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Diffstat (limited to 'src/crypto/elliptic/elliptic.go')
-rw-r--r-- | src/crypto/elliptic/elliptic.go | 242 |
1 files changed, 242 insertions, 0 deletions
diff --git a/src/crypto/elliptic/elliptic.go b/src/crypto/elliptic/elliptic.go new file mode 100644 index 0000000..8c0b60b --- /dev/null +++ b/src/crypto/elliptic/elliptic.go @@ -0,0 +1,242 @@ +// 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. +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). +type Curve interface { + // Params returns the parameters for the curve. + Params() *CurveParams + // IsOnCurve reports whether the given (x,y) lies on the curve. + IsOnCurve(x, y *big.Int) bool + // Add returns the sum of (x1,y1) and (x2,y2) + Add(x1, y1, x2, y2 *big.Int) (x, y *big.Int) + // Double returns 2*(x,y) + Double(x1, y1 *big.Int) (x, y *big.Int) + // ScalarMult returns k*(Bx,By) where k is a number in big-endian form. + 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. + 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. +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. +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. +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 +} |