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https://github.com/golang/go
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crypto/elliptic: refactor package structure
Not quite golang.org/wiki/TargetSpecific compliant, but almost. The only substantial code change is in randFieldElement: it used to use Params().BitSize instead of Params().N.BitLen(), which is semantically incorrect, even if the two values are the same for all named curves. For #52182 Change-Id: Ibc47450552afe23ea74fcf55d1d799d5d7e5487c Reviewed-on: https://go-review.googlesource.com/c/go/+/315273 Run-TryBot: Filippo Valsorda <filippo@golang.org> Reviewed-by: Than McIntosh <thanm@google.com> Reviewed-by: Roland Shoemaker <roland@golang.org> TryBot-Result: Gopher Robot <gobot@golang.org> Reviewed-by: Russ Cox <rsc@golang.org>
This commit is contained in:
Filippo Valsorda
parent
24b570354c
commit
6796a7924c
@ -128,7 +128,7 @@ func randFieldElement(c elliptic.Curve, rand io.Reader) (k *big.Int, err error)
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params := c.Params()
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// Note that for P-521 this will actually be 63 bits more than the order, as
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// division rounds down, but the extra bit is inconsequential.
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b := make([]byte, params.BitSize/8+8) // TODO: use params.N.BitLen()
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b := make([]byte, params.N.BitLen()/8+8)
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_, err = io.ReadFull(rand, b)
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if err != nil {
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return
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@ -228,13 +228,13 @@ func Sign(rand io.Reader, priv *PrivateKey, hash []byte) (r, s *big.Int, err err
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// Create a CSPRNG that xors a stream of zeros with
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// the output of the AES-CTR instance.
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csprng := cipher.StreamReader{
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csprng := &cipher.StreamReader{
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R: zeroReader,
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S: cipher.NewCTR(block, []byte(aesIV)),
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}
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c := priv.PublicKey.Curve
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return sign(priv, &csprng, c, hash)
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return sign(priv, csprng, c, hash)
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}
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func signGeneric(priv *PrivateKey, csprng *cipher.StreamReader, c elliptic.Curve, hash []byte) (r, s *big.Int, err error) {
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@ -353,16 +353,14 @@ func VerifyASN1(pub *PublicKey, hash, sig []byte) bool {
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return Verify(pub, hash, r, s)
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}
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type zr struct {
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io.Reader
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}
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type zr struct{}
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// Read replaces the contents of dst with zeros.
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func (z *zr) Read(dst []byte) (n int, err error) {
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// Read replaces the contents of dst with zeros. It is safe for concurrent use.
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func (zr) Read(dst []byte) (n int, err error) {
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for i := range dst {
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dst[i] = 0
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}
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return len(dst), nil
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}
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var zeroReader = &zr{}
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var zeroReader = zr{}
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@ -36,295 +36,6 @@ type Curve interface {
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ScalarBaseMult(k []byte) (x, y *big.Int)
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}
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func matchesSpecificCurve(params *CurveParams, available ...Curve) (Curve, bool) {
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for _, c := range available {
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if params == c.Params() {
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return c, true
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}
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}
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return nil, false
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}
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// CurveParams contains the parameters of an elliptic curve and also provides
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// a generic, non-constant time implementation of Curve.
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type CurveParams struct {
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P *big.Int // the order of the underlying field
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N *big.Int // the order of the base point
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B *big.Int // the constant of the curve equation
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Gx, Gy *big.Int // (x,y) of the base point
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BitSize int // the size of the underlying field
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Name string // the canonical name of the curve
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}
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func (curve *CurveParams) Params() *CurveParams {
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return curve
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}
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// CurveParams operates, internally, on Jacobian coordinates. For a given
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// (x, y) position on the curve, the Jacobian coordinates are (x1, y1, z1)
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// where x = x1/z1² and y = y1/z1³. The greatest speedups come when the whole
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// calculation can be performed within the transform (as in ScalarMult and
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// ScalarBaseMult). But even for Add and Double, it's faster to apply and
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// reverse the transform than to operate in affine coordinates.
