Fixing tests in #64

.github/workflows/tests.yml

@@ -16,12 +16,12 @@ jobs:
     runs-on: ubuntu-latest
     steps:
       - name: Checkout
-        uses: actions/checkout@v2
+        uses: actions/checkout@v5
 
       - name: Install Go
-        uses: actions/setup-go@v2
+        uses: actions/setup-go@v6
         with:
-          go-version: '1.18'
+          go-version: '1.25'
 
       - name: Run tests
         run: make test

Makefile

@@ -2,8 +2,8 @@
 
 .PHONY: fetch-dependencies
 fetch-dependencies:
-	go get -v -t -d ./...
+	go get -v -t ./...
 
 .PHONY: test
 test: fetch-dependencies
-	go test -v ./...
+	go test -race -v ./...

README.md

@@ -37,7 +37,7 @@ main package is.
 Installing
 ----------
 
-First make sure you have [Go](https://golang.org) version 1.11 or newer installed.
+First make sure you have [Go](https://golang.org) version 1.24 or newer installed.
 
 The basic crypto library requires only Go and a few
 third-party Go-language dependencies that can be installed automatically
@@ -47,7 +47,7 @@ as follows:
 
 You can recursively test all the packages in the library as follows:
 
-	go test -v ./...
+	go test -race -v ./...
 
 A note on deriving shared secrets
 ---------------------------------

encrypt/ibe/ibe.go

@@ -6,6 +6,7 @@ import (
 	"encoding/binary"
 	"errors"
 	"fmt"
+
 	"github.com/drand/kyber"
 	"github.com/drand/kyber/group/mod"
 	"github.com/drand/kyber/pairing"
@@ -70,7 +71,7 @@ func EncryptCCAonG1(s pairing.Suite, master kyber.Point, ID, msg []byte) (*Ciphe
 		return nil, err
 	}
 	// 4. Compute U = rP
-	U := s.G1().Point().Mul(r, s.G1().Point().Base())
+	U := s.G1().Point().Mul(r, nil)
 
 	// 5. Compute V = sigma XOR H2(rGid)
 	rGid := Gid.Mul(r, Gid) // even in Gt, it's additive notation
@@ -124,7 +125,7 @@ func DecryptCCAonG1(s pairing.Suite, private kyber.Point, c *Ciphertext) ([]byte
 	if err != nil {
 		return nil, err
 	}
-	rP := s.G1().Point().Mul(r, s.G1().Point().Base())
+	rP := s.G1().Point().Mul(r, nil)
 	if !rP.Equal(c.U) {
 		return nil, fmt.Errorf("invalid proof: rP check failed")
 	}
@@ -165,7 +166,7 @@ func EncryptCCAonG2(s pairing.Suite, master kyber.Point, ID, msg []byte) (*Ciphe
 		return nil, err
 	}
 	// 4. Compute U = rP
-	U := s.G2().Point().Mul(r, s.G2().Point().Base())
+	U := s.G2().Point().Mul(r, nil)
 
 	// 5. Compute V = sigma XOR H2(rGid)
 	rGid := Gid.Mul(r, Gid) // even in Gt, it's additive notation
@@ -219,9 +220,9 @@ func DecryptCCAonG2(s pairing.Suite, private kyber.Point, c *Ciphertext) ([]byte
 	if err != nil {
 		return nil, err
 	}
-	rP := s.G2().Point().Mul(r, s.G2().Point().Base())
+	rP := s.G2().Point().Mul(r, nil)
 	if !rP.Equal(c.U) {
-		return nil, fmt.Errorf("invalid proof: rP check failed")
+		return nil, fmt.Errorf("invalid proof: rP check failed on msg %s, r %x", msg, r)
 	}
 	return msg, nil
 }
@@ -230,6 +231,10 @@ func DecryptCCAonG2(s pairing.Suite, private kyber.Point, c *Ciphertext) ([]byte
 func h3(s pairing.Suite, sigma, msg []byte) (kyber.Scalar, error) {
 	h := s.Hash()
 
