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-rw-r--r--src/crypto/elliptic/elliptic.go280
-rw-r--r--src/crypto/elliptic/elliptic_test.go413
-rw-r--r--src/crypto/elliptic/nistec.go294
-rw-r--r--src/crypto/elliptic/nistec_p256.go29
-rw-r--r--src/crypto/elliptic/p224_test.go325
-rw-r--r--src/crypto/elliptic/p256_test.go152
-rw-r--r--src/crypto/elliptic/params.go334
7 files changed, 1827 insertions, 0 deletions
diff --git a/src/crypto/elliptic/elliptic.go b/src/crypto/elliptic/elliptic.go
new file mode 100644
index 0000000..96555ad
--- /dev/null
+++ b/src/crypto/elliptic/elliptic.go
@@ -0,0 +1,280 @@
+// Copyright 2010 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 implements the standard NIST P-224, P-256, P-384, and P-521
+// elliptic curves over prime fields.
+//
+// Direct use of this package is deprecated, beyond the [P224], [P256], [P384],
+// and [P521] values necessary to use [crypto/ecdsa]. Most other uses
+// should migrate to the more efficient and safer [crypto/ecdh], or to
+// third-party modules for lower-level functionality.
+package elliptic
+
+import (
+ "io"
+ "math/big"
+ "sync"
+)
+
+// A Curve represents a short-form Weierstrass curve with a=-3.
+//
+// The behavior of Add, Double, and ScalarMult when the input is not a point on
+// the curve is undefined.
+//
+// Note that the conventional point at infinity (0, 0) is not considered on the
+// curve, although it can be returned by Add, Double, ScalarMult, or
+// ScalarBaseMult (but not the Unmarshal or UnmarshalCompressed functions).
+//
+// Using Curve implementations besides those returned by P224(), P256(), P384(),
+// and P521() is deprecated.
+type Curve interface {
+ // Params returns the parameters for the curve.
+ Params() *CurveParams
+
+ // IsOnCurve reports whether the given (x,y) lies on the curve.
+ //
+ // Deprecated: this is a low-level unsafe API. For ECDH, use the crypto/ecdh
+ // package. The NewPublicKey methods of NIST curves in crypto/ecdh accept
+ // the same encoding as the Unmarshal function, and perform on-curve checks.
+ IsOnCurve(x, y *big.Int) bool
+
+ // Add returns the sum of (x1,y1) and (x2,y2).
+ //
+ // Deprecated: this is a low-level unsafe API.
+ Add(x1, y1, x2, y2 *big.Int) (x, y *big.Int)
+
+ // Double returns 2*(x,y).
+ //
+ // Deprecated: this is a low-level unsafe API.
+ Double(x1, y1 *big.Int) (x, y *big.Int)
+
+ // ScalarMult returns k*(x,y) where k is an integer in big-endian form.
+ //
+ // Deprecated: this is a low-level unsafe API. For ECDH, use the crypto/ecdh
+ // package. Most uses of ScalarMult can be replaced by a call to the ECDH
+ // methods of NIST curves in crypto/ecdh.
+ ScalarMult(x1, y1 *big.Int, k []byte) (x, y *big.Int)
+
+ // ScalarBaseMult returns k*G, where G is the base point of the group
+ // and k is an integer in big-endian form.
+ //
+ // Deprecated: this is a low-level unsafe API. For ECDH, use the crypto/ecdh
+ // package. Most uses of ScalarBaseMult can be replaced by a call to the
+ // PrivateKey.PublicKey method in crypto/ecdh.
+ ScalarBaseMult(k []byte) (x, y *big.Int)
+}
+
+var mask = []byte{0xff, 0x1, 0x3, 0x7, 0xf, 0x1f, 0x3f, 0x7f}
+
+// GenerateKey returns a public/private key pair. The private key is
+// generated using the given reader, which must return random data.
+//
+// Deprecated: for ECDH, use the GenerateKey methods of the crypto/ecdh package;
+// for ECDSA, use the GenerateKey function of the crypto/ecdsa package.
+func GenerateKey(curve Curve, rand io.Reader) (priv []byte, x, y *big.Int, err error) {
+ N := curve.Params().N
+ bitSize := N.BitLen()
+ byteLen := (bitSize + 7) / 8
+ priv = make([]byte, byteLen)
+
+ for x == nil {
+ _, err = io.ReadFull(rand, priv)
+ if err != nil {
+ return
+ }
+ // We have to mask off any excess bits in the case that the size of the
+ // underlying field is not a whole number of bytes.
+ priv[0] &= mask[bitSize%8]
+ // This is because, in tests, rand will return all zeros and we don't
+ // want to get the point at infinity and loop forever.
+ priv[1] ^= 0x42
+
+ // If the scalar is out of range, sample another random number.
+ if new(big.Int).SetBytes(priv).Cmp(N) >= 0 {
+ continue
+ }
+
+ x, y = curve.ScalarBaseMult(priv)
+ }
+ return
+}
+
+// Marshal converts a point on the curve into the uncompressed form specified in
+// SEC 1, Version 2.0, Section 2.3.3. If the point is not on the curve (or is
+// the conventional point at infinity), the behavior is undefined.
+//
+// Deprecated: for ECDH, use the crypto/ecdh package. This function returns an
+// encoding equivalent to that of PublicKey.Bytes in crypto/ecdh.
+func Marshal(curve Curve, x, y *big.Int) []byte {
+ panicIfNotOnCurve(curve, x, y)
+
+ byteLen := (curve.Params().BitSize + 7) / 8
+
+ ret := make([]byte, 1+2*byteLen)
+ ret[0] = 4 // uncompressed point
+
+ x.FillBytes(ret[1 : 1+byteLen])
+ y.FillBytes(ret[1+byteLen : 1+2*byteLen])
+
+ return ret
+}
+
+// MarshalCompressed converts a point on the curve into the compressed form
+// specified in SEC 1, Version 2.0, Section 2.3.3. If the point is not on the
+// curve (or is the conventional point at infinity), the behavior is undefined.
+func MarshalCompressed(curve Curve, x, y *big.Int) []byte {
+ panicIfNotOnCurve(curve, x, y)
+ byteLen := (curve.Params().BitSize + 7) / 8
+ compressed := make([]byte, 1+byteLen)
+ compressed[0] = byte(y.Bit(0)) | 2
+ x.FillBytes(compressed[1:])
+ return compressed
+}
+
+// unmarshaler is implemented by curves with their own constant-time Unmarshal.
+//
+// There isn't an equivalent interface for Marshal/MarshalCompressed because
+// that doesn't involve any mathematical operations, only FillBytes and Bit.
+type unmarshaler interface {
+ Unmarshal([]byte) (x, y *big.Int)
+ UnmarshalCompressed([]byte) (x, y *big.Int)
+}
+
+// Assert that the known curves implement unmarshaler.
+var _ = []unmarshaler{p224, p256, p384, p521}
+
+// Unmarshal converts a point, serialized by Marshal, into an x, y pair. It is
+// an error if the point is not in uncompressed form, is not on the curve, or is
+// the point at infinity. On error, x = nil.
+//
+// Deprecated: for ECDH, use the crypto/ecdh package. This function accepts an
+// encoding equivalent to that of the NewPublicKey methods in crypto/ecdh.
+func Unmarshal(curve Curve, data []byte) (x, y *big.Int) {
+ if c, ok := curve.(unmarshaler); ok {
+ return c.Unmarshal(data)
+ }
+
+ byteLen := (curve.Params().BitSize + 7) / 8
+ if len(data) != 1+2*byteLen {
+ return nil, nil
+ }
+ if data[0] != 4 { // uncompressed form
+ return nil, nil
+ }
+ p := curve.Params().P
+ x = new(big.Int).SetBytes(data[1 : 1+byteLen])
+ y = new(big.Int).SetBytes(data[1+byteLen:])
+ if x.Cmp(p) >= 0 || y.Cmp(p) >= 0 {
+ return nil, nil
+ }
+ if !curve.IsOnCurve(x, y) {
+ return nil, nil
+ }
+ return
+}
+
+// UnmarshalCompressed converts a point, serialized by MarshalCompressed, into
+// an x, y pair. It is an error if the point is not in compressed form, is not
+// on the curve, or is the point at infinity. On error, x = nil.
+func UnmarshalCompressed(curve Curve, data []byte) (x, y *big.Int) {
+ if c, ok := curve.(unmarshaler); ok {
+ return c.UnmarshalCompressed(data)
+ }
+
+ byteLen := (curve.Params().BitSize + 7) / 8
+ if len(data) != 1+byteLen {
+ return nil, nil
+ }
+ if data[0] != 2 && data[0] != 3 { // compressed form
+ return nil, nil
+ }
+ p := curve.Params().P
+ x = new(big.Int).SetBytes(data[1:])
+ if x.Cmp(p) >= 0 {
+ return nil, nil
+ }
+ // y² = x³ - 3x + b
+ y = curve.Params().polynomial(x)
+ y = y.ModSqrt(y, p)
+ if y == nil {
+ return nil, nil
+ }
+ if byte(y.Bit(0)) != data[0]&1 {
+ y.Neg(y).Mod(y, p)
+ }
+ if !curve.IsOnCurve(x, y) {
+ return nil, nil
+ }
+ return
+}
+
+func panicIfNotOnCurve(curve Curve, x, y *big.Int) {
+ // (0, 0) is the point at infinity by convention. It's ok to operate on it,
+ // although IsOnCurve is documented to return false for it. See Issue 37294.
