--- libgo/Makefile.am.jj 2014-01-08 13:53:06.000000000 +0100
+++ libgo/Makefile.am 2014-03-05 15:20:09.938466093 +0100
@@ -1133,7 +1133,6 @@ go_crypto_ecdsa_files = \
go/crypto/ecdsa/ecdsa.go
go_crypto_elliptic_files = \
go/crypto/elliptic/elliptic.go \
- go/crypto/elliptic/p224.go \
go/crypto/elliptic/p256.go
go_crypto_hmac_files = \
go/crypto/hmac/hmac.go
--- libgo/Makefile.in.jj 2014-01-08 13:53:06.000000000 +0100
+++ libgo/Makefile.in 2014-03-05 15:20:20.372465471 +0100
@@ -1291,7 +1291,6 @@ go_crypto_ecdsa_files = \
go_crypto_elliptic_files = \
go/crypto/elliptic/elliptic.go \
- go/crypto/elliptic/p224.go \
go/crypto/elliptic/p256.go
go_crypto_hmac_files = \
--- libgo/go/crypto/elliptic/elliptic.go.jj 2013-11-07 11:59:09.000000000 +0100
+++ libgo/go/crypto/elliptic/elliptic.go 2014-03-05 15:21:04.186462859 +0100
@@ -326,7 +326,6 @@ var p384 *CurveParams
var p521 *CurveParams
func initAll() {
- initP224()
initP256()
initP384()
initP521()
--- libgo/go/crypto/elliptic/elliptic_test.go.jj 2013-11-07 11:59:09.000000000 +0100
+++ libgo/go/crypto/elliptic/elliptic_test.go 2014-03-05 15:46:03.739373453 +0100
@@ -5,26 +5,16 @@
package elliptic
import (
- "crypto/rand"
- "encoding/hex"
- "fmt"
"math/big"
"testing"
)
-func TestOnCurve(t *testing.T) {
- p224 := P224()
- if !p224.IsOnCurve(p224.Params().Gx, p224.Params().Gy) {
- t.Errorf("FAIL")
- }
-}
-
type baseMultTest struct {
k string
x, y string
}
-var p224BaseMultTests = []baseMultTest{
+var p256BaseMultTests = []baseMultTest{
{
"1",
"b70e0cbd6bb4bf7f321390b94a03c1d356c21122343280d6115c1d21",
@@ -287,47 +277,12 @@ var p224BaseMultTests = []baseMultTest{
},
}
-func TestBaseMult(t *testing.T) {
- p224 := P224()
- for i, e := range p224BaseMultTests {
- k, ok := new(big.Int).SetString(e.k, 10)
- if !ok {
- t.Errorf("%d: bad value for k: %s", i, e.k)
- }
- x, y := p224.ScalarBaseMult(k.Bytes())
- if fmt.Sprintf("%x", x) != e.x || fmt.Sprintf("%x", y) != e.y {
- t.Errorf("%d: bad output for k=%s: got (%x, %x), want (%s, %s)", i, e.k, x, y, e.x, e.y)
- }
- if testing.Short() && i > 5 {
- break
- }
- }
-}
-
-func TestGenericBaseMult(t *testing.T) {
- // We use the P224 CurveParams directly in order to test the generic implementation.
- p224 := P224().Params()
- for i, e := range p224BaseMultTests {
- k, ok := new(big.Int).SetString(e.k, 10)
- if !ok {
- t.Errorf("%d: bad value for k: %s", i, e.k)
- }
- x, y := p224.ScalarBaseMult(k.Bytes())
- if fmt.Sprintf("%x", x) != e.x || fmt.Sprintf("%x", y) != e.y {
- t.Errorf("%d: bad output for k=%s: got (%x, %x), want (%s, %s)", i, e.k, x, y, e.x, e.y)
- }
- if testing.Short() && i > 5 {
- break
- }
- }
-}
-
func TestP256BaseMult(t *testing.T) {
p256 := P256()
p256Generic := p256.Params()
- scalars := make([]*big.Int, 0, len(p224BaseMultTests)+1)
- for _, e := range p224BaseMultTests {
+ scalars := make([]*big.Int, 0, len(p256BaseMultTests)+1)
+ for _, e := range p256BaseMultTests {
k, _ := new(big.Int).SetString(e.k, 10)
scalars = append(scalars, k)
}
@@ -352,7 +307,7 @@ func TestP256Mult(t *testing.T) {
p256 := P256()
p256Generic := p256.Params()
- for i, e := range p224BaseMultTests {
+ for i, e := range p256BaseMultTests {
x, _ := new(big.Int).SetString(e.x, 16)
y, _ := new(big.Int).SetString(e.y, 16)
k, _ := new(big.Int).SetString(e.k, 10)
@@ -373,7 +328,6 @@ func TestInfinity(t *testing.T) {
name string
curve Curve
}{
- {"p224", P224()},
{"p256", P256()},
}
@@ -406,53 +360,13 @@ func TestInfinity(t *testing.T) {
}
}
-func BenchmarkBaseMult(b *testing.B) {
- b.ResetTimer()
- p224 := P224()
- e := p224BaseMultTests[25]
- k, _ := new(big.Int).SetString(e.k, 10)
- b.StartTimer()
- for i := 0; i < b.N; i++ {
- p224.ScalarBaseMult(k.Bytes())
- }
-}
-
func BenchmarkBaseMultP256(b *testing.B) {
b.ResetTimer()
p256 := P256()
- e := p224BaseMultTests[25]
+ e := p256BaseMultTests[25]
k, _ := new(big.Int).SetString(e.k, 10)
b.StartTimer()
for i := 0; i < b.N; i++ {
p256.ScalarBaseMult(k.Bytes())
}
}
-
-func TestMarshal(t *testing.T) {
- p224 := P224()
- _, x, y, err := GenerateKey(p224, rand.Reader)
- if err != nil {
- t.Error(err)
- return
- }
- serialized := Marshal(p224, x, y)
- xx, yy := Unmarshal(p224, serialized)
- if xx == nil {
- t.Error("failed to unmarshal")
- return
- }
- if xx.Cmp(x) != 0 || yy.Cmp(y) != 0 {
- t.Error("unmarshal returned different values")
- return
- }
-}
-
-func TestP224Overflow(t *testing.T) {
- // This tests for a specific bug in the P224 implementation.