+	if h.Size() != s.G1().ScalarLen() {
+		return nil, fmt.Errorf("hash size mismatch with scalar length %d != %d", h.Size(), s.G1().ScalarLen())
+	}
+
 	if _, err := h.Write(H3Tag()); err != nil {
 		return nil, fmt.Errorf("err hashing h3 tag: %v", err)
 	}
@@ -339,13 +344,15 @@ type CiphertextCPA struct {
 // H1: {0,1}^n -> G1
 // H2: GT -> {0,1}^n
 // ID: Qid = H1(ID) = xP \in G2
-// 	secret did = s*Qid \in G2
+//
+//	secret did = s*Qid \in G2
+//
 // Encrypt:
-// - random r scalar
-// - Gid = e(Ppub, r*Qid) == e(P, P)^(x*s*r) \in GT
-// 		 = GidT
-// - U = rP \in G1,
-// - V = M XOR H2(Gid)) = M XOR H2(GidT)  \in {0,1}^n
+//   - random r scalar
+//   - Gid = e(Ppub, r*Qid) == e(P, P)^(x*s*r) \in GT
+//     = GidT
+//   - U = rP \in G1,
+//   - V = M XOR H2(Gid)) = M XOR H2(GidT)  \in {0,1}^n
 func EncryptCPAonG1(s pairing.Suite, basePoint, public kyber.Point, ID, msg []byte) (*CiphertextCPA, error) {
 	if len(msg)>>16 > 0 {
 		// we're using blake2 as XOF which only outputs 2^16-1 length
@@ -382,9 +389,9 @@ func EncryptCPAonG1(s pairing.Suite, basePoint, public kyber.Point, ID, msg []by
 // SigGroup = G2 (large secret identities)
 // KeyGroup = G1 (short master public keys)
 // Decrypt:
-// - V XOR H2(e(U, did)) = V XOR H2(e(rP, s*Qid))
-//   = V XOR H2(e(P, P)^(r*s*x))
-//   = V XOR H2(GidT) = M
+//   - V XOR H2(e(U, did)) = V XOR H2(e(rP, s*Qid))
+//     = V XOR H2(e(P, P)^(r*s*x))
+//     = V XOR H2(GidT) = M
 func DecryptCPAonG1(s pairing.Suite, private kyber.Point, c *CiphertextCPA) ([]byte, error) {
 	GidT := s.Pair(c.RP, private)
 	hGidT, err := gtToHash(s, GidT, len(c.C))

go.mod

@@ -1,28 +1,25 @@
 module github.com/drand/kyber
 
-go 1.18
+go 1.24.0
 
 require (
-	github.com/cloudflare/circl v1.3.7
-	github.com/consensys/gnark-crypto v0.12.1
-	github.com/drand/kyber-bls12381 v0.3.1
-	github.com/jonboulle/clockwork v0.4.0
-	github.com/stretchr/testify v1.9.0
+	github.com/cloudflare/circl v1.6.1
+	github.com/consensys/gnark-crypto v0.19.2
+	github.com/drand/kyber-bls12381 v0.3.3
+	github.com/jonboulle/clockwork v0.5.0
+	github.com/stretchr/testify v1.11.1
 	go.dedis.ch/fixbuf v1.0.3
 	go.dedis.ch/protobuf v1.0.11
-	golang.org/x/crypto v0.21.0
-	golang.org/x/sys v0.18.0
+	golang.org/x/crypto v0.43.0
 )
 
 require (
-	github.com/bits-and-blooms/bitset v1.13.0 // indirect
-	github.com/consensys/bavard v0.1.13 // indirect
+	github.com/bits-and-blooms/bitset v1.24.3 // indirect
 	github.com/davecgh/go-spew v1.1.1 // indirect
 	github.com/kilic/bls12-381 v0.1.0 // indirect
 	github.com/kr/text v0.2.0 // indirect
-	github.com/mmcloughlin/addchain v0.4.0 // indirect
 	github.com/pmezard/go-difflib v1.0.0 // indirect
-	github.com/rogpeppe/go-internal v1.9.0 // indirect
+	github.com/rogpeppe/go-internal v1.14.1 // indirect
+	golang.org/x/sys v0.38.0 // indirect
 	gopkg.in/yaml.v3 v3.0.1 // indirect
-	rsc.io/tmplfunc v0.0.3 // indirect
 )

