10)))
+	toReturn[20].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<1*6)))
+	toReturn[21].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<1*14)))
+	toReturn[22].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<1*1)))
+	toReturn[23].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<1*9)))
+	toReturn[24].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<1*5)))
+	toReturn[25].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<1*13)))
+	toReturn[26].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<1*3)))
+	toReturn[27].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<1*11)))
+	toReturn[28].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<1*7)))
+	toReturn[29].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<1*15)))
+	toReturn[30].Mul(&r, &s)
+	s = shifter
+	for k := 0; k < 0; k++ {
+		s.Square(&s)
+	}
+	toReturn[31] = s
+	r.Exp(generator, e.SetUint64(uint64(1<<0*16)))
+	toReturn[32].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*8)))
+	toReturn[33].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*24)))
+	toReturn[34].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*4)))
+	toReturn[35].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*20)))
+	toReturn[36].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*12)))
+	toReturn[37].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*28)))
+	toReturn[38].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*2)))
+	toReturn[39].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*18)))
+	toReturn[40].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*10)))
+	toReturn[41].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*26)))
+	toReturn[42].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*6)))
+	toReturn[43].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*22)))
+	toReturn[44].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*14)))
+	toReturn[45].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*30)))
+	toReturn[46].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*1)))
+	toReturn[47].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*17)))
+	toReturn[48].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*9)))
+	toReturn[49].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*25)))
+	toReturn[50].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*5)))
+	toReturn[51].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*21)))
+	toReturn[52].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*13)))
+	toReturn[53].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*29)))
+	toReturn[54].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*3)))
+	toReturn[55].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*19)))
+	toReturn[56].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*11)))
+	toReturn[57].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*27)))
+	toReturn[58].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*7)))
+	toReturn[59].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*23)))
+	toReturn[60].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*15)))
+	toReturn[61].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*31)))
+	toReturn[62].Mul(&r, &s)
 	return toReturn
 }
diff --git a/ecc/bls12-377/fr/sis/sis_test.go b/ecc/bls12-377/fr/sis/sis_test.go
index ddccf9222d..e15626f8e1 100644
--- a/ecc/bls12-377/fr/sis/sis_test.go
+++ b/ecc/bls12-377/fr/sis/sis_test.go
@@ -142,7 +142,7 @@ func TestMulMod(t *testing.T) {
 	// and random.
 	var shift fr.Element
 	shift.SetString("19540430494807482326159819597004422086093766032135589407132600596362845576832")
-	domain := fft.NewDomain(uint64(size), shift)
+	domain := fft.NewDomain(uint64(size), fft.WithShift(shift))
 
 	// mul mod
 	domain.FFT(p, fft.DIF, fft.OnCoset())
@@ -415,7 +415,7 @@ func TestUnrolledFFT(t *testing.T) {
 
 	const size = 64
 	assert := require.New(t)
-	domain := fft.NewDomain(size, shift)
+	domain := fft.NewDomain(size, fft.WithShift(shift))
 
 	k1 := make([]fr.Element, size)
 	for i := 0; i < size; i++ {
@@ -428,7 +428,7 @@ func TestUnrolledFFT(t *testing.T) {
 	domain.FFT(k1, fft.DIF, fft.OnCoset(), fft.WithNbTasks(1))
 
 	// unrolled FFT
-	twiddlesCoset := precomputeTwiddlesCoset(domain.Twiddles, domain.FrMultiplicativeGen)
+	twiddlesCoset := precomputeTwiddlesCoset(domain.Generator, domain.FrMultiplicativeGen)
 	fft64(k2, twiddlesCoset)
 
 	// compare results
diff --git a/ecc/bn254/fr/sis/sis.go b/ecc/bn254/fr/sis/sis.go
index 6ffdc5e999..dce215b141 100644
--- a/ecc/bn254/fr/sis/sis.go
+++ b/ecc/bn254/fr/sis/sis.go
@@ -129,7 +129,7 @@ func NewRSis(seed int64, logTwoDegree, logTwoBound, maxNbElementsToHash int) (*R
 	}
 	if r.LogTwoBound == 8 && r.Degree == 64 {
 		// TODO @gbotrel fixme, that's dirty.
-		r.twiddleCosets = precomputeTwiddlesCoset(r.Domain.Twiddles, r.Domain.FrMultiplicativeGen)
+		r.twiddleCosets = precomputeTwiddlesCoset(r.Domain.Generator, r.Domain.FrMultiplicativeGen)
 	}
 