+ if x.Sign() == 0 && y.Sign() == 0 {
+ return
+ }
+
+ if !curve.IsOnCurve(x, y) {
+ panic("crypto/elliptic: attempted operation on invalid point")
+ }
+}
+
+var initonce sync.Once
+
+func initAll() {
+ initP224()
+ initP256()
+ initP384()
+ initP521()
+}
+
+// P224 returns a Curve which implements NIST P-224 (FIPS 186-3, section D.2.2),
+// also known as secp224r1. The CurveParams.Name of this Curve is "P-224".
+//
+// Multiple invocations of this function will return the same value, so it can
+// be used for equality checks and switch statements.
+//
+// The cryptographic operations are implemented using constant-time algorithms.
+func P224() Curve {
+ initonce.Do(initAll)
+ return p224
+}
+
+// P256 returns a Curve which implements NIST P-256 (FIPS 186-3, section D.2.3),
+// also known as secp256r1 or prime256v1. The CurveParams.Name of this Curve is
+// "P-256".
+//
+// Multiple invocations of this function will return the same value, so it can
+// be used for equality checks and switch statements.
+//
+// The cryptographic operations are implemented using constant-time algorithms.
+func P256() Curve {
+ initonce.Do(initAll)
+ return p256
+}
+
+// P384 returns a Curve which implements NIST P-384 (FIPS 186-3, section D.2.4),
+// also known as secp384r1. The CurveParams.Name of this Curve is "P-384".
+//
+// Multiple invocations of this function will return the same value, so it can
+// be used for equality checks and switch statements.
+//
+// The cryptographic operations are implemented using constant-time algorithms.
+func P384() Curve {
+ initonce.Do(initAll)
+ return p384
+}
+
+// P521 returns a Curve which implements NIST P-521 (FIPS 186-3, section D.2.5),
+// also known as secp521r1. The CurveParams.Name of this Curve is "P-521".
+//
+// Multiple invocations of this function will return the same value, so it can
+// be used for equality checks and switch statements.
+//
+// The cryptographic operations are implemented using constant-time algorithms.
+func P521() Curve {
+ initonce.Do(initAll)
+ return p521
+}
diff --git a/src/crypto/elliptic/elliptic_test.go b/src/crypto/elliptic/elliptic_test.go
new file mode 100644
index 0000000..aedbefc
--- /dev/null
+++ b/src/crypto/elliptic/elliptic_test.go
@@ -0,0 +1,413 @@
+// Copyright 2010 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 (
+ "bytes"
+ "crypto/rand"
+ "encoding/hex"
+ "math/big"
+ "testing"
+)
+
+// genericParamsForCurve returns the dereferenced CurveParams for
+// the specified curve. This is used to avoid the logic for
+// upgrading a curve to its specific implementation, forcing
+// usage of the generic implementation.
+func genericParamsForCurve(c Curve) *CurveParams {
+ d := *(c.Params())
+ return &d
+}
+
+func testAllCurves(t *testing.T, f func(*testing.T, Curve)) {
+ tests := []struct {
+ name string
+ curve Curve
+ }{
+ {"P256", P256()},
+ {"P256/Params", genericParamsForCurve(P256())},
+ {"P224", P224()},
+ {"P224/Params", genericParamsForCurve(P224())},
+ {"P384", P384()},
+ {"P384/Params", genericParamsForCurve(P384())},
+ {"P521", P521()},
+ {"P521/Params", genericParamsForCurve(P521())},
+ }
+ if testing.Short() {
+ tests = tests[:1]
+ }
+ for _, test := range tests {
+ curve := test.curve
+ t.Run(test.name, func(t *testing.T) {
+ t.Parallel()
+ f(t, curve)
+ })
+ }
+}
+
+func TestOnCurve(t *testing.T) {
+ t.Parallel()
+ testAllCurves(t, func(t *testing.T, curve Curve) {
+ if !curve.IsOnCurve(curve.Params().Gx, curve.Params().Gy) {
+ t.Error("basepoint is not on the curve")
+ }
+ })
+}
+
+func TestOffCurve(t *testing.T) {
+ t.Parallel()
+ testAllCurves(t, func(t *testing.T, curve Curve) {
+ x, y := new(big.Int).SetInt64(1), new(big.Int).SetInt64(1)
+ if curve.IsOnCurve(x, y) {
+ t.Errorf("point off curve is claimed to be on the curve")
+ }
+
+ byteLen := (curve.Params().BitSize + 7) / 8
+ b := make([]byte, 1+2*byteLen)
+ b[0] = 4 // uncompressed point
+ x.FillBytes(b[1 : 1+byteLen])
+ y.FillBytes(b[1+byteLen : 1+2*byteLen])
+
+ x1, y1 := Unmarshal(curve, b)
+ if x1 != nil || y1 != nil {
+ t.Errorf("unmarshaling a point not on the curve succeeded")
+ }
+ })
+}
+
+func TestInfinity(t *testing.T) {
+ t.Parallel()
+ testAllCurves(t, testInfinity)
+}
+
+func isInfinity(x, y *big.Int) bool {
+ return x.Sign() == 0 && y.Sign() == 0
+}
+
+func testInfinity(t *testing.T, curve Curve) {
+ x0, y0 := new(big.Int), new(big.Int)
+ xG, yG := curve.Params().Gx, curve.Params().Gy
+
+ if !isInfinity(curve.ScalarMult(xG, yG, curve.Params().N.Bytes())) {
+ t.Errorf("x^q != ∞")
+ }
+ if !isInfinity(curve.ScalarMult(xG, yG, []byte{0})) {
+ t.Errorf("x^0 != ∞")
+ }
+
+ if !isInfinity(curve.ScalarMult(x0, y0, []byte{1, 2, 3})) {
+ t.Errorf("∞^k != ∞")
+ }
+ if !isInfinity(curve.ScalarMult(x0, y0, []byte{0})) {
+ t.Errorf("∞^0 != ∞")
+ }
+
+ if !isInfinity(curve.ScalarBaseMult(curve.Params().N.Bytes())) {
+ t.Errorf("b^q != ∞")
+ }
+ if !isInfinity(curve.ScalarBaseMult([]byte{0})) {
+ t.Errorf("b^0 != ∞")
+ }
+
+ if !isInfinity(curve.Double(x0, y0)) {
+ t.Errorf("2∞ != ∞")
+ }
+ // There is no other point of order two on the NIST curves (as they have
+ // cofactor one), so Double can't otherwise return the point at infinity.
+
+ nMinusOne := new(big.Int).Sub(curve.Params().N, big.NewInt(1))
+ x, y := curve.ScalarMult(xG, yG, nMinusOne.Bytes())
+ x, y = curve.Add(x, y, xG, yG)
+ if !isInfinity(x, y) {
+ t.Errorf("x^(q-1) + x != ∞")
+ }
+ x, y = curve.Add(xG, yG, x0, y0)
+ if x.Cmp(xG) != 0 || y.Cmp(yG) != 0 {
+ t.Errorf("x+∞ != x")
+ }
+ x, y = curve.Add(x0, y0, xG, yG)
+ if x.Cmp(xG) != 0 || y.Cmp(yG) != 0 {
+ t.Errorf("∞+x != x")
+ }
+
+ if curve.IsOnCurve(x0, y0) {
+ t.Errorf("IsOnCurve(∞) == true")
+ }
+
+ if xx, yy := Unmarshal(curve, Marshal(curve, x0, y0)); xx != nil || yy != nil {
+ t.Errorf("Unmarshal(Marshal(∞)) did not return an error")
+ }
+ // We don't test UnmarshalCompressed(MarshalCompressed(∞)) because there are
+ // two valid points with x = 0.
+ if xx, yy := Unmarshal(curve, []byte{0x00}); xx != nil || yy != nil {
+ t.Errorf("Unmarshal(∞) did not return an error")
+ }
+ byteLen := (curve.Params().BitSize + 7) / 8
+ buf := make([]byte, byteLen*2+1)
+ buf[0] = 4 // Uncompressed format.
+ if xx, yy := Unmarshal(curve, buf); xx != nil || yy != nil {
+ t.Errorf("Unmarshal((0,0)) did not return an error")
+ }
+}
+
+func TestMarshal(t *testing.T) {
+ t.Parallel()
+ testAllCurves(t, func(t *testing.T, curve Curve) {
+ _, x, y, err := GenerateKey(curve, rand.Reader)
+ if err != nil {
+ t.Fatal(err)
+ }
+ serialized := Marshal(curve, x, y)
+ xx, yy := Unmarshal(curve, serialized)
+ if xx == nil {
+ t.Fatal("failed to unmarshal")
+ }
+ if xx.Cmp(x) != 0 || yy.Cmp(y) != 0 {
+ t.Fatal("unmarshal returned different values")
+ }
+ })
+}
+
+func TestUnmarshalToLargeCoordinates(t *testing.T) {
+ t.Parallel()
+ // See https://golang.org/issues/20482.
+ testAllCurves(t, testUnmarshalToLargeCoordinates)
+}
+
+func testUnmarshalToLargeCoordinates(t *testing.T, curve Curve) {
+ p := curve.Params().P
+ byteLen := (p.BitLen() + 7) / 8
+
+ // Set x to be greater than curve's parameter P – specifically, to P+5.
+ // Set y to mod_sqrt(x^3 - 3x + B)) so that (x mod P = 5 , y) is on the
+ // curve.
+ x := new(big.Int).Add(p, big.NewInt(5))
+ y := curve.Params().polynomial(x)
+ y.ModSqrt(y, p)
+
+ invalid := make([]byte, byteLen*2+1)
+ invalid[0] = 4 // uncompressed encoding
+ x.FillBytes(invalid[1 : 1+byteLen])
+ y.FillBytes(invalid[1+byteLen:])
+
+ if X, Y := Unmarshal(curve, invalid); X != nil || Y != nil {
+ t.Errorf("Unmarshal accepts invalid X coordinate")
+ }
+
+ if curve == p256 {
+ // This is a point on the curve with a small y value, small enough that
+ // we can add p and still be within 32 bytes.
