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Diffstat (limited to 'src/pkg/crypto/elliptic/elliptic.go')
-rw-r--r-- | src/pkg/crypto/elliptic/elliptic.go | 381 |
1 files changed, 0 insertions, 381 deletions
diff --git a/src/pkg/crypto/elliptic/elliptic.go b/src/pkg/crypto/elliptic/elliptic.go deleted file mode 100644 index 41835f1a9..000000000 --- a/src/pkg/crypto/elliptic/elliptic.go +++ /dev/null @@ -1,381 +0,0 @@ -// 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 several standard elliptic curves over prime -// fields. -package elliptic - -// This package 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. - -import ( - "big" - "io" - "os" - "sync" -) - -// A Curve represents a short-form Weierstrass curve with a=-3. -// See http://www.hyperelliptic.org/EFD/g1p/auto-shortw.html -type Curve 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 -} - -// IsOnCurve returns true if the given (x,y) lies on the curve. -func (curve *Curve) IsOnCurve(x, y *big.Int) bool { - // y² = x³ - 3x + b - y2 := new(big.Int).Mul(y, y) - y2.Mod(y2, curve.P) - - 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.Cmp(y2) == 0 -} - -// affineFromJacobian reverses the Jacobian transform. See the comment at the -// top of the file. -func (curve *Curve) affineFromJacobian(x, y, z *big.Int) (xOut, yOut *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 returns the sum of (x1,y1) and (x2,y2) -func (curve *Curve) Add(x1, y1, x2, y2 *big.Int) (*big.Int, *big.Int) { - z := new(big.Int).SetInt64(1) - return curve.affineFromJacobian(curve.addJacobian(x1, y1, z, x2, y2, z)) -} - -// addJacobian takes two points in Jacobian coordinates, (x1, y1, z1) and -// (x2, y2, z2) and returns their sum, also in Jacobian form. -func (curve *Curve) addJacobian(x1, y1, z1, x2, y2, z2 *big.Int) (*big.Int, *big.Int, *big.Int) { - // See http://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#addition-add-2007-bl - 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) - 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) - } - r.Lsh(r, 1) - v := new(big.Int).Mul(u1, i) - - x3 := new(big.Int).Set(r) - x3.Mul(x3, x3) - x3.Sub(x3, j) - x3.Sub(x3, v) - x3.Sub(x3, v) - x3.Mod(x3, curve.P) - - y3 := new(big.Int).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 := new(big.Int).Add(z1, z2) - z3.Mul(z3, z3) - z3.Sub(z3, z1z1) - if z3.Sign() == -1 { - z3.Add(z3, curve.P) - } - z3.Sub(z3, z2z2) - if z3.Sign() == -1 { - z3.Add(z3, curve.P) - } - z3.Mul(z3, h) - z3.Mod(z3, curve.P) - - return x3, y3, z3 -} - -// Double returns 2*(x,y) -func (curve *Curve) Double(x1, y1 *big.Int) (*big.Int, *big.Int) { - z1 := new(big.Int).SetInt64(1) - 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 *Curve) doubleJacobian(x, y, z *big.Int) (*big.Int, *big.Int, *big.Int) { - // See http://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) - x3.Sub(x3, beta8) - for 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 returns k*(Bx,By) where k is a number in big-endian form. -func (curve *Curve) ScalarMult(Bx, By *big.Int, k []byte) (*big.Int, *big.Int) { - // We have a slight problem in that the identity of the group (the - // point at infinity) cannot be represented in (x, y) form on a finite - // machine. Thus the standard add/double algorithm has to be tweaked - // slightly: our initial state is not the identity, but x, and we - // ignore the first true bit in |k|. If we don't find any true bits in - // |k|, then we return nil, nil, because we cannot return the identity - // element. - - Bz := new(big.Int).SetInt64(1) - x := Bx - y := By - z := Bz - - seenFirstTrue := false - for _, byte := range k { - for bitNum := 0; bitNum < 8; bitNum++ { - if seenFirstTrue { - x, y, z = curve.doubleJacobian(x, y, z) - } - if byte&0x80 == 0x80 { - if !seenFirstTrue { - seenFirstTrue = true - } else { - x, y, z = curve.addJacobian(Bx, By, Bz, x, y, z) - } - } - byte <<= 1 - } - } - - if !seenFirstTrue { - return nil, nil - } - - return curve.affineFromJacobian(x, y, z) -} - -// ScalarBaseMult returns k*G, where G is the base point of the group and k is -// an integer in big-endian form. -func (curve *Curve) ScalarBaseMult(k []byte) (*big.Int, *big.Int) { - return curve.ScalarMult(curve.Gx, curve.Gy, k) -} - -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 (curve *Curve) GenerateKey(rand io.Reader) (priv []byte, x, y *big.Int, err os.Error) { - byteLen := (curve.BitSize + 7) >> 3 - 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[curve.