go.sum

@@ -1,37 +1,37 @@
-github.com/bits-and-blooms/bitset v1.13.0 h1:bAQ9OPNFYbGHV6Nez0tmNI0RiEu7/hxlYJRUA0wFAVE=
-github.com/bits-and-blooms/bitset v1.13.0/go.mod h1:7hO7Gc7Pp1vODcmWvKMRA9BNmbv6a/7QIWpPxHddWR8=
-github.com/cloudflare/circl v1.3.7 h1:qlCDlTPz2n9fu58M0Nh1J/JzcFpfgkFHHX3O35r5vcU=
-github.com/cloudflare/circl v1.3.7/go.mod h1:sRTcRWXGLrKw6yIGJ+l7amYJFfAXbZG0kBSc8r4zxgA=
-github.com/consensys/bavard v0.1.13 h1:oLhMLOFGTLdlda/kma4VOJazblc7IM5y5QPd2A/YjhQ=
-github.com/consensys/bavard v0.1.13/go.mod h1:9ItSMtA/dXMAiL7BG6bqW2m3NdSEObYWoH223nGHukI=
-github.com/consensys/gnark-crypto v0.12.1 h1:lHH39WuuFgVHONRl3J0LRBtuYdQTumFSDtJF7HpyG8M=
-github.com/consensys/gnark-crypto v0.12.1/go.mod h1:v2Gy7L/4ZRosZ7Ivs+9SfUDr0f5UlG+EM5t7MPHiLuY=
+github.com/bits-and-blooms/bitset v1.24.2 h1:M7/NzVbsytmtfHbumG+K2bremQPMJuqv1JD3vOaFxp0=
+github.com/bits-and-blooms/bitset v1.24.2/go.mod h1:7hO7Gc7Pp1vODcmWvKMRA9BNmbv6a/7QIWpPxHddWR8=
+github.com/bits-and-blooms/bitset v1.24.3 h1:Bte86SlO3lwPQqww+7BE9ZuUCKIjfqnG5jtEyqA9y9Y=
+github.com/bits-and-blooms/bitset v1.24.3/go.mod h1:7hO7Gc7Pp1vODcmWvKMRA9BNmbv6a/7QIWpPxHddWR8=
+github.com/cloudflare/circl v1.6.1 h1:zqIqSPIndyBh1bjLVVDHMPpVKqp8Su/V+6MeDzzQBQ0=
+github.com/cloudflare/circl v1.6.1/go.mod h1:uddAzsPgqdMAYatqJ0lsjX1oECcQLIlRpzZh3pJrofs=
+github.com/consensys/gnark-crypto v0.19.0 h1:zXCqeY2txSaMl6G5wFpZzMWJU9HPNh8qxPnYJ1BL9vA=
+github.com/consensys/gnark-crypto v0.19.0/go.mod h1:rT23F0XSZqE0mUA0+pRtnL56IbPxs6gp4CeRsBk4XS0=
+github.com/consensys/gnark-crypto v0.19.2 h1:qrEAIXq3T4egxqiliFFoNrepkIWVEeIYwt3UL0fvS80=
+github.com/consensys/gnark-crypto v0.19.2/go.mod h1:rT23F0XSZqE0mUA0+pRtnL56IbPxs6gp4CeRsBk4XS0=
 github.com/creack/pty v1.1.9/go.mod h1:oKZEueFk5CKHvIhNR5MUki03XCEU+Q6VDXinZuGJ33E=
 github.com/davecgh/go-spew v1.1.0/go.mod h1:J7Y8YcW2NihsgmVo/mv3lAwl/skON4iLHjSsI+c5H38=
 github.com/davecgh/go-spew v1.1.1 h1:vj9j/u1bqnvCEfJOwUhtlOARqs3+rkHYY13jYWTU97c=
 github.com/davecgh/go-spew v1.1.1/go.mod h1:J7Y8YcW2NihsgmVo/mv3lAwl/skON4iLHjSsI+c5H38=
-github.com/drand/kyber-bls12381 v0.3.1 h1:KWb8l/zYTP5yrvKTgvhOrk2eNPscbMiUOIeWBnmUxGo=
-github.com/drand/kyber-bls12381 v0.3.1/go.mod h1:H4y9bLPu7KZA/1efDg+jtJ7emKx+ro3PU7/jWUVt140=
-github.com/google/subcommands v1.2.0/go.mod h1:ZjhPrFU+Olkh9WazFPsl27BQ4UPiG37m3yTrtFlrHVk=
-github.com/jonboulle/clockwork v0.4.0 h1:p4Cf1aMWXnXAUh8lVfewRBx1zaTSYKrKMF2g3ST4RZ4=