 	// filling A
diff --git a/ecc/bn254/fr/sis/sis_fft.go b/ecc/bn254/fr/sis/sis_fft.go
index 336805ebe3..70b4d32d9d 100644
--- a/ecc/bn254/fr/sis/sis_fft.go
+++ b/ecc/bn254/fr/sis/sis_fft.go
@@ -18,6 +18,7 @@ package sis
 
 import (
 	"github.com/consensys/gnark-crypto/ecc/bn254/fr"
+	"math/big"
 )
 
 // fft64 is generated by gnark-crypto and contains the unrolled code for FFT (DIF) on 64 elements
@@ -413,82 +414,154 @@ func fft64(a []fr.Element, twiddlesCoset []fr.Element) {
 
 // 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)
+func precomputeTwiddlesCoset(generator, shifter fr.Element) []fr.Element {
+	toReturn := make([]fr.Element, 63)
+	var r, s fr.Element
+	e := new(big.Int)
 
-	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])
+	s = shifter
+	for k := 0; k < 5; k++ {
+		s.Square(&s)
+	}
+	toReturn[0] = s
+	s = shifter
+	for k := 0; k < 4; k++ {
+		s.Square(&s)
+	}
+	toReturn[1] = s
+	r.Exp(generator, e.SetUint64(uint64(1<<4*1)))
+	toReturn[2].Mul(&r, &s)
+	s = shifter
+	for k := 0; k < 3; k++ {
+		s.Square(&s)
+	}
+	toReturn[3] = s
+	r.Exp(generator, e.SetUint64(uint64(1<<3*2)))
+	toReturn[4].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<3*1)))
+	toReturn[5].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<3*3)))
+	toReturn[6].Mul(&r, &s)
+	s = shifter
+	for k := 0; k < 2; k++ {
+		s.Square(&s)
+	}
+	toReturn[7] = s
+	r.Exp(generator, e.SetUint64(uint64(1<<2*4)))
+	toReturn[8].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<2*2)))
+	toReturn[9].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<2*6)))
+	toReturn[10].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<2*1)))
+	toReturn[11].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<2*5)))
+	toReturn[12].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<2*3)))
+	toReturn[13].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<2*7)))
+	toReturn[14].Mul(&r, &s)
+	s = shifter
+	for k := 0; k < 1; k++ {
+		s.Square(&s)
+	}
+	toReturn[15] = s
+	r.Exp(generator, e.SetUint64(uint64(1<<1*8)))
+	toReturn[16].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<1*4)))
+	toReturn[17].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<1*12)))
+	toReturn[18].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<1*2)))
+	toReturn[19].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<1*10)))
+	toReturn[20].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<1*6)))
+	toReturn[21].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<1*14)))
+	toReturn[22].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<1*1)))
+	toReturn[23].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<1*9)))
+	toReturn[24].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<1*5)))
+	toReturn[25].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<1*13)))
+	toReturn[26].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<1*3)))
+	toReturn[27].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<1*11)))
+	toReturn[28].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<1*7)))
+	toReturn[29].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<1*15)))
+	toReturn[30].Mul(&r, &s)
+	s = shifter
+	for k := 0; k < 0; k++ {
+		s.Square(&s)
+	}
+	toReturn[31] = s
+	r.Exp(generator, e.SetUint64(uint64(1<<0*16)))
+	toReturn[32].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*8)))
+	toReturn[33].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*24)))
+	toReturn[34].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*4)))
+	toReturn[35].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*20)))
+	toReturn[36].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*12)))
+	toReturn[37].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*28)))
+	toReturn[38].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*2)))
+	toReturn[39].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*18)))
+	toReturn[40].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*10)))
+	toReturn[41].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*26)))
+	toReturn[42].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*6)))
+	toReturn[43].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*22)))
+	toReturn[44].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*14)))
+	toReturn[45].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*30)))
+	toReturn[46].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*1)))
+	toReturn[47].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*17)))
+	toReturn[48].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*9)))
+	toReturn[49].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*25)))
+	toReturn[50].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*5)))
+	toReturn[51].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*21)))
+	toReturn[52].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*13)))
+	toReturn[53].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*29)))
+	toReturn[54].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*3)))
+	toReturn[55].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*19)))
+	toReturn[56].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*11)))
+	toReturn[57].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*27)))
+	toReturn[58].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*7)))
+	toReturn[59].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*23)))
+	toReturn[60].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*15)))
+	toReturn[61].Mul(&r, &s)
+	r.Exp(generator, e.SetUint64(uint64(1<<0*31)))
+	toReturn[62].Mul(&r, &s)
 	return toReturn
 }
diff --git a/ecc/bn254/fr/sis/sis_test.go b/ecc/bn254/fr/sis/sis_test.go
index 9cbba969e8..cde678d214 100644
--- a/ecc/bn254/fr/sis/sis_test.go
+++ b/ecc/bn254/fr/sis/sis_test.go
@@ -427,7 +427,7 @@ func TestUnrolledFFT(t *testing.T) {
 	domain.FFT(k1, fft.DIF, fft.OnCoset(), fft.WithNbTasks(1))
 