- p224 := P224()
- pointData, _ := hex.DecodeString("049B535B45FB0A2072398A6831834624C7E32CCFD5A4B933BCEAF77F1DD945E08BBE5178F5EDF5E733388F196D2A631D2E075BB16CBFEEA15B")
- x, y := Unmarshal(p224, pointData)
- if !p224.IsOnCurve(x, y) {
- t.Error("P224 failed to validate a correct point")
- }
-}
--- libgo/go/crypto/ecdsa/ecdsa_test.go.jj 2012-11-15 18:26:56.000000000 +0100
+++ libgo/go/crypto/ecdsa/ecdsa_test.go 2014-03-05 15:26:38.461442929 +0100
@@ -33,7 +33,6 @@ func testKeyGeneration(t *testing.T, c e
}
func TestKeyGeneration(t *testing.T) {
- testKeyGeneration(t, elliptic.P224(), "p224")
if testing.Short() {
return
}
@@ -63,7 +62,6 @@ func testSignAndVerify(t *testing.T, c e
}
func TestSignAndVerify(t *testing.T) {
- testSignAndVerify(t, elliptic.P224(), "p224")
if testing.Short() {
return
}
@@ -129,8 +127,6 @@ func TestVectors(t *testing.T) {
parts := strings.SplitN(line, ",", 2)
switch parts[0] {
- case "P-224":
- pub.Curve = elliptic.P224()
case "P-256":
pub.Curve = elliptic.P256()
case "P-384":
--- libgo/go/crypto/x509/x509.go.jj 2013-11-07 11:59:09.000000000 +0100
+++ libgo/go/crypto/x509/x509.go 2014-03-05 15:27:37.022439437 +0100
@@ -305,9 +305,6 @@ func getPublicKeyAlgorithmFromOID(oid as
// RFC 5480, 2.1.1.1. Named Curve
//
-// secp224r1 OBJECT IDENTIFIER ::= {
-// iso(1) identified-organization(3) certicom(132) curve(0) 33 }
-//
// secp256r1 OBJECT IDENTIFIER ::= {
// iso(1) member-body(2) us(840) ansi-X9-62(10045) curves(3)
// prime(1) 7 }
@@ -320,7 +317,6 @@ func getPublicKeyAlgorithmFromOID(oid as
//
// NB: secp256r1 is equivalent to prime256v1
var (
- oidNamedCurveP224 = asn1.ObjectIdentifier{1, 3, 132, 0, 33}
oidNamedCurveP256 = asn1.ObjectIdentifier{1, 2, 840, 10045, 3, 1, 7}
oidNamedCurveP384 = asn1.ObjectIdentifier{1, 3, 132, 0, 34}
oidNamedCurveP521 = asn1.ObjectIdentifier{1, 3, 132, 0, 35}
@@ -328,8 +324,6 @@ var (
func namedCurveFromOID(oid asn1.ObjectIdentifier) elliptic.Curve {
switch {
- case oid.Equal(oidNamedCurveP224):
- return elliptic.P224()
case oid.Equal(oidNamedCurveP256):
return elliptic.P256()
case oid.Equal(oidNamedCurveP384):
@@ -342,8 +336,6 @@ func namedCurveFromOID(oid asn1.ObjectId
func oidFromNamedCurve(curve elliptic.Curve) (asn1.ObjectIdentifier, bool) {
switch curve {
- case elliptic.P224():
- return oidNamedCurveP224, true
case elliptic.P256():
return oidNamedCurveP256, true
case elliptic.P384():
@@ -1373,7 +1365,7 @@ func CreateCertificate(rand io.Reader, t
hashFunc = crypto.SHA1
case *ecdsa.PrivateKey:
switch priv.Curve {
- case elliptic.P224(), elliptic.P256():
+ case elliptic.P256():
hashFunc = crypto.SHA256
signatureAlgorithm.Algorithm = oidSignatureECDSAWithSHA256
case elliptic.P384():
--- libgo/go/crypto/elliptic/p224.go.jj 2012-11-15 18:26:57.000000000 +0100
+++ libgo/go/crypto/elliptic/p224.go 2014-03-05 15:30:01.189430842 +0100
@@ -1,765 +0,0 @@
-// Copyright 2012 The Go Authors. All rights reserved.
-// Use of this source code is governed by a BSD-style
-// license that can be found in the LICENSE file.
-
-package elliptic
-
-// This is a constant-time, 32-bit implementation of P224. See FIPS 186-3,
-// section D.2.2.
-//
-// See http://www.imperialviolet.org/2010/12/04/ecc.html ([1]) for background.