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 - x, y = curve.ScalarBaseMult(priv) - } - return -} - -// Marshal converts a point into the form specified in section 4.3.6 of ANSI -// X9.62. -func (curve *Curve) Marshal(x, y *big.Int) []byte { - byteLen := (curve.BitSize + 7) >> 3 - - ret := make([]byte, 1+2*byteLen) - ret[0] = 4 // uncompressed point - - xBytes := x.Bytes() - copy(ret[1+byteLen-len(xBytes):], xBytes) - yBytes := y.Bytes() - copy(ret[1+2*byteLen-len(yBytes):], yBytes) - return ret -} - -// Unmarshal converts a point, serialized by Marshal, into an x, y pair. On -// error, x = nil. -func (curve *Curve) Unmarshal(data []byte) (x, y *big.Int) { - byteLen := (curve.BitSize + 7) >> 3 - if len(data) != 1+2*byteLen { - return - } - if data[0] != 4 { // uncompressed form - return - } - x = new(big.Int).SetBytes(data[1 : 1+byteLen]) - y = new(big.Int).SetBytes(data[1+byteLen:]) - return -} - -var initonce sync.Once -var p224 *Curve -var p256 *Curve -var p384 *Curve -var p521 *Curve - -func initAll() { - initP224() - initP256() - initP384() - initP521() -} - -func initP224() { - // See FIPS 186-3, section D.2.2 - p224 = new(Curve) - 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 -} - -func initP256() { - // See FIPS 186-3, section D.2.3 - p256 = new(Curve) - p256.P, _ = new(big.Int).SetString("115792089210356248762697446949407573530086143415290314195533631308867097853951", 10) - p256.N, _ = new(big.Int).SetString("115792089210356248762697446949407573529996955224135760342422259061068512044369", 10) - p256.B, _ = new(big.Int).SetString("5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b", 16) - p256.Gx, _ = new(big.Int).SetString("6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296", 16) - p256.Gy, _ = new(big.Int).SetString("4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5", 16) - p256.BitSize = 256 -} - -func initP384() { - // See FIPS 186-3, section D.2.4 - p384 = new(Curve) - p384.P, _ = new(big.Int).SetString("39402006196394479212279040100143613805079739270465446667948293404245721771496870329047266088258938001861606973112319", 10) - p384.N, _ = new(big.Int).SetString("39402006196394479212279040100143613805079739270465446667946905279627659399113263569398956308152294913554433653942643", 10) - p384.B, _ = new(big.Int).SetString("b3312fa7e23ee7e4988e056be3f82d19181d9c6efe8141120314088f5013875ac656398d8a2ed19d2a85c8edd3ec2aef", 16) - p384.Gx, _ = new(big.Int).SetString("aa87ca22be8b05378eb1c71ef320ad746e1d3b628ba79b9859f741e082542a385502f25dbf55296c3a545e3872760ab7", 16) - p384.Gy, _ = new(big.Int).SetString("3617de4a96262c6f5d9e98bf9292dc29f8f41dbd289a147ce9da3113b5f0b8c00a60b1ce1d7e819d7a431d7c90ea0e5f", 16) - p384.BitSize = 384 -} - -func initP521() { - // See FIPS 186-3, section D.2.5 - p521 = new(Curve) - p521.P, _ = new(big.Int).SetString("6864797660130609714981900799081393217269435300143305409394463459185543183397656052122559640661454554977296311391480858037121987999716643812574028291115057151", 10) - p521.N, _ = new(big.Int).SetString("6864797660130609714981900799081393217269435300143305409394463459185543183397655394245057746333217197532963996371363321113864768612440380340372808892707005449", 10) - p521.B, _ = new(big.Int).SetString("051953eb9618e1c9a1f929a21a0b68540eea2da725b99b315f3b8b489918ef109e156193951ec7e937b1652c0bd3bb1bf073573df883d2c34f1ef451fd46b503f00", 16) - p521.Gx, _ = new(big.Int).SetString("c6858e06b70404e9cd9e3ecb662395b4429c648139053fb521f828af606b4d3dbaa14b5e77efe75928fe1dc127a2ffa8de3348b3c1856a429bf97e7e31c2e5bd66", 16) - p521.Gy, _ = new(big.Int).SetString("11839296a789a3bc0045c8a5fb42c7d1bd998f54449579b446817afbd17273e662c97ee72995ef42640c550b9013fad0761353c7086a272c24088be94769fd16650", 16) - p521.BitSize = 521 -} - -// P224 returns a Curve which implements P-224 (see FIPS 186-3, section D.2.2) -func P224() *Curve { - initonce.Do(initAll) - return p224 -} - -// P256 returns a Curve which implements P-256 (see FIPS 186-3, section D.2.3) -func P256() *Curve { - initonce.Do(initAll) - return p256 -} - -// P384 returns a Curve which implements P-384 (see FIPS 186-3, section D.2.4) -func P384() *Curve { - initonce.Do(initAll) - return p384 -} - -// P256 returns a Curve which implements P-521 (see FIPS 186-3, section D.2.5) -func P521() *Curve { - initonce.Do(initAll) - return p521 -} |