 	// unrolled FFT
-	twiddlesCoset := precomputeTwiddlesCoset(domain.Twiddles, domain.FrMultiplicativeGen)
+	twiddlesCoset := precomputeTwiddlesCoset(domain.Generator, domain.FrMultiplicativeGen)
 	fft64(k2, twiddlesCoset)
 
 	// compare results
diff --git a/internal/generator/main.go b/internal/generator/main.go
index 3c9903b8a2..389f96c2e0 100644
--- a/internal/generator/main.go
+++ b/internal/generator/main.go
@@ -92,7 +92,7 @@ func main() {
 			// generate fft on fr
 			assertNoError(fft.Generate(conf, filepath.Join(curveDir, "fr", "fft"), bgen))
 
-			if conf.Equal(config.BN254) {
+			if conf.Equal(config.BN254) || conf.Equal(config.BLS12_377) {
 				assertNoError(sis.Generate(conf, filepath.Join(curveDir, "fr", "sis"), bgen))
 			}
 
diff --git a/internal/generator/sis/template/fft.go.tmpl b/internal/generator/sis/template/fft.go.tmpl
index 36cdace6ce..91938f81d0 100644
--- a/internal/generator/sis/template/fft.go.tmpl
+++ b/internal/generator/sis/template/fft.go.tmpl
@@ -1,5 +1,6 @@
 import (
-	"github.com/consensys/gnark-crypto/ecc/bn254/fr"
+	"github.com/consensys/gnark-crypto/ecc/{{ .Name }}/fr"
+	"math/big"
 )
 
 // fft64 is generated by gnark-crypto and contains the unrolled code for FFT (DIF) on 64 elements
@@ -48,28 +49,31 @@ func fft64(a []fr.Element,  twiddlesCoset []fr.Element) {
 
 // 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)
+func precomputeTwiddlesCoset(generator, shifter fr.Element) []fr.Element {
+	toReturn := make([]fr.Element,  63)
+	var r, s fr.Element
+	e := new(big.Int)
 	{{ $n := 64}}
 	{{ $m := div $n 2}}
 	{{ $split := 1}}
 	{{ $split = div $split 1}}
+	{{ $j := 0}}
 	{{- range $step := reverse (iterate 0 6)}} 
-
+		s = shifter
+		for k:=0; k <{{$step}};k++ {
+			s.Square(&s)
+		}
+		
 		{{- $offset := 0}}
 		{{- range $s := iterate 0 $split}}
-			toReturn = append(toReturn, r[{{$step}}][{{bitReverse $split $s}}])
+			{{- $exp := bitReverse $split $s}}
+			{{- if eq $exp 0}}
+				toReturn[{{$j}}] = s
+			{{- else}}
+				r.Exp(generator, e.SetUint64(uint64(1<<{{$step}} * {{$exp}})))
+				toReturn[{{$j}}].Mul(&r, &s)
+			{{- end}}
+			{{- $j = add $j 1}}
 		{{- end}}
 
 		{{- $split = mul $split 2}}