-
-import (
- "math/big"
-)
-
-var p224 p224Curve
-
-type p224Curve struct {
- *CurveParams
- gx, gy, b p224FieldElement
-}
-
-func initP224() {
- // See FIPS 186-3, section D.2.2
- p224.CurveParams = new(CurveParams)
- p224.P, _ = new(big.Int).SetString("26959946667150639794667015087019630673557916260026308143510066298881", 10)
- p224.N, _ = new(big.Int).SetString("26959946667150639794667015087019625940457807714424391721682722368061", 10)
- p224.B, _ = new(big.Int).SetString("b4050a850c04b3abf54132565044b0b7d7bfd8ba270b39432355ffb4", 16)
- p224.Gx, _ = new(big.Int).SetString("b70e0cbd6bb4bf7f321390b94a03c1d356c21122343280d6115c1d21", 16)
- p224.Gy, _ = new(big.Int).SetString("bd376388b5f723fb4c22dfe6cd4375a05a07476444d5819985007e34", 16)
- p224.BitSize = 224
-
- p224FromBig(&p224.gx, p224.Gx)
- p224FromBig(&p224.gy, p224.Gy)
- p224FromBig(&p224.b, p224.B)
-}
-
-// P224 returns a Curve which implements P-224 (see FIPS 186-3, section D.2.2)
-func P224() Curve {
- initonce.Do(initAll)
- return p224
-}
-
-func (curve p224Curve) Params() *CurveParams {
- return curve.CurveParams
-}
-
-func (curve p224Curve) IsOnCurve(bigX, bigY *big.Int) bool {
- var x, y p224FieldElement
- p224FromBig(&x, bigX)
- p224FromBig(&y, bigY)
-
- // y² = x³ - 3x + b
- var tmp p224LargeFieldElement
- var x3 p224FieldElement
- p224Square(&x3, &x, &tmp)
- p224Mul(&x3, &x3, &x, &tmp)
-
- for i := 0; i < 8; i++ {
- x[i] *= 3
- }
- p224Sub(&x3, &x3, &x)
- p224Reduce(&x3)
- p224Add(&x3, &x3, &curve.b)
- p224Contract(&x3, &x3)
-
- p224Square(&y, &y, &tmp)
- p224Contract(&y, &y)
-
- for i := 0; i < 8; i++ {
- if y[i] != x3[i] {
- return false
- }
- }
- return true
-}
-
-func (p224Curve) Add(bigX1, bigY1, bigX2, bigY2 *big.Int) (x, y *big.Int) {
- var x1, y1, z1, x2, y2, z2, x3, y3, z3 p224FieldElement
-
- p224FromBig(&x1, bigX1)
- p224FromBig(&y1, bigY1)
- if bigX1.Sign() != 0 || bigY1.Sign() != 0 {
- z1[0] = 1
- }
- p224FromBig(&x2, bigX2)
- p224FromBig(&y2, bigY2)
- if bigX2.Sign() != 0 || bigY2.Sign() != 0 {
- z2[0] = 1
- }
-
- p224AddJacobian(&x3, &y3, &z3, &x1, &y1, &z1, &x2, &y2, &z2)
- return p224ToAffine(&x3, &y3, &z3)
-}
-
-func (p224Curve) Double(bigX1, bigY1 *big.Int) (x, y *big.Int) {
- var x1, y1, z1, x2, y2, z2 p224FieldElement
-
- p224FromBig(&x1, bigX1)
- p224FromBig(&y1, bigY1)
- z1[0] = 1
-
- p224DoubleJacobian(&x2, &y2, &z2, &x1, &y1, &z1)
- return p224ToAffine(&x2, &y2, &z2)
-}
-
-func (p224Curve) ScalarMult(bigX1, bigY1 *big.Int, scalar []byte) (x, y *big.Int) {
- var x1, y1, z1, x2, y2, z2 p224FieldElement
-
- p224FromBig(&x1, bigX1)
- p224FromBig(&y1, bigY1)
- z1[0] = 1
-
- p224ScalarMult(&x2, &y2, &z2, &x1, &y1, &z1, scalar)
- return p224ToAffine(&x2, &y2, &z2)
-}
-
-func (curve p224Curve) ScalarBaseMult(scalar []byte) (x, y *big.Int) {
- var z1, x2, y2, z2 p224FieldElement
-
- z1[0] = 1
- p224ScalarMult(&x2, &y2, &z2, &curve.gx, &curve.gy, &z1, scalar)
- return p224ToAffine(&x2, &y2, &z2)
-}
-
-// Field element functions.
-//
-// The field that we're dealing with is ℤ/pℤ where p = 2**224 - 2**96 + 1.
-//
-// Field elements are represented by a FieldElement, which is a typedef to an
-// array of 8 uint32's. The value of a FieldElement, a, is:
-// a[0] + 2**28·a[1] + 2**56·a[1] + ... + 2**196·a[7]
-//
-// Using 28-bit limbs means that there's only 4 bits of headroom, which is less
-// than we would really like. But it has the useful feature that we hit 2**224
-// exactly, making the reflections during a reduce much nicer.
-type p224FieldElement [8]uint32
-
-// p224P is the order of the field, represented as a p224FieldElement.
-var p224P = [8]uint32{1, 0, 0, 0xffff000, 0xfffffff, 0xfffffff, 0xfffffff, 0xfffffff}
-
-// p224IsZero returns 1 if a == 0 mod p and 0 otherwise.
-//
-// a[i] < 2**29
-func p224IsZero(a *p224FieldElement) uint32 {
- // Since a p224FieldElement contains 224 bits there are two possible
- // representations of 0: 0 and p.