+ x, _ = new(big.Int).SetString("31931927535157963707678568152204072984517581467226068221761862915403492091210", 10)
+ y, _ = new(big.Int).SetString("5208467867388784005506817585327037698770365050895731383201516607147", 10)
+ y.Add(y, p)
+
+ if p.Cmp(y) > 0 || y.BitLen() != 256 {
+ t.Fatal("y not within expected range")
+ }
+
+ // marshal
+ x.FillBytes(invalid[1 : 1+byteLen])
+ y.FillBytes(invalid[1+byteLen:])
+
+ if X, Y := Unmarshal(curve, invalid); X != nil || Y != nil {
+ t.Errorf("Unmarshal accepts invalid Y coordinate")
+ }
+ }
+}
+
+// TestInvalidCoordinates tests big.Int values that are not valid field elements
+// (negative or bigger than P). They are expected to return false from
+// IsOnCurve, all other behavior is undefined.
+func TestInvalidCoordinates(t *testing.T) {
+ t.Parallel()
+ testAllCurves(t, testInvalidCoordinates)
+}
+
+func testInvalidCoordinates(t *testing.T, curve Curve) {
+ checkIsOnCurveFalse := func(name string, x, y *big.Int) {
+ if curve.IsOnCurve(x, y) {
+ t.Errorf("IsOnCurve(%s) unexpectedly returned true", name)
+ }
+ }
+
+ p := curve.Params().P
+ _, x, y, _ := GenerateKey(curve, rand.Reader)
+ xx, yy := new(big.Int), new(big.Int)
+
+ // Check if the sign is getting dropped.
+ xx.Neg(x)
+ checkIsOnCurveFalse("-x, y", xx, y)
+ yy.Neg(y)
+ checkIsOnCurveFalse("x, -y", x, yy)
+
+ // Check if negative values are reduced modulo P.
+ xx.Sub(x, p)
+ checkIsOnCurveFalse("x-P, y", xx, y)
+ yy.Sub(y, p)
+ checkIsOnCurveFalse("x, y-P", x, yy)
+
+ // Check if positive values are reduced modulo P.
+ xx.Add(x, p)
+ checkIsOnCurveFalse("x+P, y", xx, y)
+ yy.Add(y, p)
+ checkIsOnCurveFalse("x, y+P", x, yy)
+
+ // Check if the overflow is dropped.
+ xx.Add(x, new(big.Int).Lsh(big.NewInt(1), 535))
+ checkIsOnCurveFalse("x+2⁵³⁵, y", xx, y)
+ yy.Add(y, new(big.Int).Lsh(big.NewInt(1), 535))
+ checkIsOnCurveFalse("x, y+2⁵³⁵", x, yy)
+
+ // Check if P is treated like zero (if possible).
+ // y^2 = x^3 - 3x + B
+ // y = mod_sqrt(x^3 - 3x + B)
+ // y = mod_sqrt(B) if x = 0
+ // If there is no modsqrt, there is no point with x = 0, can't test x = P.
+ if yy := new(big.Int).ModSqrt(curve.Params().B, p); yy != nil {
+ if !curve.IsOnCurve(big.NewInt(0), yy) {
+ t.Fatal("(0, mod_sqrt(B)) is not on the curve?")
+ }
+ checkIsOnCurveFalse("P, y", p, yy)
+ }
+}
+
+func TestMarshalCompressed(t *testing.T) {
+ t.Parallel()
+ t.Run("P-256/03", func(t *testing.T) {
+ data, _ := hex.DecodeString("031e3987d9f9ea9d7dd7155a56a86b2009e1e0ab332f962d10d8beb6406ab1ad79")
+ x, _ := new(big.Int).SetString("13671033352574878777044637384712060483119675368076128232297328793087057702265", 10)
+ y, _ := new(big.Int).SetString("66200849279091436748794323380043701364391950689352563629885086590854940586447", 10)
+ testMarshalCompressed(t, P256(), x, y, data)
+ })
+ t.Run("P-256/02", func(t *testing.T) {
+ data, _ := hex.DecodeString("021e3987d9f9ea9d7dd7155a56a86b2009e1e0ab332f962d10d8beb6406ab1ad79")
+ x, _ := new(big.Int).SetString("13671033352574878777044637384712060483119675368076128232297328793087057702265", 10)
+ y, _ := new(big.Int).SetString("49591239931264812013903123569363872165694192725937750565648544718012157267504", 10)
+ testMarshalCompressed(t, P256(), x, y, data)
+ })
+
+ t.Run("Invalid", func(t *testing.T) {
+ data, _ := hex.DecodeString("02fd4bf61763b46581fd9174d623516cf3c81edd40e29ffa2777fb6cb0ae3ce535")
+ X, Y := UnmarshalCompressed(P256(), data)
+ if X != nil || Y != nil {
+ t.Error("expected an error for invalid encoding")
+ }
+ })
+
+ if testing.Short() {
+ t.Skip("skipping other curves on short test")
+ }
+
+ testAllCurves(t, func(t *testing.T, curve Curve) {
+ _, x, y, err := GenerateKey(curve, rand.Reader)
+ if err != nil {
+ t.Fatal(err)
+ }
+ testMarshalCompressed(t, curve, x, y, nil)
+ })
+
+}
+
+func testMarshalCompressed(t *testing.T, curve Curve, x, y *big.Int, want []byte) {
+ if !curve.IsOnCurve(x, y) {
+ t.Fatal("invalid test point")
+ }
+ got := MarshalCompressed(curve, x, y)
+ if want != nil && !bytes.Equal(got, want) {
+ t.Errorf("got unexpected MarshalCompressed result: got %x, want %x", got, want)
+ }
+
+ X, Y := UnmarshalCompressed(curve, got)
+ if X == nil || Y == nil {
+ t.Fatalf("UnmarshalCompressed failed unexpectedly")
+ }
+
+ if !curve.IsOnCurve(X, Y) {
+ t.Error("UnmarshalCompressed returned a point not on the curve")
+ }
+ if X.Cmp(x) != 0 || Y.Cmp(y) != 0 {
+ t.Errorf("point did not round-trip correctly: got (%v, %v), want (%v, %v)", X, Y, x, y)
+ }
+}
+
+func TestLargeIsOnCurve(t *testing.T) {
+ t.Parallel()
+ testAllCurves(t, func(t *testing.T, curve Curve) {
+ large := big.NewInt(1)
+ large.Lsh(large, 1000)
+ if curve.IsOnCurve(large, large) {
+ t.Errorf("(2^1000, 2^1000) is reported on the curve")
+ }
+ })
+}
+
+func benchmarkAllCurves(b *testing.B, f func(*testing.B, Curve)) {
+ tests := []struct {
+ name string
+ curve Curve
+ }{
+ {"P256", P256()},
+ {"P224", P224()},
+ {"P384", P384()},
+ {"P521", P521()},
+ }
+ for _, test := range tests {
+ curve := test.curve
+ b.Run(test.name, func(b *testing.B) {
+ f(b, curve)
+ })
+ }
+}
+
+func BenchmarkScalarBaseMult(b *testing.B) {
+ benchmarkAllCurves(b, func(b *testing.B, curve Curve) {
+ priv, _, _, _ := GenerateKey(curve, rand.Reader)
+ b.ReportAllocs()
+ b.ResetTimer()
+ for i := 0; i < b.N; i++ {
+ x, _ := curve.ScalarBaseMult(priv)
+ // Prevent the compiler from optimizing out the operation.