-github.com/jonboulle/clockwork v0.4.0/go.mod h1:xgRqUGwRcjKCO1vbZUEtSLrqKoPSsUpK7fnezOII0kc=
+github.com/drand/kyber-bls12381 v0.3.3 h1:sLl0ILJtB4+POHAKq6tdnWyg+iXADE0LjVKN91RI8JI=
+github.com/drand/kyber-bls12381 v0.3.3/go.mod h1:uVRWtcZDAApOWFMwoJVcTfC4csVxXmpkdoSCUZJ5QOY=
+github.com/jonboulle/clockwork v0.5.0 h1:Hyh9A8u51kptdkR+cqRpT1EebBwTn1oK9YfGYbdFz6I=
+github.com/jonboulle/clockwork v0.5.0/go.mod h1:3mZlmanh0g2NDKO5TWZVJAfofYk64M7XN3SzBPjZF60=
 github.com/kilic/bls12-381 v0.1.0 h1:encrdjqKMEvabVQ7qYOKu1OvhqpK4s47wDYtNiPtlp4=
 github.com/kilic/bls12-381 v0.1.0/go.mod h1:vDTTHJONJ6G+P2R74EhnyotQDTliQDnFEwhdmfzw1ig=
 github.com/kr/pretty v0.3.1 h1:flRD4NNwYAUpkphVc1HcthR4KEIFJ65n8Mw5qdRn3LE=
+github.com/kr/pretty v0.3.1/go.mod h1:hoEshYVHaxMs3cyo3Yncou5ZscifuDolrwPKZanG3xk=
 github.com/kr/text v0.2.0 h1:5Nx0Ya0ZqY2ygV366QzturHI13Jq95ApcVaJBhpS+AY=
 github.com/kr/text v0.2.0/go.mod h1:eLer722TekiGuMkidMxC/pM04lWEeraHUUmBw8l2grE=
-github.com/leanovate/gopter v0.2.9 h1:fQjYxZaynp97ozCzfOyOuAGOU4aU/z37zf/tOujFk7c=
-github.com/mmcloughlin/addchain v0.4.0 h1:SobOdjm2xLj1KkXN5/n0xTIWyZA2+s99UCY1iPfkHRY=
-github.com/mmcloughlin/addchain v0.4.0/go.mod h1:A86O+tHqZLMNO4w6ZZ4FlVQEadcoqkyU72HC5wJ4RlU=
-github.com/mmcloughlin/profile v0.1.1/go.mod h1:IhHD7q1ooxgwTgjxQYkACGA77oFTDdFVejUS1/tS/qU=
+github.com/leanovate/gopter v0.2.11 h1:vRjThO1EKPb/1NsDXuDrzldR28RLkBflWYcU9CvzWu4=
+github.com/leanovate/gopter v0.2.11/go.mod h1:aK3tzZP/C+p1m3SPRE4SYZFGP7jjkuSI4f7Xvpt0S9c=
 github.com/pmezard/go-difflib v1.0.0 h1:4DBwDE0NGyQoBHbLQYPwSUPoCMWR5BEzIk/f1lZbAQM=
 github.com/pmezard/go-difflib v1.0.0/go.mod h1:iKH77koFhYxTK1pcRnkKkqfTogsbg7gZNVY4sRDYZ/4=
-github.com/rogpeppe/go-internal v1.9.0 h1:73kH8U+JUqXU8lRuOHeVHaa/SZPifC7BkcraZVejAe8=
-github.com/rogpeppe/go-internal v1.9.0/go.mod h1:WtVeX8xhTBvf0smdhujwtBcq4Qrzq/fJaraNFVN+nFs=
+github.com/rogpeppe/go-internal v1.14.1 h1:UQB4HGPB6osV0SQTLymcB4TgvyWu6ZyliaW0tI/otEQ=
+github.com/rogpeppe/go-internal v1.14.1/go.mod h1:MaRKkUm5W0goXpeCfT7UZI6fk/L7L7so1lCWt35ZSgc=
 github.com/stretchr/objx v0.1.0/go.mod h1:HFkY916IF+rwdDfMAkV7OtwuqBVzrE8GR6GFx+wExME=
 github.com/stretchr/testify v1.3.0/go.mod h1:M5WIy9Dh21IEIfnGCwXGc5bZfKNJtfHm1UVUgZn+9EI=
-github.com/stretchr/testify v1.9.0 h1:HtqpIVDClZ4nwg75+f6Lvsy/wHu+3BoSGCbBAcpTsTg=
-github.com/stretchr/testify v1.9.0/go.mod h1:r2ic/lqez/lEtzL7wO/rwa5dbSLXVDPFyf8C91i36aY=