- var minimal p224FieldElement
- p224Contract(&minimal, a)
-
- var isZero, isP uint32
- for i, v := range minimal {
- isZero |= v
- isP |= v - p224P[i]
- }
-
- // If either isZero or isP is 0, then we should return 1.
- isZero |= isZero >> 16
- isZero |= isZero >> 8
- isZero |= isZero >> 4
- isZero |= isZero >> 2
- isZero |= isZero >> 1
-
- isP |= isP >> 16
- isP |= isP >> 8
- isP |= isP >> 4
- isP |= isP >> 2
- isP |= isP >> 1
-
- // For isZero and isP, the LSB is 0 iff all the bits are zero.
- result := isZero & isP
- result = (^result) & 1
-
- return result
-}
-
-// p224Add computes *out = a+b
-//
-// a[i] + b[i] < 2**32
-func p224Add(out, a, b *p224FieldElement) {
- for i := 0; i < 8; i++ {
- out[i] = a[i] + b[i]
- }
-}
-
-const two31p3 = 1<<31 + 1<<3
-const two31m3 = 1<<31 - 1<<3
-const two31m15m3 = 1<<31 - 1<<15 - 1<<3
-
-// p224ZeroModP31 is 0 mod p where bit 31 is set in all limbs so that we can
-// subtract smaller amounts without underflow. See the section "Subtraction" in
-// [1] for reasoning.
-var p224ZeroModP31 = []uint32{two31p3, two31m3, two31m3, two31m15m3, two31m3, two31m3, two31m3, two31m3}
-
-// p224Sub computes *out = a-b
-//
-// a[i], b[i] < 2**30
-// out[i] < 2**32
-func p224Sub(out, a, b *p224FieldElement) {
- for i := 0; i < 8; i++ {
- out[i] = a[i] + p224ZeroModP31[i] - b[i]
- }
-}
-
-// LargeFieldElement also represents an element of the field. The limbs are
-// still spaced 28-bits apart and in little-endian order. So the limbs are at
-// 0, 28, 56, ..., 392 bits, each 64-bits wide.
-type p224LargeFieldElement [15]uint64
-
-const two63p35 = 1<<63 + 1<<35
-const two63m35 = 1<<63 - 1<<35
-const two63m35m19 = 1<<63 - 1<<35 - 1<<19
-
-// p224ZeroModP63 is 0 mod p where bit 63 is set in all limbs. See the section
-// "Subtraction" in [1] for why.
-var p224ZeroModP63 = [8]uint64{two63p35, two63m35, two63m35, two63m35, two63m35m19, two63m35, two63m35, two63m35}
-
-const bottom12Bits = 0xfff
-const bottom28Bits = 0xfffffff
-
-// p224Mul computes *out = a*b
-//
-// a[i] < 2**29, b[i] < 2**30 (or vice versa)
-// out[i] < 2**29
-func p224Mul(out, a, b *p224FieldElement, tmp *p224LargeFieldElement) {
- for i := 0; i < 15; i++ {
- tmp[i] = 0
- }
-
- for i := 0; i < 8; i++ {
- for j := 0; j < 8; j++ {
- tmp[i+j] += uint64(a[i]) * uint64(b[j])
- }
- }
-
- p224ReduceLarge(out, tmp)
-}
-
-// Square computes *out = a*a
-//
-// a[i] < 2**29
-// out[i] < 2**29
-func p224Square(out, a *p224FieldElement, tmp *p224LargeFieldElement) {
- for i := 0; i < 15; i++ {
- tmp[i] = 0
- }
-
- for i := 0; i < 8; i++ {
- for j := 0; j <= i; j++ {
- r := uint64(a[i]) * uint64(a[j])
- if i == j {
- tmp[i+j] += r
- } else {
- tmp[i+j] += r << 1
- }
- }
- }
-
- p224ReduceLarge(out, tmp)
-}
-
-// ReduceLarge converts a p224LargeFieldElement to a p224FieldElement.
-//
-// in[i] < 2**62
-func p224ReduceLarge(out *p224FieldElement, in *p224LargeFieldElement) {
- for i := 0; i < 8; i++ {
- in[i] += p224ZeroModP63[i]
- }
-
- // Eliminate the coefficients at 2**224 and greater.
- for i := 14; i >= 8; i-- {
- in[i-8] -= in[i]
- in[i-5] += (in[i] & 0xffff) << 12
- in[i-4] += in[i] >> 16
- }
- in[8] = 0
- // in[0..8] < 2**64
-
- // As the values become small enough, we start to store them in |out|
- // and use 32-bit operations.
- for i := 1; i < 8; i++ {
- in[i+1] += in[i] >> 28
- out[i] = uint32(in[i] & bottom28Bits)
- }
- in[0] -= in[8]
- out[3] += uint32(in[8]&0xffff) << 12
- out[4] += uint32(in[8] >> 16)
- // in[0] < 2**64
- // out[3] < 2**29
- // out[4] < 2**29
- // out[1,2,5..7] < 2**28
-
- out[0] = uint32(in[0] & bottom28Bits)
- out[1] += uint32((in[0] >> 28) & bottom28Bits)
- out[2] += uint32(in[0] >> 56)
- // out[0] < 2**28
- // out[1..4] < 2**29
- // out[5..7] < 2**28
-}
-
-// Reduce reduces the coefficients of a to smaller bounds.