+ priv[0] ^= byte(x.Bits()[0])
+ }
+ })
+}
+
+func BenchmarkScalarMult(b *testing.B) {
+ benchmarkAllCurves(b, func(b *testing.B, curve Curve) {
+ _, x, y, _ := GenerateKey(curve, rand.Reader)
+ priv, _, _, _ := GenerateKey(curve, rand.Reader)
+ b.ReportAllocs()
+ b.ResetTimer()
+ for i := 0; i < b.N; i++ {
+ x, y = curve.ScalarMult(x, y, priv)
+ }
+ })
+}
+
+func BenchmarkMarshalUnmarshal(b *testing.B) {
+ benchmarkAllCurves(b, func(b *testing.B, curve Curve) {
+ _, x, y, _ := GenerateKey(curve, rand.Reader)
+ b.Run("Uncompressed", func(b *testing.B) {
+ b.ReportAllocs()
+ for i := 0; i < b.N; i++ {
+ buf := Marshal(curve, x, y)
+ xx, yy := Unmarshal(curve, buf)
+ if xx.Cmp(x) != 0 || yy.Cmp(y) != 0 {
+ b.Error("Unmarshal output different from Marshal input")
+ }
+ }
+ })
+ b.Run("Compressed", func(b *testing.B) {
+ b.ReportAllocs()
+ for i := 0; i < b.N; i++ {
+ buf := MarshalCompressed(curve, x, y)
+ xx, yy := UnmarshalCompressed(curve, buf)
+ if xx.Cmp(x) != 0 || yy.Cmp(y) != 0 {
+ b.Error("Unmarshal output different from Marshal input")
+ }
+ }
+ })
+ })
+}
diff --git a/src/crypto/elliptic/nistec.go b/src/crypto/elliptic/nistec.go
new file mode 100644
index 0000000..d906c57
--- /dev/null
+++ b/src/crypto/elliptic/nistec.go
@@ -0,0 +1,294 @@
+// Copyright 2013 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 (
+ "crypto/internal/nistec"
+ "errors"
+ "math/big"
+)
+
+var p224 = &nistCurve[*nistec.P224Point]{
+ newPoint: nistec.NewP224Point,
+}
+
+func initP224() {
+ p224.params = &CurveParams{
+ Name: "P-224",
+ BitSize: 224,
+ // FIPS 186-4, section D.1.2.2
+ P: bigFromDecimal("26959946667150639794667015087019630673557916260026308143510066298881"),
+ N: bigFromDecimal("26959946667150639794667015087019625940457807714424391721682722368061"),
+ B: bigFromHex("b4050a850c04b3abf54132565044b0b7d7bfd8ba270b39432355ffb4"),
+ Gx: bigFromHex("b70e0cbd6bb4bf7f321390b94a03c1d356c21122343280d6115c1d21"),
+ Gy: bigFromHex("bd376388b5f723fb4c22dfe6cd4375a05a07476444d5819985007e34"),
+ }
+}
+
+type p256Curve struct {
+ nistCurve[*nistec.P256Point]
+}
+
+var p256 = &p256Curve{nistCurve[*nistec.P256Point]{
+ newPoint: nistec.NewP256Point,
+}}
+
+func initP256() {
+ p256.params = &CurveParams{
+ Name: "P-256",
+ BitSize: 256,
+ // FIPS 186-4, section D.1.2.3
+ P: bigFromDecimal("115792089210356248762697446949407573530086143415290314195533631308867097853951"),
+ N: bigFromDecimal("115792089210356248762697446949407573529996955224135760342422259061068512044369"),
+ B: bigFromHex("5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b"),
+ Gx: bigFromHex("6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296"),
+ Gy: bigFromHex("4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5"),
+ }
+}
+
+var p384 = &nistCurve[*nistec.P384Point]{
+ newPoint: nistec.NewP384Point,
+}
+
+func initP384() {
+ p384.params = &CurveParams{
+ Name: "P-384",
+ BitSize: 384,
+ // FIPS 186-4, section D.1.2.4
+ P: bigFromDecimal("394020061963944792122790401001436138050797392704654" +
+ "46667948293404245721771496870329047266088258938001861606973112319"),
+ N: bigFromDecimal("394020061963944792122790401001436138050797392704654" +
+ "46667946905279627659399113263569398956308152294913554433653942643"),
+ B: bigFromHex("b3312fa7e23ee7e4988e056be3f82d19181d9c6efe8141120314088" +
+ "f5013875ac656398d8a2ed19d2a85c8edd3ec2aef"),
+ Gx: bigFromHex("aa87ca22be8b05378eb1c71ef320ad746e1d3b628ba79b9859f741" +
+ "e082542a385502f25dbf55296c3a545e3872760ab7"),
+ Gy: bigFromHex("3617de4a96262c6f5d9e98bf9292dc29f8f41dbd289a147ce9da31" +
+ "13b5f0b8c00a60b1ce1d7e819d7a431d7c90ea0e5f"),
+ }
+}
+
+var p521 = &nistCurve[*nistec.P521Point]{
+ newPoint: nistec.NewP521Point,
+}
+
+func initP521() {
+ p521.params = &CurveParams{
+ Name: "P-521",
+ BitSize: 521,
+ // FIPS 186-4, section D.1.2.5
+ P: bigFromDecimal("68647976601306097149819007990813932172694353001433" +
+ "0540939446345918554318339765605212255964066145455497729631139148" +
+ "0858037121987999716643812574028291115057151"),
+ N: bigFromDecimal("68647976601306097149819007990813932172694353001433" +
+ "0540939446345918554318339765539424505774633321719753296399637136" +
+ "3321113864768612440380340372808892707005449"),
+ B: bigFromHex("0051953eb9618e1c9a1f929a21a0b68540eea2da725b99b315f3b8" +
+ "b489918ef109e156193951ec7e937b1652c0bd3bb1bf073573df883d2c34f1ef" +
+ "451fd46b503f00"),
+ Gx: bigFromHex("00c6858e06b70404e9cd9e3ecb662395b4429c648139053fb521f8" +
+ "28af606b4d3dbaa14b5e77efe75928fe1dc127a2ffa8de3348b3c1856a429bf9" +
+ "7e7e31c2e5bd66"),
+ Gy: bigFromHex("011839296a789a3bc0045c8a5fb42c7d1bd998f54449579b446817" +
+ "afbd17273e662c97ee72995ef42640c550b9013fad0761353c7086a272c24088" +
+ "be94769fd16650"),
+ }
+}
+
+// nistCurve is a Curve implementation based on a nistec Point.
+//
+// It's a wrapper that exposes the big.Int-based Curve interface and encodes the
+// legacy idiosyncrasies it requires, such as invalid and infinity point
+// handling.
+//
+// To interact with the nistec package, points are encoded into and decoded from
+// properly formatted byte slices. All big.Int use is limited to this package.
+// Encoding and decoding is 1/1000th of the runtime of a scalar multiplication,
+// so the overhead is acceptable.
+type nistCurve[Point nistPoint[Point]] struct {
+ newPoint func() Point
+ params *CurveParams
+}
+
+// nistPoint is a generic constraint for the nistec Point types.
+type nistPoint[T any] interface {
+ Bytes() []byte
+ SetBytes([]byte) (T, error)
+ Add(T, T) T
+ Double(T) T
+ ScalarMult(T, []byte) (T, error)
+ ScalarBaseMult([]byte) (T, error)
+}
+
+func (curve *nistCurve[Point]) Params() *CurveParams {
+ return curve.params
+}
+
+func (curve *nistCurve[Point]) IsOnCurve(x, y *big.Int) bool {
+ // IsOnCurve is documented to reject (0, 0), the conventional point at
+ // infinity, which however is accepted by pointFromAffine.
+ if x.Sign() == 0 && y.Sign() == 0 {
+ return false
+ }
+ _, err := curve.pointFromAffine(x, y)
+ return err == nil
+}
+
+func (curve *nistCurve[Point]) pointFromAffine(x, y *big.Int) (p Point, err error) {
+ // (0, 0) is by convention the point at infinity, which can't be represented
+ // in affine coordinates. See Issue 37294.
+ if x.Sign() == 0 && y.Sign() == 0 {
+ return curve.newPoint(), nil
+ }
+ // Reject values that would not get correctly encoded.
+ if x.Sign() < 0 || y.Sign() < 0 {
+ return p, errors.New("negative coordinate")
+ }
+ if x.BitLen() > curve.params.BitSize || y.BitLen() > curve.params.BitSize {
+ return p, errors.New("overflowing coordinate")
+ }
+ // Encode the coordinates and let SetBytes reject invalid points.
+ byteLen := (curve.params.BitSize + 7) / 8
+ buf := make([]byte, 1+2*byteLen)
+ buf[0] = 4 // uncompressed point
+ x.FillBytes(buf[1 : 1+byteLen])
+ y.FillBytes(buf[1+byteLen : 1+2*byteLen])
+ return curve.newPoint().SetBytes(buf)
+}
+
+func (curve *nistCurve[Point]) pointToAffine(p Point) (x, y *big.Int) {
+ out := p.Bytes()
+ if len(out) == 1 && out[0] == 0 {
+ // This is the encoding of the point at infinity, which the affine
+ // coordinates API represents as (0, 0) by convention.
+ return new(big.Int), new(big.Int)
+ }
+ byteLen := (curve.params.BitSize + 7) / 8
+ x = new(big.Int).SetBytes(out[1 : 1+byteLen])
+ y = new(big.Int).SetBytes(out[1+byteLen:])
+ return x, y
+}
+
+func (curve *nistCurve[Point]) Add(x1, y1, x2, y2 *big.Int) (*big.Int, *big.Int) {
+ p1, err := curve.pointFromAffine(x1, y1)
+ if err != nil {
+ panic("crypto/elliptic: Add was called on an invalid point")
+ }
+ p2, err := curve.pointFromAffine(x2, y2)
+ if err != nil {
+ panic("crypto/elliptic: Add was called on an invalid point")
+ }
+ return curve.pointToAffine(p1.Add(p1, p2))
+}
+
+func (curve *nistCurve[Point]) Double(x1, y1 *big.Int) (*big.Int, *big.Int) {
+ p, err := curve.pointFromAffine(x1, y1)
+ if err != nil {
+ panic("crypto/elliptic: Double was called on an invalid point")
+ }
+ return curve.pointToAffine(p.Double(p))
+}
+
+// normalizeScalar brings the scalar within the byte size of the order of the
+// curve, as expected by the nistec scalar multiplication functions.
+func (curve *nistCurve[Point]) normalizeScalar(scalar []byte) []byte {
+ byteSize := (curve.params.N.BitLen() + 7) / 8
+ if len(scalar) == byteSize {
+ return scalar
+ }
+ s := new(big.Int).SetBytes(scalar)
+ if len(scalar) > byteSize {
+ s.Mod(s, curve.params.N)
+ }
+ out := make([]byte, byteSize)
+ return s.FillBytes(out)
+}
+
+func (curve *nistCurve[Point]) ScalarMult(Bx, By *big.Int, scalar []byte) (*big.Int, *big.Int) {
+ p, err := curve.pointFromAffine(Bx, By)
+ if err != nil {
+ panic("crypto/elliptic: ScalarMult was called on an invalid point")
+ }
+ scalar = curve.normalizeScalar(scalar)
+ p, err = p.ScalarMult(p, scalar)
+ if err != nil {
+ panic("crypto/elliptic: nistec rejected normalized scalar")
+ }
+ return curve.pointToAffine(p)
+}
+
+func (curve *nistCurve[Point]) ScalarBaseMult(scalar []byte) (*big.Int, *big.Int) {
+ scalar = curve.normalizeScalar(scalar)
+ p, err := curve.newPoint().ScalarBaseMult(scalar)
+ if err != nil {
+ panic("crypto/elliptic: nistec rejected normalized scalar")
+ }
+ return curve.pointToAffine(p)
+}
+
+// CombinedMult returns [s1]G + [s2]P where G is the generator. It's used
+// through an interface upgrade in crypto/ecdsa.
