| // 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) { |
| p = curve.newPoint() |
| // (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 p, 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 p.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 |
| } |