-//
-// On entry: a[i] < 2**31 + 2**30
-// On exit: a[i] < 2**29
-func p224Reduce(a *p224FieldElement) {
- for i := 0; i < 7; i++ {
- a[i+1] += a[i] >> 28
- a[i] &= bottom28Bits
- }
- top := a[7] >> 28
- a[7] &= bottom28Bits
-
- // top < 2**4
- mask := top
- mask |= mask >> 2
- mask |= mask >> 1
- mask <<= 31
- mask = uint32(int32(mask) >> 31)
- // Mask is all ones if top != 0, all zero otherwise
-
- a[0] -= top
- a[3] += top << 12
-
- // We may have just made a[0] negative but, if we did, then we must
- // have added something to a[3], this it's > 2**12. Therefore we can
- // carry down to a[0].
- a[3] -= 1 & mask
- a[2] += mask & (1<<28 - 1)
- a[1] += mask & (1<<28 - 1)
- a[0] += mask & (1 << 28)
-}
-
-// p224Invert calculates *out = in**-1 by computing in**(2**224 - 2**96 - 1),
-// i.e. Fermat's little theorem.
-func p224Invert(out, in *p224FieldElement) {
- var f1, f2, f3, f4 p224FieldElement
- var c p224LargeFieldElement
-
- p224Square(&f1, in, &c) // 2
- p224Mul(&f1, &f1, in, &c) // 2**2 - 1
- p224Square(&f1, &f1, &c) // 2**3 - 2
- p224Mul(&f1, &f1, in, &c) // 2**3 - 1
- p224Square(&f2, &f1, &c) // 2**4 - 2
- p224Square(&f2, &f2, &c) // 2**5 - 4
- p224Square(&f2, &f2, &c) // 2**6 - 8
- p224Mul(&f1, &f1, &f2, &c) // 2**6 - 1
- p224Square(&f2, &f1, &c) // 2**7 - 2
- for i := 0; i < 5; i++ { // 2**12 - 2**6
- p224Square(&f2, &f2, &c)
- }
- p224Mul(&f2, &f2, &f1, &c) // 2**12 - 1
- p224Square(&f3, &f2, &c) // 2**13 - 2
- for i := 0; i < 11; i++ { // 2**24 - 2**12
- p224Square(&f3, &f3, &c)
- }
- p224Mul(&f2, &f3, &f2, &c) // 2**24 - 1
- p224Square(&f3, &f2, &c) // 2**25 - 2
- for i := 0; i < 23; i++ { // 2**48 - 2**24
- p224Square(&f3, &f3, &c)
- }
- p224Mul(&f3, &f3, &f2, &c) // 2**48 - 1
- p224Square(&f4, &f3, &c) // 2**49 - 2
- for i := 0; i < 47; i++ { // 2**96 - 2**48
- p224Square(&f4, &f4, &c)
- }
- p224Mul(&f3, &f3, &f4, &c) // 2**96 - 1
- p224Square(&f4, &f3, &c) // 2**97 - 2
- for i := 0; i < 23; i++ { // 2**120 - 2**24
- p224Square(&f4, &f4, &c)
- }
- p224Mul(&f2, &f4, &f2, &c) // 2**120 - 1
- for i := 0; i < 6; i++ { // 2**126 - 2**6
- p224Square(&f2, &f2, &c)
- }
- p224Mul(&f1, &f1, &f2, &c) // 2**126 - 1
- p224Square(&f1, &f1, &c) // 2**127 - 2
- p224Mul(&f1, &f1, in, &c) // 2**127 - 1
- for i := 0; i < 97; i++ { // 2**224 - 2**97
- p224Square(&f1, &f1, &c)
- }
- p224Mul(out, &f1, &f3, &c) // 2**224 - 2**96 - 1
-}
-
-// p224Contract converts a FieldElement to its unique, minimal form.
-//
-// On entry, in[i] < 2**29
-// On exit, in[i] < 2**28
-func p224Contract(out, in *p224FieldElement) {
- copy(out[:], in[:])
-
- for i := 0; i < 7; i++ {
- out[i+1] += out[i] >> 28
- out[i] &= bottom28Bits
- }
- top := out[7] >> 28
- out[7] &= bottom28Bits
-
- out[0] -= top
- out[3] += top << 12
-
- // We may just have made out[i] negative. So we carry down. If we made
- // out[0] negative then we know that out[3] is sufficiently positive
- // because we just added to it.
- for i := 0; i < 3; i++ {
- mask := uint32(int32(out[i]) >> 31)
- out[i] += (1 << 28) & mask
- out[i+1] -= 1 & mask
- }
-
- // We might have pushed out[3] over 2**28 so we perform another, partial,
- // carry chain.
- for i := 3; i < 7; i++ {
- out[i+1] += out[i] >> 28
- out[i] &= bottom28Bits
- }
- top = out[7] >> 28
- out[7] &= bottom28Bits
-
- // Eliminate top while maintaining the same value mod p.
- out[0] -= top
- out[3] += top << 12
-
- // There are two cases to consider for out[3]:
- // 1) The first time that we eliminated top, we didn't push out[3] over
- // 2**28. In this case, the partial carry chain didn't change any values
- // and top is zero.
- // 2) We did push out[3] over 2**28 the first time that we eliminated top.
- // The first value of top was in [0..16), therefore, prior to eliminating
- // the first top, 0xfff1000 <= out[3] <= 0xfffffff. Therefore, after
- // overflowing and being reduced by the second carry chain, out[3] <=
- // 0xf000. Thus it cannot have overflowed when we eliminated top for the
- // second time.
-
- // Again, we may just have made out[0] negative, so do the same carry down.