+func (curve *nistCurve[Point]) CombinedMult(Px, Py *big.Int, s1, s2 []byte) (x, y *big.Int) {
+ s1 = curve.normalizeScalar(s1)
+ q, err := curve.newPoint().ScalarBaseMult(s1)
+ if err != nil {
+ panic("crypto/elliptic: nistec rejected normalized scalar")
+ }
+ p, err := curve.pointFromAffine(Px, Py)
+ if err != nil {
+ panic("crypto/elliptic: CombinedMult was called on an invalid point")
+ }
+ s2 = curve.normalizeScalar(s2)
+ p, err = p.ScalarMult(p, s2)
+ if err != nil {
+ panic("crypto/elliptic: nistec rejected normalized scalar")
+ }
+ return curve.pointToAffine(p.Add(p, q))
+}
+
+func (curve *nistCurve[Point]) Unmarshal(data []byte) (x, y *big.Int) {
+ if len(data) == 0 || data[0] != 4 {
+ return nil, nil
+ }
+ // Use SetBytes to check that data encodes a valid point.
+ _, err := curve.newPoint().SetBytes(data)
+ if err != nil {
+ return nil, nil
+ }
+ // We don't use pointToAffine because it involves an expensive field
+ // inversion to convert from Jacobian to affine coordinates, which we
+ // already have.
+ byteLen := (curve.params.BitSize + 7) / 8
+ x = new(big.Int).SetBytes(data[1 : 1+byteLen])
+ y = new(big.Int).SetBytes(data[1+byteLen:])
+ return x, y
+}
+
+func (curve *nistCurve[Point]) UnmarshalCompressed(data []byte) (x, y *big.Int) {
+ if len(data) == 0 || (data[0] != 2 && data[0] != 3) {
+ return nil, nil
+ }
+ p, err := curve.newPoint().SetBytes(data)
+ if err != nil {
+ return nil, nil
+ }
+ return curve.pointToAffine(p)
+}
+
+func bigFromDecimal(s string) *big.Int {
+ b, ok := new(big.Int).SetString(s, 10)
+ if !ok {
+ panic("crypto/elliptic: internal error: invalid encoding")
+ }
+ return b
+}
+
+func bigFromHex(s string) *big.Int {
+ b, ok := new(big.Int).SetString(s, 16)
+ if !ok {
+ panic("crypto/elliptic: internal error: invalid encoding")
+ }
+ return b
+}
diff --git a/src/crypto/elliptic/nistec_p256.go b/src/crypto/elliptic/nistec_p256.go
new file mode 100644
index 0000000..304f8f2
--- /dev/null
+++ b/src/crypto/elliptic/nistec_p256.go
@@ -0,0 +1,29 @@
+// Copyright 2022 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.
+
+//go:build amd64 || arm64
+
+package elliptic
+
+import (
+ "crypto/internal/nistec"
+ "math/big"
+)
+
+func (c p256Curve) Inverse(k *big.Int) *big.Int {
+ if k.Sign() < 0 {
+ // This should never happen.
+ k = new(big.Int).Neg(k)
+ }
+ if k.Cmp(c.params.N) >= 0 {
+ // This should never happen.
+ k = new(big.Int).Mod(k, c.params.N)
+ }
+ scalar := k.FillBytes(make([]byte, 32))
+ inverse, err := nistec.P256OrdInverse(scalar)
+ if err != nil {
+ panic("crypto/elliptic: nistec rejected normalized scalar")
+ }
+ return new(big.Int).SetBytes(inverse)
+}
diff --git a/src/crypto/elliptic/p224_test.go b/src/crypto/elliptic/p224_test.go
new file mode 100644
index 0000000..7971f63
--- /dev/null
+++ b/src/crypto/elliptic/p224_test.go
@@ -0,0 +1,325 @@
+// 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 (
+ "encoding/hex"
+ "fmt"
+ "math/big"
+ "testing"
+)
+
+type baseMultTest struct {
+ k string
+ x, y string
+}
+
+var p224BaseMultTests = []baseMultTest{
+ {
+ "1",
+ "b70e0cbd6bb4bf7f321390b94a03c1d356c21122343280d6115c1d21",
+ "bd376388b5f723fb4c22dfe6cd4375a05a07476444d5819985007e34",
+ },
+ {
+ "2",
+ "706a46dc76dcb76798e60e6d89474788d16dc18032d268fd1a704fa6",
+ "1c2b76a7bc25e7702a704fa986892849fca629487acf3709d2e4e8bb",
+ },
+ {
+ "3",
+ "df1b1d66a551d0d31eff822558b9d2cc75c2180279fe0d08fd896d04",
+ "a3f7f03cadd0be444c0aa56830130ddf77d317344e1af3591981a925",
+ },
+ {
+ "4",
+ "ae99feebb5d26945b54892092a8aee02912930fa41cd114e40447301",
+ "482580a0ec5bc47e88bc8c378632cd196cb3fa058a7114eb03054c9",
+ },
+ {
+ "5",
+ "31c49ae75bce7807cdff22055d94ee9021fedbb5ab51c57526f011aa",
+ "27e8bff1745635ec5ba0c9f1c2ede15414c6507d29ffe37e790a079b",
+ },
+ {
+ "6",
+ "1f2483f82572251fca975fea40db821df8ad82a3c002ee6c57112408",
+ "89faf0ccb750d99b553c574fad7ecfb0438586eb3952af5b4b153c7e",
+ },
+ {
+ "7",
+ "db2f6be630e246a5cf7d99b85194b123d487e2d466b94b24a03c3e28",
+ "f3a30085497f2f611ee2517b163ef8c53b715d18bb4e4808d02b963",
+ },
+ {
+ "8",
+ "858e6f9cc6c12c31f5df124aa77767b05c8bc021bd683d2b55571550",
+ "46dcd3ea5c43898c5c5fc4fdac7db39c2f02ebee4e3541d1e78047a",
+ },
+ {
+ "9",
+ "2fdcccfee720a77ef6cb3bfbb447f9383117e3daa4a07e36ed15f78d",
+ "371732e4f41bf4f7883035e6a79fcedc0e196eb07b48171697517463",
+ },
+ {
+ "10",
+ "aea9e17a306517eb89152aa7096d2c381ec813c51aa880e7bee2c0fd",
+ "39bb30eab337e0a521b6cba1abe4b2b3a3e524c14a3fe3eb116b655f",
+ },
+ {
+ "11",
+ "ef53b6294aca431f0f3c22dc82eb9050324f1d88d377e716448e507c",
+ "20b510004092e96636cfb7e32efded8265c266dfb754fa6d6491a6da",
+ },
+ {
+ "12",
+ "6e31ee1dc137f81b056752e4deab1443a481033e9b4c93a3044f4f7a",
+ "207dddf0385bfdeab6e9acda8da06b3bbef224a93ab1e9e036109d13",
+ },
+ {
+ "13",
+ "34e8e17a430e43289793c383fac9774247b40e9ebd3366981fcfaeca",
+ "252819f71c7fb7fbcb159be337d37d3336d7feb963724fdfb0ecb767",
+ },
+ {
+ "14",
+ "a53640c83dc208603ded83e4ecf758f24c357d7cf48088b2ce01e9fa",
+ "d5814cd724199c4a5b974a43685fbf5b8bac69459c9469bc8f23ccaf",
+ },
+ {
+ "15",
+ "baa4d8635511a7d288aebeedd12ce529ff102c91f97f867e21916bf9",
+ "979a5f4759f80f4fb4ec2e34f5566d595680a11735e7b61046127989",
+ },
+ {
+ "16",
+ "b6ec4fe1777382404ef679997ba8d1cc5cd8e85349259f590c4c66d",
+ "3399d464345906b11b00e363ef429221f2ec720d2f665d7dead5b482",
+ },
+ {
+ "17",
+ "b8357c3a6ceef288310e17b8bfeff9200846ca8c1942497c484403bc",
+ "ff149efa6606a6bd20ef7d1b06bd92f6904639dce5174db6cc554a26",
+ },
+ {
+ "18",
+ "c9ff61b040874c0568479216824a15eab1a838a797d189746226e4cc",
+ "ea98d60e5ffc9b8fcf999fab1df7e7ef7084f20ddb61bb045a6ce002",
+ },
+ {
+ "19",
+ "a1e81c04f30ce201c7c9ace785ed44cc33b455a022f2acdbc6cae83c",
+ "dcf1f6c3db09c70acc25391d492fe25b4a180babd6cea356c04719cd",
+ },
+ {
+ "20",
+ "fcc7f2b45df1cd5a3c0c0731ca47a8af75cfb0347e8354eefe782455",
+ "d5d7110274cba7cdee90e1a8b0d394c376a5573db6be0bf2747f530",
+ },
+ {
+ "112233445566778899",
+ "61f077c6f62ed802dad7c2f38f5c67f2cc453601e61bd076bb46179e",
+ "2272f9e9f5933e70388ee652513443b5e289dd135dcc0d0299b225e4",
+ },
+ {
+ "112233445566778899112233445566778899",
+ "29895f0af496bfc62b6ef8d8a65c88c613949b03668aab4f0429e35",
+ "3ea6e53f9a841f2019ec24bde1a75677aa9b5902e61081c01064de93",
+ },
+ {
+ "6950511619965839450988900688150712778015737983940691968051900319680",