+github.com/stretchr/testify v1.11.1 h1:7s2iGBzp5EwR7/aIZr8ao5+dra3wiQyKjjFuvgVKu7U=
+github.com/stretchr/testify v1.11.1/go.mod h1:wZwfW3scLgRK+23gO65QZefKpKQRnfz6sD981Nm4B6U=
 go.dedis.ch/fixbuf v1.0.3 h1:hGcV9Cd/znUxlusJ64eAlExS+5cJDIyTyEG+otu5wQs=
 go.dedis.ch/fixbuf v1.0.3/go.mod h1:yzJMt34Wa5xD37V5RTdmp38cz3QhMagdGoem9anUalw=
 go.dedis.ch/kyber/v3 v3.0.4/go.mod h1:OzvaEnPvKlyrWyp3kGXlFdp7ap1VC6RkZDTaPikqhsQ=
@@ -42,15 +42,16 @@ go.dedis.ch/protobuf v1.0.7/go.mod h1:pv5ysfkDX/EawiPqcW3ikOxsL5t+BqnV6xHSmE79KI
 go.dedis.ch/protobuf v1.0.11 h1:FTYVIEzY/bfl37lu3pR4lIj+F9Vp1jE8oh91VmxKgLo=
 go.dedis.ch/protobuf v1.0.11/go.mod h1:97QR256dnkimeNdfmURz0wAMNVbd1VmLXhG1CrTYrJ4=
 golang.org/x/crypto v0.0.0-20190123085648-057139ce5d2b/go.mod h1:6SG95UA2DQfeDnfUPMdvaQW0Q7yPrPDi9nlGo2tz2b4=
-golang.org/x/crypto v0.21.0 h1:X31++rzVUdKhX5sWmSOFZxx8UW/ldWx55cbf08iNAMA=
-golang.org/x/crypto v0.21.0/go.mod h1:0BP7YvVV9gBbVKyeTG0Gyn+gZm94bibOW5BjDEYAOMs=
+golang.org/x/crypto v0.43.0 h1:dduJYIi3A3KOfdGOHX8AVZ/jGiyPa3IbBozJ5kNuE04=
+golang.org/x/crypto v0.43.0/go.mod h1:BFbav4mRNlXJL4wNeejLpWxB7wMbc79PdRGhWKncxR0=
 golang.org/x/sys v0.0.0-20190124100055-b90733256f2e/go.mod h1:STP8DvDyc/dI5b8T5hshtkjS+E42TnysNCUPdjciGhY=
 golang.org/x/sys v0.0.0-20201101102859-da207088b7d1/go.mod h1:h1NjWce9XRLGQEsW7wpKNCjG9DtNlClVuFLEZdDNbEs=
-golang.org/x/sys v0.18.0 h1:DBdB3niSjOA/O0blCZBqDefyWNYveAYMNF1Wum0DYQ4=
-golang.org/x/sys v0.18.0/go.mod h1:/VUhepiaJMQUp4+oa/7Zr1D23ma6VTLIYjOOTFZPUcA=
+golang.org/x/sys v0.37.0 h1:fdNQudmxPjkdUTPnLn5mdQv7Zwvbvpaxqs831goi9kQ=
+golang.org/x/sys v0.37.0/go.mod h1:OgkHotnGiDImocRcuBABYBEXf8A9a87e/uXjp9XT3ks=
+golang.org/x/sys v0.38.0 h1:3yZWxaJjBmCWXqhN1qh02AkOnCQ1poK6oF+a7xWL6Gc=
+golang.org/x/sys v0.38.0/go.mod h1:OgkHotnGiDImocRcuBABYBEXf8A9a87e/uXjp9XT3ks=
 gopkg.in/check.v1 v0.0.0-20161208181325-20d25e280405/go.mod h1:Co6ibVJAznAaIkqp8huTwlJQCZ016jof/cbN4VW5Yz0=
 gopkg.in/check.v1 v1.0.0-20201130134442-10cb98267c6c h1:Hei/4ADfdWqJk1ZMxUNpqntNwaWcugrBjAiHlqqRiVk=
+gopkg.in/check.v1 v1.0.0-20201130134442-10cb98267c6c/go.mod h1:JHkPIbrfpd72SG/EVd6muEfDQjcINNoR0C8j2r3qZ4Q=
 gopkg.in/yaml.v3 v3.0.1 h1:fxVm/GzAzEWqLHuvctI91KS9hhNmmWOoWu0XTYJS7CA=
 gopkg.in/yaml.v3 v3.0.1/go.mod h1:K4uyk7z7BCEPqu6E+C64Yfv1cQ7kz7rIZviUmN+EgEM=
-rsc.io/tmplfunc v0.0.3 h1:53XFQh69AfOa8Tw0Jm7t+GV7KZhOi6jzsCzTtKbMvzU=
-rsc.io/tmplfunc v0.0.3/go.mod h1:AG3sTPzElb1Io3Yg4voV9AGZJuleGAwaVRxL9M49PhA=