- // As before, if we made out[0] negative then we know that out[3] is
- // sufficiently positive.
- for i := 0; i < 3; i++ {
- mask := uint32(int32(out[i]) >> 31)
- out[i] += (1 << 28) & mask
- out[i+1] -= 1 & mask
- }
-
- // Now we see if the value is >= p and, if so, subtract p.
-
- // First we build a mask from the top four limbs, which must all be
- // equal to bottom28Bits if the whole value is >= p. If top4AllOnes
- // ends up with any zero bits in the bottom 28 bits, then this wasn't
- // true.
- top4AllOnes := uint32(0xffffffff)
- for i := 4; i < 8; i++ {
- top4AllOnes &= out[i]
- }
- top4AllOnes |= 0xf0000000
- // Now we replicate any zero bits to all the bits in top4AllOnes.
- top4AllOnes &= top4AllOnes >> 16
- top4AllOnes &= top4AllOnes >> 8
- top4AllOnes &= top4AllOnes >> 4
- top4AllOnes &= top4AllOnes >> 2
- top4AllOnes &= top4AllOnes >> 1
- top4AllOnes = uint32(int32(top4AllOnes<<31) >> 31)
-
- // Now we test whether the bottom three limbs are non-zero.
- bottom3NonZero := out[0] | out[1] | out[2]
- bottom3NonZero |= bottom3NonZero >> 16
- bottom3NonZero |= bottom3NonZero >> 8
- bottom3NonZero |= bottom3NonZero >> 4
- bottom3NonZero |= bottom3NonZero >> 2
- bottom3NonZero |= bottom3NonZero >> 1
- bottom3NonZero = uint32(int32(bottom3NonZero<<31) >> 31)
-
- // Everything depends on the value of out[3].
- // If it's > 0xffff000 and top4AllOnes != 0 then the whole value is >= p
- // If it's = 0xffff000 and top4AllOnes != 0 and bottom3NonZero != 0,
- // then the whole value is >= p
- // If it's < 0xffff000, then the whole value is < p
- n := out[3] - 0xffff000
- out3Equal := n
- out3Equal |= out3Equal >> 16
- out3Equal |= out3Equal >> 8
- out3Equal |= out3Equal >> 4
- out3Equal |= out3Equal >> 2
- out3Equal |= out3Equal >> 1
- out3Equal = ^uint32(int32(out3Equal<<31) >> 31)
-
- // If out[3] > 0xffff000 then n's MSB will be zero.
- out3GT := ^uint32(int32(n) >> 31)
-
- mask := top4AllOnes & ((out3Equal & bottom3NonZero) | out3GT)
- out[0] -= 1 & mask
- out[3] -= 0xffff000 & mask
- out[4] -= 0xfffffff & mask
- out[5] -= 0xfffffff & mask
- out[6] -= 0xfffffff & mask
- out[7] -= 0xfffffff & mask
-}
-
-// Group element functions.
-//
-// These functions deal with group elements. The group is an elliptic curve
-// group with a = -3 defined in FIPS 186-3, section D.2.2.
-
-// p224AddJacobian computes *out = a+b where a != b.
-func p224AddJacobian(x3, y3, z3, x1, y1, z1, x2, y2, z2 *p224FieldElement) {
- // See http://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#addition-p224Add-2007-bl
- var z1z1, z2z2, u1, u2, s1, s2, h, i, j, r, v p224FieldElement
- var c p224LargeFieldElement
-
- z1IsZero := p224IsZero(z1)
- z2IsZero := p224IsZero(z2)
-
- // Z1Z1 = Z1²
- p224Square(&z1z1, z1, &c)
- // Z2Z2 = Z2²
- p224Square(&z2z2, z2, &c)
- // U1 = X1*Z2Z2
- p224Mul(&u1, x1, &z2z2, &c)
- // U2 = X2*Z1Z1
- p224Mul(&u2, x2, &z1z1, &c)
- // S1 = Y1*Z2*Z2Z2
- p224Mul(&s1, z2, &z2z2, &c)
- p224Mul(&s1, y1, &s1, &c)
- // S2 = Y2*Z1*Z1Z1
- p224Mul(&s2, z1, &z1z1, &c)
- p224Mul(&s2, y2, &s2, &c)
- // H = U2-U1
- p224Sub(&h, &u2, &u1)
- p224Reduce(&h)
- xEqual := p224IsZero(&h)
- // I = (2*H)²
- for j := 0; j < 8; j++ {
- i[j] = h[j] << 1
- }
- p224Reduce(&i)
- p224Square(&i, &i, &c)
- // J = H*I
- p224Mul(&j, &h, &i, &c)
- // r = 2*(S2-S1)
- p224Sub(&r, &s2, &s1)
- p224Reduce(&r)
- yEqual := p224IsZero(&r)
- if xEqual == 1 && yEqual == 1 && z1IsZero == 0 && z2IsZero == 0 {
- p224DoubleJacobian(x3, y3, z3, x1, y1, z1)
- return
- }
- for i := 0; i < 8; i++ {
- r[i] <<= 1
- }
- p224Reduce(&r)
- // V = U1*I
- p224Mul(&v, &u1, &i, &c)
- // Z3 = ((Z1+Z2)²-Z1Z1-Z2Z2)*H
- p224Add(&z1z1, &z1z1, &z2z2)
- p224Add(&z2z2, z1, z2)
- p224Reduce(&z2z2)
- p224Square(&z2z2, &z2z2, &c)
- p224Sub(z3, &z2z2, &z1z1)
- p224Reduce(z3)
- p224Mul(z3, z3, &h, &c)
- // X3 = r²-J-2*V
- for i := 0; i < 8; i++ {
- z1z1[i] = v[i] << 1
- }
- p224Add(&z1z1, &j, &z1z1)
- p224Reduce(&z1z1)
- p224Square(x3, &r, &c)
- p224Sub(x3, x3, &z1z1)
- p224Reduce(x3)
- // Y3 = r*(V-X3)-2*S1*J
- for i := 0; i < 8; i++ {
- s1[i] <<= 1
- }
- p224Mul(&s1, &s1, &j, &c)
- p224Sub(&z1z1, &v, x3)
- p224Reduce(&z1z1)
- p224Mul(&z1z1, &z1z1, &r, &c)
- p224Sub(y3, &z1z1, &s1)
- p224Reduce(y3)
-
- p224CopyConditional(x3, x2, z1IsZero)
- p224CopyConditional(x3, x1, z2IsZero)
- p224CopyConditional(y3, y2, z1IsZero)
- p224CopyConditional(y3, y1, z2IsZero)
- p224CopyConditional(z3, z2, z1IsZero)
- p224CopyConditional(z3, z1, z2IsZero)
-}
-
-// p224DoubleJacobian computes *out = a+a.