+ "ab689930bcae4a4aa5f5cb085e823e8ae30fd365eb1da4aba9cf0379",
+ "3345a121bbd233548af0d210654eb40bab788a03666419be6fbd34e7",
+ },
+ {
+ "13479972933410060327035789020509431695094902435494295338570602119423",
+ "bdb6a8817c1f89da1c2f3dd8e97feb4494f2ed302a4ce2bc7f5f4025",
+ "4c7020d57c00411889462d77a5438bb4e97d177700bf7243a07f1680",
+ },
+ {
+ "13479971751745682581351455311314208093898607229429740618390390702079",
+ "d58b61aa41c32dd5eba462647dba75c5d67c83606c0af2bd928446a9",
+ "d24ba6a837be0460dd107ae77725696d211446c5609b4595976b16bd",
+ },
+ {
+ "13479972931865328106486971546324465392952975980343228160962702868479",
+ "dc9fa77978a005510980e929a1485f63716df695d7a0c18bb518df03",
+ "ede2b016f2ddffc2a8c015b134928275ce09e5661b7ab14ce0d1d403",
+ },
+ {
+ "11795773708834916026404142434151065506931607341523388140225443265536",
+ "499d8b2829cfb879c901f7d85d357045edab55028824d0f05ba279ba",
+ "bf929537b06e4015919639d94f57838fa33fc3d952598dcdbb44d638",
+ },
+ {
+ "784254593043826236572847595991346435467177662189391577090",
+ "8246c999137186632c5f9eddf3b1b0e1764c5e8bd0e0d8a554b9cb77",
+ "e80ed8660bc1cb17ac7d845be40a7a022d3306f116ae9f81fea65947",
+ },
+ {
+ "13479767645505654746623887797783387853576174193480695826442858012671",
+ "6670c20afcceaea672c97f75e2e9dd5c8460e54bb38538ebb4bd30eb",
+ "f280d8008d07a4caf54271f993527d46ff3ff46fd1190a3f1faa4f74",
+ },
+ {
+ "205688069665150753842126177372015544874550518966168735589597183",
+ "eca934247425cfd949b795cb5ce1eff401550386e28d1a4c5a8eb",
+ "d4c01040dba19628931bc8855370317c722cbd9ca6156985f1c2e9ce",
+ },
+ {
+ "13479966930919337728895168462090683249159702977113823384618282123295",
+ "ef353bf5c73cd551b96d596fbc9a67f16d61dd9fe56af19de1fba9cd",
+ "21771b9cdce3e8430c09b3838be70b48c21e15bc09ee1f2d7945b91f",
+ },
+ {
+ "50210731791415612487756441341851895584393717453129007497216",
+ "4036052a3091eb481046ad3289c95d3ac905ca0023de2c03ecd451cf",
+ "d768165a38a2b96f812586a9d59d4136035d9c853a5bf2e1c86a4993",
+ },
+ {
+ "26959946667150639794667015087019625940457807714424391721682722368041",
+ "fcc7f2b45df1cd5a3c0c0731ca47a8af75cfb0347e8354eefe782455",
+ "f2a28eefd8b345832116f1e574f2c6b2c895aa8c24941f40d8b80ad1",
+ },
+ {
+ "26959946667150639794667015087019625940457807714424391721682722368042",
+ "a1e81c04f30ce201c7c9ace785ed44cc33b455a022f2acdbc6cae83c",
+ "230e093c24f638f533dac6e2b6d01da3b5e7f45429315ca93fb8e634",
+ },
+ {
+ "26959946667150639794667015087019625940457807714424391721682722368043",
+ "c9ff61b040874c0568479216824a15eab1a838a797d189746226e4cc",
+ "156729f1a003647030666054e208180f8f7b0df2249e44fba5931fff",
+ },
+ {
+ "26959946667150639794667015087019625940457807714424391721682722368044",
+ "b8357c3a6ceef288310e17b8bfeff9200846ca8c1942497c484403bc",
+ "eb610599f95942df1082e4f9426d086fb9c6231ae8b24933aab5db",
+ },
+ {
+ "26959946667150639794667015087019625940457807714424391721682722368045",
+ "b6ec4fe1777382404ef679997ba8d1cc5cd8e85349259f590c4c66d",
+ "cc662b9bcba6f94ee4ff1c9c10bd6ddd0d138df2d099a282152a4b7f",
+ },
+ {
+ "26959946667150639794667015087019625940457807714424391721682722368046",
+ "baa4d8635511a7d288aebeedd12ce529ff102c91f97f867e21916bf9",
+ "6865a0b8a607f0b04b13d1cb0aa992a5a97f5ee8ca1849efb9ed8678",
+ },
+ {
+ "26959946667150639794667015087019625940457807714424391721682722368047",
+ "a53640c83dc208603ded83e4ecf758f24c357d7cf48088b2ce01e9fa",
+ "2a7eb328dbe663b5a468b5bc97a040a3745396ba636b964370dc3352",
+ },
+ {
+ "26959946667150639794667015087019625940457807714424391721682722368048",
+ "34e8e17a430e43289793c383fac9774247b40e9ebd3366981fcfaeca",
+ "dad7e608e380480434ea641cc82c82cbc92801469c8db0204f13489a",
+ },
+ {
+ "26959946667150639794667015087019625940457807714424391721682722368049",
+ "6e31ee1dc137f81b056752e4deab1443a481033e9b4c93a3044f4f7a",
+ "df82220fc7a4021549165325725f94c3410ddb56c54e161fc9ef62ee",
+ },
+ {
+ "26959946667150639794667015087019625940457807714424391721682722368050",
+ "ef53b6294aca431f0f3c22dc82eb9050324f1d88d377e716448e507c",
+ "df4aefffbf6d1699c930481cd102127c9a3d992048ab05929b6e5927",
+ },
+ {
+ "26959946667150639794667015087019625940457807714424391721682722368051",
+ "aea9e17a306517eb89152aa7096d2c381ec813c51aa880e7bee2c0fd",
+ "c644cf154cc81f5ade49345e541b4d4b5c1adb3eb5c01c14ee949aa2",
+ },
+ {
+ "26959946667150639794667015087019625940457807714424391721682722368052",
+ "2fdcccfee720a77ef6cb3bfbb447f9383117e3daa4a07e36ed15f78d",
+ "c8e8cd1b0be40b0877cfca1958603122f1e6914f84b7e8e968ae8b9e",
+ },
+ {
+ "26959946667150639794667015087019625940457807714424391721682722368053",
+ "858e6f9cc6c12c31f5df124aa77767b05c8bc021bd683d2b55571550",
+ "fb9232c15a3bc7673a3a03b0253824c53d0fd1411b1cabe2e187fb87",
+ },
+ {
+ "26959946667150639794667015087019625940457807714424391721682722368054",
+ "db2f6be630e246a5cf7d99b85194b123d487e2d466b94b24a03c3e28",
+ "f0c5cff7ab680d09ee11dae84e9c1072ac48ea2e744b1b7f72fd469e",
+ },
+ {
+ "26959946667150639794667015087019625940457807714424391721682722368055",
+ "1f2483f82572251fca975fea40db821df8ad82a3c002ee6c57112408",
+ "76050f3348af2664aac3a8b05281304ebc7a7914c6ad50a4b4eac383",
+ },
+ {
+ "26959946667150639794667015087019625940457807714424391721682722368056",
+ "31c49ae75bce7807cdff22055d94ee9021fedbb5ab51c57526f011aa",
+ "d817400e8ba9ca13a45f360e3d121eaaeb39af82d6001c8186f5f866",
+ },
+ {
+ "26959946667150639794667015087019625940457807714424391721682722368057",
+ "ae99feebb5d26945b54892092a8aee02912930fa41cd114e40447301",
+ "fb7da7f5f13a43b81774373c879cd32d6934c05fa758eeb14fcfab38",
+ },
+ {
+ "26959946667150639794667015087019625940457807714424391721682722368058",
+ "df1b1d66a551d0d31eff822558b9d2cc75c2180279fe0d08fd896d04",
+ "5c080fc3522f41bbb3f55a97cfecf21f882ce8cbb1e50ca6e67e56dc",
+ },
+ {
+ "26959946667150639794667015087019625940457807714424391721682722368059",
+ "706a46dc76dcb76798e60e6d89474788d16dc18032d268fd1a704fa6",
+ "e3d4895843da188fd58fb0567976d7b50359d6b78530c8f62d1b1746",
+ },
+ {
+ "26959946667150639794667015087019625940457807714424391721682722368060",
+ "b70e0cbd6bb4bf7f321390b94a03c1d356c21122343280d6115c1d21",
+ "42c89c774a08dc04b3dd201932bc8a5ea5f8b89bbb2a7e667aff81cd",
+ },
+}
+
+func TestP224BaseMult(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 TestP224GenericBaseMult(t *testing.T) {
+ // We use the P224 CurveParams directly in order to test the generic implementation.