group/curve25519/ext.go

@@ -68,7 +68,6 @@ func (P *extPoint) UnmarshalFrom(r io.Reader) (int, error) {
 //	(X1/Z1,Y1/Z1) == (X2/Z2,Y2/Z2)
 //		iff
 //	(X1*Z2,Y1*Z2) == (X2*Z1,Y2*Z1)
-//
 func (P *extPoint) Equal(CP2 kyber.Point) bool {
 	P2 := CP2.(*extPoint)
 	var t1, t2 mod.Int
@@ -120,14 +119,6 @@ func (P *extPoint) normalize() {
 	P.T.Mul(&P.X, &P.Y)
 }
 
-// Check the validity of the T coordinate
-func (P *extPoint) checkT() {
-	var t1, t2 mod.Int
-	if !t1.Mul(&P.X, &P.Y).Equal(t2.Mul(&P.Z, &P.T)) {
-		panic("oops")
-	}
-}
-
 func (P *extPoint) Embed(data []byte, rand cipher.Stream) kyber.Point {
 	P.c.embed(P, data, rand)
 	return P
@@ -230,7 +221,6 @@ func (P *extPoint) double() {
 // Currently doesn't implement the optimization of
 // switching between projective and extended coordinates during
 // scalar multiplication.
-//
 func (P *extPoint) Mul(s kyber.Scalar, G kyber.Point) kyber.Point {
 	v := s.(*mod.Int).V
 	if G == nil {
@@ -272,7 +262,6 @@ func (P *extPoint) Mul(s kyber.Scalar, G kyber.Point) kyber.Point {
 // special case with curve parameter a=-1.
 // We leave the task of hyperoptimization to curve-specific implementations
 // such as the ed25519 package.
-//
 type ExtendedCurve struct {
 	curve          // generic Edwards curve functionality
 	null  extPoint // Constant identity/null point (0,1)

group/edwards25519/const.go

@@ -8,9 +8,6 @@ import (
 	"math/big"
 )
 
-// prime modulus of underlying field = 2^255 - 19
-var prime, _ = new(big.Int).SetString("57896044618658097711785492504343953926634992332820282019728792003956564819949", 10)
-
 // prime order of base point = 2^252 + 27742317777372353535851937790883648493
 var primeOrder, _ = new(big.Int).SetString("7237005577332262213973186563042994240857116359379907606001950938285454250989", 10)
 
@@ -44,60 +41,13 @@ var sqrtM1 = fieldElement{
 	-32595792, -7943725, 9377950, 3500415, 12389472, -272473, -25146209, -2005654, 326686, 11406482,
 }
 