-func p224DoubleJacobian(x3, y3, z3, x1, y1, z1 *p224FieldElement) {
- var delta, gamma, beta, alpha, t p224FieldElement
- var c p224LargeFieldElement
-
- p224Square(&delta, z1, &c)
- p224Square(&gamma, y1, &c)
- p224Mul(&beta, x1, &gamma, &c)
-
- // alpha = 3*(X1-delta)*(X1+delta)
- p224Add(&t, x1, &delta)
- for i := 0; i < 8; i++ {
- t[i] += t[i] << 1
- }
- p224Reduce(&t)
- p224Sub(&alpha, x1, &delta)
- p224Reduce(&alpha)
- p224Mul(&alpha, &alpha, &t, &c)
-
- // Z3 = (Y1+Z1)²-gamma-delta
- p224Add(z3, y1, z1)
- p224Reduce(z3)
- p224Square(z3, z3, &c)
- p224Sub(z3, z3, &gamma)
- p224Reduce(z3)
- p224Sub(z3, z3, &delta)
- p224Reduce(z3)
-
- // X3 = alpha²-8*beta
- for i := 0; i < 8; i++ {
- delta[i] = beta[i] << 3
- }
- p224Reduce(&delta)
- p224Square(x3, &alpha, &c)
- p224Sub(x3, x3, &delta)
- p224Reduce(x3)
-
- // Y3 = alpha*(4*beta-X3)-8*gamma²
- for i := 0; i < 8; i++ {
- beta[i] <<= 2
- }
- p224Sub(&beta, &beta, x3)
- p224Reduce(&beta)
- p224Square(&gamma, &gamma, &c)
- for i := 0; i < 8; i++ {
- gamma[i] <<= 3
- }
- p224Reduce(&gamma)
- p224Mul(y3, &alpha, &beta, &c)
- p224Sub(y3, y3, &gamma)
- p224Reduce(y3)
-}
-
-// p224CopyConditional sets *out = *in iff the least-significant-bit of control
-// is true, and it runs in constant time.
-func p224CopyConditional(out, in *p224FieldElement, control uint32) {
- control <<= 31
- control = uint32(int32(control) >> 31)
-
- for i := 0; i < 8; i++ {
- out[i] ^= (out[i] ^ in[i]) & control
- }
-}
-
-func p224ScalarMult(outX, outY, outZ, inX, inY, inZ *p224FieldElement, scalar []byte) {
- var xx, yy, zz p224FieldElement
- for i := 0; i < 8; i++ {
- outX[i] = 0
- outY[i] = 0
- outZ[i] = 0
- }
-
- for _, byte := range scalar {
- for bitNum := uint(0); bitNum < 8; bitNum++ {
- p224DoubleJacobian(outX, outY, outZ, outX, outY, outZ)
- bit := uint32((byte >> (7 - bitNum)) & 1)
- p224AddJacobian(&xx, &yy, &zz, inX, inY, inZ, outX, outY, outZ)
- p224CopyConditional(outX, &xx, bit)
- p224CopyConditional(outY, &yy, bit)
- p224CopyConditional(outZ, &zz, bit)
- }
- }
-}
-
-// p224ToAffine converts from Jacobian to affine form.
-func p224ToAffine(x, y, z *p224FieldElement) (*big.Int, *big.Int) {
- var zinv, zinvsq, outx, outy p224FieldElement
- var tmp p224LargeFieldElement
-
- if isPointAtInfinity := p224IsZero(z); isPointAtInfinity == 1 {
- return new(big.Int), new(big.Int)
- }
-
- p224Invert(&zinv, z)
- p224Square(&zinvsq, &zinv, &tmp)
- p224Mul(x, x, &zinvsq, &tmp)
- p224Mul(&zinvsq, &zinvsq, &zinv, &tmp)
- p224Mul(y, y, &zinvsq, &tmp)
-
- p224Contract(&outx, x)
- p224Contract(&outy, y)
- return p224ToBig(&outx), p224ToBig(&outy)
-}
-
-// get28BitsFromEnd returns the least-significant 28 bits from buf>>shift,
-// where buf is interpreted as a big-endian number.
-func get28BitsFromEnd(buf []byte, shift uint) (uint32, []byte) {
- var ret uint32
-
- for i := uint(0); i < 4; i++ {
- var b byte
- if l := len(buf); l > 0 {
- b = buf[l-1]
- // We don't remove the byte if we're about to return and we're not
- // reading all of it.