+ p224 := genericParamsForCurve(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 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")
+ }
+}
diff --git a/src/crypto/elliptic/p256_test.go b/src/crypto/elliptic/p256_test.go
new file mode 100644
index 0000000..a607766
--- /dev/null
+++ b/src/crypto/elliptic/p256_test.go
@@ -0,0 +1,152 @@
+// Copyright 2021 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"
+)
+
+type scalarMultTest struct {
+ k string
+ xIn, yIn string
+ xOut, yOut string
+}
+
+var p256MultTests = []scalarMultTest{
+ {
+ "2a265f8bcbdcaf94d58519141e578124cb40d64a501fba9c11847b28965bc737",
+ "023819813ac969847059028ea88a1f30dfbcde03fc791d3a252c6b41211882ea",
+ "f93e4ae433cc12cf2a43fc0ef26400c0e125508224cdb649380f25479148a4ad",
+ "4d4de80f1534850d261075997e3049321a0864082d24a917863366c0724f5ae3",
+ "a22d2b7f7818a3563e0f7a76c9bf0921ac55e06e2e4d11795b233824b1db8cc0",
+ },
+ {
+ "313f72ff9fe811bf573176231b286a3bdb6f1b14e05c40146590727a71c3bccd",
+ "cc11887b2d66cbae8f4d306627192522932146b42f01d3c6f92bd5c8ba739b06",
+ "a2f08a029cd06b46183085bae9248b0ed15b70280c7ef13a457f5af382426031",
+ "831c3f6b5f762d2f461901577af41354ac5f228c2591f84f8a6e51e2e3f17991",
+ "93f90934cd0ef2c698cc471c60a93524e87ab31ca2412252337f364513e43684",
+ },
+}
+
+func TestP256BaseMult(t *testing.T) {
+ p256 := P256()
+ p256Generic := genericParamsForCurve(p256)
+
+ scalars := make([]*big.Int, 0, len(p224BaseMultTests)+1)
+ for _, e := range p224BaseMultTests {
+ k, _ := new(big.Int).SetString(e.k, 10)
+ scalars = append(scalars, k)
+ }
+ k := new(big.Int).SetInt64(1)
+ k.Lsh(k, 500)
+ scalars = append(scalars, k)
+
+ for i, k := range scalars {
+ x, y := p256.ScalarBaseMult(k.Bytes())
+ x2, y2 := p256Generic.ScalarBaseMult(k.Bytes())
+ if x.Cmp(x2) != 0 || y.Cmp(y2) != 0 {
+ t.Errorf("#%d: got (%x, %x), want (%x, %x)", i, x, y, x2, y2)
+ }
+
+ if testing.Short() && i > 5 {
+ break
+ }
+ }
+}
+
+func TestP256Mult(t *testing.T) {
+ p256 := P256()
+ for i, e := range p256MultTests {
+ x, _ := new(big.Int).SetString(e.xIn, 16)
+ y, _ := new(big.Int).SetString(e.yIn, 16)
+ k, _ := new(big.Int).SetString(e.k, 16)
+ expectedX, _ := new(big.Int).SetString(e.xOut, 16)
+ expectedY, _ := new(big.Int).SetString(e.yOut, 16)
+
+ xx, yy := p256.ScalarMult(x, y, k.Bytes())
+ if xx.Cmp(expectedX) != 0 || yy.Cmp(expectedY) != 0 {
+ t.Errorf("#%d: got (%x, %x), want (%x, %x)", i, xx, yy, expectedX, expectedY)
+ }
+ }
+}
+
+type synthCombinedMult struct {
+ Curve
+}
+
+func (s synthCombinedMult) CombinedMult(bigX, bigY *big.Int, baseScalar, scalar []byte) (x, y *big.Int) {
+ x1, y1 := s.ScalarBaseMult(baseScalar)
+ x2, y2 := s.ScalarMult(bigX, bigY, scalar)
+ return s.Add(x1, y1, x2, y2)
+}
+
+func TestP256CombinedMult(t *testing.T) {
+ type combinedMult interface {
+ Curve
+ CombinedMult(bigX, bigY *big.Int, baseScalar, scalar []byte) (x, y *big.Int)
+ }
+
+ p256, ok := P256().(combinedMult)
+ if !ok {
+ p256 = &synthCombinedMult{P256()}
+ }
+
+ gx := p256.Params().Gx
+ gy := p256.Params().Gy
+
+ zero := make([]byte, 32)
+ one := make([]byte, 32)
+ one[31] = 1
+ two := make([]byte, 32)
+ two[31] = 2
+
+ // 0×G + 0×G = ∞
+ x, y := p256.CombinedMult(gx, gy, zero, zero)
+ if x.Sign() != 0 || y.Sign() != 0 {
+ t.Errorf("0×G + 0×G = (%d, %d), should be ∞", x, y)
+ }
+
+ // 1×G + 0×G = G
+ x, y = p256.CombinedMult(gx, gy, one, zero)
+ if x.Cmp(gx) != 0 || y.Cmp(gy) != 0 {
+ t.Errorf("1×G + 0×G = (%d, %d), should be (%d, %d)", x, y, gx, gy)
+ }
+
+ // 0×G + 1×G = G
+ x, y = p256.CombinedMult(gx, gy, zero, one)
+ if x.Cmp(gx) != 0 || y.Cmp(gy) != 0 {
+ t.Errorf("0×G + 1×G = (%d, %d), should be (%d, %d)", x, y, gx, gy)
+ }
+
+ // 1×G + 1×G = 2×G
+ x, y = p256.CombinedMult(gx, gy, one, one)
+ ggx, ggy := p256.ScalarBaseMult(two)
+ if x.Cmp(ggx) != 0 || y.Cmp(ggy) != 0 {
+ t.Errorf("1×G + 1×G = (%d, %d), should be (%d, %d)", x, y, ggx, ggy)
+ }
+
+ minusOne := new(big.Int).Sub(p256.Params().N, big.NewInt(1))
+ // 1×G + (-1)×G = ∞
+ x, y = p256.CombinedMult(gx, gy, one, minusOne.Bytes())
+ if x.Sign() != 0 || y.Sign() != 0 {
+ t.Errorf("1×G + (-1)×G = (%d, %d), should be ∞", x, y)
+ }
+}
+
+func TestIssue52075(t *testing.T) {
+ Gx, Gy := P256().Params().Gx, P256().Params().Gy
+ scalar := make([]byte, 33)
+ scalar[32] = 1
+ x, y := P256().ScalarBaseMult(scalar)
+ if x.Cmp(Gx) != 0 || y.Cmp(Gy) != 0 {
+ t.Errorf("unexpected output (%v,%v)", x, y)
+ }
+ x, y = P256().ScalarMult(Gx, Gy, scalar)
+ if x.Cmp(Gx) != 0 || y.Cmp(Gy) != 0 {
+ t.Errorf("unexpected output (%v,%v)", x, y)
+ }
+}
diff --git a/src/crypto/elliptic/params.go b/src/crypto/elliptic/params.go
new file mode 100644
index 0000000..1ae57fa
--- /dev/null
+++ b/src/crypto/elliptic/params.go
@@ -0,0 +1,334 @@
+// Copyright 2021 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"
+
+// CurveParams contains the parameters of an elliptic curve and also provides
+// a generic, non-constant time implementation of Curve.
+//
+// The generic Curve implementation is deprecated, and using custom curves
+// (those not returned by P224(), P256(), P384(), and P521()) is not guaranteed
+// to provide any security property.
+type CurveParams struct {
+ P *big.Int // the order of the underlying field
+ N *big.Int // the order of the base point
+ B *big.Int // the constant of the curve equation
+ Gx, Gy *big.Int // (x,y) of the base point
+ BitSize int // the size of the underlying field
+ Name string // the canonical name of the curve
+}
+
+func (curve *CurveParams) Params() *CurveParams {
+ return curve
+}
+
+// CurveParams operates, internally, on Jacobian coordinates. For a given
+// (x, y) position on the curve, the Jacobian coordinates are (x1, y1, z1)
+// where x = x1/z1² and y = y1/z1³. The greatest speedups come when the whole
+// calculation can be performed within the transform (as in ScalarMult and
+// ScalarBaseMult). But even for Add and Double, it's faster to apply and
+// reverse the transform than to operate in affine coordinates.
+
+// polynomial returns x³ - 3x + b.
+func (curve *CurveParams) polynomial(x *big.Int) *big.Int {
+ x3 := new(big.Int).Mul(x, x)
+ x3.Mul(x3, x)
+
+ threeX := new(big.Int).Lsh(x, 1)
+ threeX.Add(threeX, x)
+
+ x3.Sub(x3, threeX)
+ x3.Add(x3, curve.B)
+ x3.Mod(x3, curve.P)
+
+ return x3
+}
+
+// IsOnCurve implements Curve.IsOnCurve.
+//
+// Deprecated: the CurveParams methods are deprecated and are not guaranteed to
+// provide any security property. For ECDH, use the crypto/ecdh package.
+// For ECDSA, use the crypto/ecdsa package with a Curve value returned directly
+// from P224(), P256(), P384(), or P521().
+func (curve *CurveParams) IsOnCurve(x, y *big.Int) bool {
+ // If there is a dedicated constant-time implementation for this curve operation,
+ // use that instead of the generic one.
+ if specific, ok := matchesSpecificCurve(curve); ok {
+ return specific.IsOnCurve(x, y)
+ }
+
+ if x.Sign() < 0 || x.Cmp(curve.P) >= 0 ||
+ y.Sign() < 0 || y.Cmp(curve.P) >= 0 {
+ return false
+ }
+
+ // y² = x³ - 3x + b
+ y2 := new(big.Int).Mul(y, y)
+ y2.Mod(y2, curve.P)
+
+ return curve.polynomial(x).Cmp(y2) == 0
+}
+
+// zForAffine returns a Jacobian Z value for the affine point (x, y). If x and
+// y are zero, it assumes that they represent the point at infinity because (0,
+// 0) is not on the any of the curves handled here.
+func zForAffine(x, y *big.Int) *big.Int {
+ z := new(big.Int)
+ if x.Sign() != 0 || y.Sign() != 0 {
+ z.SetInt64(1)
+ }
+ return z
+}
+
+// affineFromJacobian reverses the Jacobian transform. See the comment at the
+// top of the file. If the point is ∞ it returns 0, 0.
+func (curve *CurveParams) affineFromJacobian(x, y, z *big.Int) (xOut, yOut *big.Int) {
+ if z.Sign() == 0 {
+ return new(big.Int), new(big.Int)
+ }
+
+ zinv := new(big.Int).ModInverse(z, curve.P)
+ zinvsq := new(big.Int).Mul(zinv, zinv)
+
+ xOut = new(big.Int).Mul(x, zinvsq)
+ xOut.Mod(xOut, curve.P)
+ zinvsq.Mul(zinvsq, zinv)
+ yOut = new(big.Int).Mul(y, zinvsq)
+ yOut.Mod(yOut, curve.P)
+ return
+}
+
+// Add implements Curve.Add.