-var paramA = fieldElement{
-	486662, 0, 0, 0, 0, 0, 0, 0, 0, 0,
-}
-
 var baseext = extendedGroupElement{
 	fieldElement{25485296, 5318399, 8791791, -8299916, -14349720, 6939349, -3324311, -7717049, 7287234, -6577708},
 	fieldElement{-758052, -1832720, 13046421, -4857925, 6576754, 14371947, -13139572, 6845540, -2198883, -4003719},
 	fieldElement{-947565, 6097708, -469190, 10704810, -8556274, -15589498, -16424464, -16608899, 14028613, -5004649},
 	fieldElement{6966464, -2456167, 7033433, 6781840, 28785542, 12262365, -2659449, 13959020, -21013759, -5262166},
 }
 
-var bi = [8]preComputedGroupElement{
-	{
-		fieldElement{25967493, -14356035, 29566456, 3660896, -12694345, 4014787, 27544626, -11754271, -6079156, 2047605},
-		fieldElement{-12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692, 5043384, 19500929, -15469378},
-		fieldElement{-8738181, 4489570, 9688441, -14785194, 10184609, -12363380, 29287919, 11864899, -24514362, -4438546},
-	},
-	{
-		fieldElement{15636291, -9688557, 24204773, -7912398, 616977, -16685262, 27787600, -14772189, 28944400, -1550024},
-		fieldElement{16568933, 4717097, -11556148, -1102322, 15682896, -11807043, 16354577, -11775962, 7689662, 11199574},
-		fieldElement{30464156, -5976125, -11779434, -15670865, 23220365, 15915852, 7512774, 10017326, -17749093, -9920357},
-	},
-	{
-		fieldElement{10861363, 11473154, 27284546, 1981175, -30064349, 12577861, 32867885, 14515107, -15438304, 10819380},
-		fieldElement{4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668, 12483688, -12668491, 5581306},
-		fieldElement{19563160, 16186464, -29386857, 4097519, 10237984, -4348115, 28542350, 13850243, -23678021, -15815942},
-	},
-	{
-		fieldElement{5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852, 5230134, -23952439, -15175766},
-		fieldElement{-30269007, -3463509, 7665486, 10083793, 28475525, 1649722, 20654025, 16520125, 30598449, 7715701},
-		fieldElement{28881845, 14381568, 9657904, 3680757, -20181635, 7843316, -31400660, 1370708, 29794553, -1409300},
-	},
-	{
-		fieldElement{-22518993, -6692182, 14201702, -8745502, -23510406, 8844726, 18474211, -1361450, -13062696, 13821877},
-		fieldElement{-6455177, -7839871, 3374702, -4740862, -27098617, -10571707, 31655028, -7212327, 18853322, -14220951},
-		fieldElement{4566830, -12963868, -28974889, -12240689, -7602672, -2830569, -8514358, -10431137, 2207753, -3209784},
-	},
-	{
-		fieldElement{-25154831, -4185821, 29681144, 7868801, -6854661, -9423865, -12437364, -663000, -31111463, -16132436},
-		fieldElement{25576264, -2703214, 7349804, -11814844, 16472782, 9300885, 3844789, 15725684, 171356, 6466918},
-		fieldElement{23103977, 13316479, 9739013, -16149481, 817875, -15038942, 8965339, -14088058, -30714912, 16193877},
-	},
-	{
-		fieldElement{-33521811, 3180713, -2394130, 14003687, -16903474, -16270840, 17238398, 4729455, -18074513, 9256800},
-		fieldElement{-25182317, -4174131, 32336398, 5036987, -21236817, 11360617, 22616405, 9761698, -19827198, 630305},
-		fieldElement{-13720693, 2639453, -24237460, -7406481, 9494427, -5774029, -6554551, -15960994, -2449256, -14291300},
-	},
-	{
-		fieldElement{-3151181, -5046075, 9282714, 6866145, -31907062, -863023, -18940575, 15033784, 25105118, -7894876},
-		fieldElement{-24326370, 15950226, -31801215, -14592823, -11662737, -5090925, 1573892, -2625887, 2198790, -15804619},
-		fieldElement{-3099351, 10324967, -2241613, 7453183, -5446979, -2735503, -13812022, -16236442, -32461234, -12290683},
-	},
-}
-
 var base = [32][8]preComputedGroupElement{
 	{
 		{