- if i != 3 || shift == 4 {
- buf = buf[:l-1]
- }
- }
- ret |= uint32(b) << (8 * i) >> shift
- }
- ret &= bottom28Bits
- return ret, buf
-}
-
-// p224FromBig sets *out = *in.
-func p224FromBig(out *p224FieldElement, in *big.Int) {
- bytes := in.Bytes()
- out[0], bytes = get28BitsFromEnd(bytes, 0)
- out[1], bytes = get28BitsFromEnd(bytes, 4)
- out[2], bytes = get28BitsFromEnd(bytes, 0)
- out[3], bytes = get28BitsFromEnd(bytes, 4)
- out[4], bytes = get28BitsFromEnd(bytes, 0)
- out[5], bytes = get28BitsFromEnd(bytes, 4)
- out[6], bytes = get28BitsFromEnd(bytes, 0)
- out[7], bytes = get28BitsFromEnd(bytes, 4)
-}
-
-// p224ToBig returns in as a big.Int.
-func p224ToBig(in *p224FieldElement) *big.Int {
- var buf [28]byte
- buf[27] = byte(in[0])
- buf[26] = byte(in[0] >> 8)
- buf[25] = byte(in[0] >> 16)
- buf[24] = byte(((in[0] >> 24) & 0x0f) | (in[1]<<4)&0xf0)
-
- buf[23] = byte(in[1] >> 4)
- buf[22] = byte(in[1] >> 12)
- buf[21] = byte(in[1] >> 20)
-
- buf[20] = byte(in[2])
- buf[19] = byte(in[2] >> 8)
- buf[18] = byte(in[2] >> 16)
- buf[17] = byte(((in[2] >> 24) & 0x0f) | (in[3]<<4)&0xf0)
-
- buf[16] = byte(in[3] >> 4)
- buf[15] = byte(in[3] >> 12)
- buf[14] = byte(in[3] >> 20)
-
- buf[13] = byte(in[4])
- buf[12] = byte(in[4] >> 8)
- buf[11] = byte(in[4] >> 16)
- buf[10] = byte(((in[4] >> 24) & 0x0f) | (in[5]<<4)&0xf0)
-
- buf[9] = byte(in[5] >> 4)
- buf[8] = byte(in[5] >> 12)
- buf[7] = byte(in[5] >> 20)
-
- buf[6] = byte(in[6])
- buf[5] = byte(in[6] >> 8)
- buf[4] = byte(in[6] >> 16)
- buf[3] = byte(((in[6] >> 24) & 0x0f) | (in[7]<<4)&0xf0)
-
- buf[2] = byte(in[7] >> 4)
- buf[1] = byte(in[7] >> 12)
- buf[0] = byte(in[7] >> 20)
-
- return new(big.Int).SetBytes(buf[:])
-}
--- libgo/go/crypto/elliptic/p224_test.go.jj 2012-11-15 18:26:57.000000000 +0100
+++ libgo/go/crypto/elliptic/p224_test.go 2014-03-05 15:29:58.743430988 +0100
@@ -1,47 +0,0 @@
-// Copyright 2012 The Go Authors. All rights reserved.
-// Use of this source code is governed by a BSD-style
-// license that can be found in the LICENSE file.
-
-package elliptic
-
-import (
- "math/big"
- "testing"
-)
-
-var toFromBigTests = []string{
- "0",
- "1",
- "23",
- "b70e0cb46bb4bf7f321390b94a03c1d356c01122343280d6105c1d21",
- "706a46d476dcb76798e6046d89474788d164c18032d268fd10704fa6",
-}
-
-func p224AlternativeToBig(in *p224FieldElement) *big.Int {
- ret := new(big.Int)
- tmp := new(big.Int)
-
- for i := uint(0); i < 8; i++ {
- tmp.SetInt64(int64(in[i]))
- tmp.Lsh(tmp, 28*i)
- ret.Add(ret, tmp)
- }
- ret.Mod(ret, p224.P)
- return ret
-}
-
-func TestToFromBig(t *testing.T) {
- for i, test := range toFromBigTests {
- n, _ := new(big.Int).SetString(test, 16)
- var x p224FieldElement
- p224FromBig(&x, n)
- m := p224ToBig(&x)
- if n.Cmp(m) != 0 {
- t.Errorf("#%d: %x != %x", i, n, m)
- }
- q := p224AlternativeToBig(&x)
- if n.Cmp(q) != 0 {
- t.Errorf("#%d: %x != %x (alternative)", i, n, m)
- }
- }
-}
--- libgo/go/crypto/elliptic/p256.go.jj 2013-11-07 11:59:09.000000000 +0100
+++ libgo/go/crypto/elliptic/p256.go 2014-03-05 15:34:31.910414701 +0100
@@ -233,6 +233,8 @@ func p256ReduceCarry(inout *[p256Limbs]u
inout[7] += carry << 25
}
+const bottom28Bits = 0xfffffff
+
// p256Sum sets out = in+in2.
//
// On entry, in[i]+in2[i] must not overflow a 32-bit word.
@@ -265,6 +267,7 @@ const (
two31m2 = 1<<31 - 1<<2
two31p24m2 = 1<<31 + 1<<24 - 1<<2
two30m27m2 = 1<<30 - 1<<27 - 1<<2
+ two31m3 = 1<<31 - 1<<3
)
// p256Zero31 is 0 mod p.