+//
+// Deprecated: the CurveParams methods are deprecated and are not guaranteed to
+// provide any security property. For ECDH, use the crypto/ecdh package.
+// For ECDSA, use the crypto/ecdsa package with a Curve value returned directly
+// from P224(), P256(), P384(), or P521().
+func (curve *CurveParams) Add(x1, y1, x2, y2 *big.Int) (*big.Int, *big.Int) {
+ // If there is a dedicated constant-time implementation for this curve operation,
+ // use that instead of the generic one.
+ if specific, ok := matchesSpecificCurve(curve); ok {
+ return specific.Add(x1, y1, x2, y2)
+ }
+ panicIfNotOnCurve(curve, x1, y1)
+ panicIfNotOnCurve(curve, x2, y2)
+
+ z1 := zForAffine(x1, y1)
+ z2 := zForAffine(x2, y2)
+ return curve.affineFromJacobian(curve.addJacobian(x1, y1, z1, x2, y2, z2))
+}
+
+// addJacobian takes two points in Jacobian coordinates, (x1, y1, z1) and
+// (x2, y2, z2) and returns their sum, also in Jacobian form.
+func (curve *CurveParams) addJacobian(x1, y1, z1, x2, y2, z2 *big.Int) (*big.Int, *big.Int, *big.Int) {
+ // See https://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#addition-add-2007-bl
+ x3, y3, z3 := new(big.Int), new(big.Int), new(big.Int)
+ if z1.Sign() == 0 {
+ x3.Set(x2)
+ y3.Set(y2)
+ z3.Set(z2)
+ return x3, y3, z3
+ }
+ if z2.Sign() == 0 {
+ x3.Set(x1)
+ y3.Set(y1)
+ z3.Set(z1)
+ return x3, y3, z3
+ }
+
+ z1z1 := new(big.Int).Mul(z1, z1)
+ z1z1.Mod(z1z1, curve.P)
+ z2z2 := new(big.Int).Mul(z2, z2)
+ z2z2.Mod(z2z2, curve.P)
+
+ u1 := new(big.Int).Mul(x1, z2z2)
+ u1.Mod(u1, curve.P)
+ u2 := new(big.Int).Mul(x2, z1z1)
+ u2.Mod(u2, curve.P)
+ h := new(big.Int).Sub(u2, u1)
+ xEqual := h.Sign() == 0
+ if h.Sign() == -1 {
+ h.Add(h, curve.P)
+ }
+ i := new(big.Int).Lsh(h, 1)
+ i.Mul(i, i)
+ j := new(big.Int).Mul(h, i)
+
+ s1 := new(big.Int).Mul(y1, z2)
+ s1.Mul(s1, z2z2)
+ s1.Mod(s1, curve.P)
+ s2 := new(big.Int).Mul(y2, z1)
+ s2.Mul(s2, z1z1)
+ s2.Mod(s2, curve.P)
+ r := new(big.Int).Sub(s2, s1)
+ if r.Sign() == -1 {
+ r.Add(r, curve.P)
+ }
+ yEqual := r.Sign() == 0
+ if xEqual && yEqual {
+ return curve.doubleJacobian(x1, y1, z1)
+ }
+ r.Lsh(r, 1)
+ v := new(big.Int).Mul(u1, i)
+
+ x3.Set(r)
+ x3.Mul(x3, x3)
+ x3.Sub(x3, j)
+ x3.Sub(x3, v)
+ x3.Sub(x3, v)
+ x3.Mod(x3, curve.P)
+
+ y3.Set(r)
+ v.Sub(v, x3)
+ y3.Mul(y3, v)
+ s1.Mul(s1, j)
+ s1.Lsh(s1, 1)
+ y3.Sub(y3, s1)
+ y3.Mod(y3, curve.P)
+
+ z3.Add(z1, z2)
+ z3.Mul(z3, z3)
+ z3.Sub(z3, z1z1)
+ z3.Sub(z3, z2z2)
+ z3.Mul(z3, h)
+ z3.Mod(z3, curve.P)
+
+ return x3, y3, z3
+}
+
+// Double implements Curve.Double.
+//
+// Deprecated: the CurveParams methods are deprecated and are not guaranteed to
+// provide any security property. For ECDH, use the crypto/ecdh package.
+// For ECDSA, use the crypto/ecdsa package with a Curve value returned directly
+// from P224(), P256(), P384(), or P521().
+func (curve *CurveParams) Double(x1, y1 *big.Int) (*big.Int, *big.Int) {
+ // If there is a dedicated constant-time implementation for this curve operation,
+ // use that instead of the generic one.
+ if specific, ok := matchesSpecificCurve(curve); ok {
+ return specific.Double(x1, y1)
+ }
+ panicIfNotOnCurve(curve, x1, y1)
+
+ z1 := zForAffine(x1, y1)
+ return curve.affineFromJacobian(curve.doubleJacobian(x1, y1, z1))
+}
+
+// doubleJacobian takes a point in Jacobian coordinates, (x, y, z), and
+// returns its double, also in Jacobian form.
+func (curve *CurveParams) doubleJacobian(x, y, z *big.Int) (*big.Int, *big.Int, *big.Int) {
+ // See https://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#doubling-dbl-2001-b
+ delta := new(big.Int).Mul(z, z)
+ delta.Mod(delta, curve.P)
+ gamma := new(big.Int).Mul(y, y)
+ gamma.Mod(gamma, curve.P)
+ alpha := new(big.Int).Sub(x, delta)
+ if alpha.Sign() == -1 {
+ alpha.Add(alpha, curve.P)
+ }
+ alpha2 := new(big.Int).Add(x, delta)
+ alpha.Mul(alpha, alpha2)
+ alpha2.Set(alpha)
+ alpha.Lsh(alpha, 1)
+ alpha.Add(alpha, alpha2)
+
+ beta := alpha2.Mul(x, gamma)
+
+ x3 := new(big.Int).Mul(alpha, alpha)
+ beta8 := new(big.Int).Lsh(beta, 3)
+ beta8.Mod(beta8, curve.P)
+ x3.Sub(x3, beta8)
+ if x3.Sign() == -1 {
+ x3.Add(x3, curve.P)
+ }
+ x3.Mod(x3, curve.P)
+
+ z3 := new(big.Int).Add(y, z)
+ z3.Mul(z3, z3)
+ z3.Sub(z3, gamma)
+ if z3.Sign() == -1 {
+ z3.Add(z3, curve.P)
+ }
+ z3.Sub(z3, delta)
+ if z3.Sign() == -1 {
+ z3.Add(z3, curve.P)
+ }
+ z3.Mod(z3, curve.P)
+
+ beta.Lsh(beta, 2)
+ beta.Sub(beta, x3)
+ if beta.Sign() == -1 {
+ beta.Add(beta, curve.P)
+ }
+ y3 := alpha.Mul(alpha, beta)
+
+ gamma.Mul(gamma, gamma)
+ gamma.Lsh(gamma, 3)
+ gamma.Mod(gamma, curve.P)
+
+ y3.Sub(y3, gamma)
+ if y3.Sign() == -1 {
+ y3.Add(y3, curve.P)
+ }
+ y3.Mod(y3, curve.P)
+
+ return x3, y3, z3
+}
+
+// ScalarMult implements Curve.ScalarMult.
+//
+// Deprecated: the CurveParams methods are deprecated and are not guaranteed to
+// provide any security property. For ECDH, use the crypto/ecdh package.
+// For ECDSA, use the crypto/ecdsa package with a Curve value returned directly
+// from P224(), P256(), P384(), or P521().
+func (curve *CurveParams) ScalarMult(Bx, By *big.Int, k []byte) (*big.Int, *big.Int) {
+ // If there is a dedicated constant-time implementation for this curve operation,
+ // use that instead of the generic one.
+ if specific, ok := matchesSpecificCurve(curve); ok {
+ return specific.ScalarMult(Bx, By, k)
+ }
+ panicIfNotOnCurve(curve, Bx, By)
+
+ Bz := new(big.Int).SetInt64(1)
+ x, y, z := new(big.Int), new(big.Int), new(big.Int)
+
+ for _, byte := range k {
+ for bitNum := 0; bitNum < 8; bitNum++ {
+ x, y, z = curve.doubleJacobian(x, y, z)
+ if byte&0x80 == 0x80 {
+ x, y, z = curve.addJacobian(Bx, By, Bz, x, y, z)
+ }
+ byte <<= 1
+ }
+ }
+
+ return curve.affineFromJacobian(x, y, z)
+}
+
+// ScalarBaseMult implements Curve.ScalarBaseMult.
+//
+// Deprecated: the CurveParams methods are deprecated and are not guaranteed to
+// provide any security property. For ECDH, use the crypto/ecdh package.
+// For ECDSA, use the crypto/ecdsa package with a Curve value returned directly
+// from P224(), P256(), P384(), or P521().
+func (curve *CurveParams) ScalarBaseMult(k []byte) (*big.Int, *big.Int) {
+ // If there is a dedicated constant-time implementation for this curve operation,
+ // use that instead of the generic one.
+ if specific, ok := matchesSpecificCurve(curve); ok {
+ return specific.ScalarBaseMult(k)
+ }
+
+ return curve.ScalarMult(curve.Gx, curve.Gy, k)
+}
+
+func matchesSpecificCurve(params *CurveParams) (Curve, bool) {
+ for _, c := range []Curve{p224, p256, p384, p521} {
+ if params == c.Params() {
+ return c, true
+ }
+ }
+ return nil, false
+}
generated by cgit v1.2.3 (git 2.39.1) at 2024-10-10 13:25:29 +0000