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// polynomial returns x³ - 3x + b.
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func (curve *CurveParams) polynomial(x *big.Int) *big.Int {
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x3 := new(big.Int).Mul(x, x)
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x3.Mul(x3, x)
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threeX := new(big.Int).Lsh(x, 1)
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threeX.Add(threeX, x)
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x3.Sub(x3, threeX)
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x3.Add(x3, curve.B)
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x3.Mod(x3, curve.P)
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return x3
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}
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func (curve *CurveParams) IsOnCurve(x, y *big.Int) bool {
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// If there is a dedicated constant-time implementation for this curve operation,
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// use that instead of the generic one.
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if specific, ok := matchesSpecificCurve(curve, p224, p384, p521); ok {
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return specific.IsOnCurve(x, y)
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}
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if x.Sign() < 0 || x.Cmp(curve.P) >= 0 ||
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y.Sign() < 0 || y.Cmp(curve.P) >= 0 {
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return false
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}
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// y² = x³ - 3x + b
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y2 := new(big.Int).Mul(y, y)
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y2.Mod(y2, curve.P)
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return curve.polynomial(x).Cmp(y2) == 0
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}
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// zForAffine returns a Jacobian Z value for the affine point (x, y). If x and
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// y are zero, it assumes that they represent the point at infinity because (0,
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// 0) is not on the any of the curves handled here.
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func zForAffine(x, y *big.Int) *big.Int {
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z := new(big.Int)
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if x.Sign() != 0 || y.Sign() != 0 {
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z.SetInt64(1)
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}
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return z
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}
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// affineFromJacobian reverses the Jacobian transform. See the comment at the
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// top of the file. If the point is ∞ it returns 0, 0.
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func (curve *CurveParams) affineFromJacobian(x, y, z *big.Int) (xOut, yOut *big.Int) {
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if z.Sign() == 0 {
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return new(big.Int), new(big.Int)
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}
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zinv := new(big.Int).ModInverse(z, curve.P)
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zinvsq := new(big.Int).Mul(zinv, zinv)
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xOut = new(big.Int).Mul(x, zinvsq)
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xOut.Mod(xOut, curve.P)
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zinvsq.Mul(zinvsq, zinv)
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yOut = new(big.Int).Mul(y, zinvsq)
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yOut.Mod(yOut, curve.P)
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return
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}
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func (curve *CurveParams) Add(x1, y1, x2, y2 *big.Int) (*big.Int, *big.Int) {
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// If there is a dedicated constant-time implementation for this curve operation,
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// use that instead of the generic one.
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if specific, ok := matchesSpecificCurve(curve, p224, p384, p521); ok {
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return specific.Add(x1, y1, x2, y2)
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}
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z1 := zForAffine(x1, y1)
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z2 := zForAffine(x2, y2)
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return curve.affineFromJacobian(curve.addJacobian(x1, y1, z1, x2, y2, z2))
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}
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// addJacobian takes two points in Jacobian coordinates, (x1, y1, z1) and
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// (x2, y2, z2) and returns their sum, also in Jacobian form.
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func (curve *CurveParams) addJacobian(x1, y1, z1, x2, y2, z2 *big.Int) (*big.Int, *big.Int, *big.Int) {
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// See https://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#addition-add-2007-bl
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x3, y3, z3 := new(big.Int), new(big.Int), new(big.Int)
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if z1.Sign() == 0 {
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x3.Set(x2)
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y3.Set(y2)
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z3.Set(z2)
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return x3, y3, z3
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}
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if z2.Sign() == 0 {
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x3.Set(x1)
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y3.Set(y1)
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z3.Set(z1)
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return x3, y3, z3
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}
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z1z1 := new(big.Int).Mul(z1, z1)
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z1z1.Mod(z1z1, curve.P)
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z2z2 := new(big.Int).Mul(z2, z2)
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z2z2.Mod(z2z2, curve.P)
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u1 := new(big.Int).Mul(x1, z2z2)
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u1.Mod(u1, curve.P)
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u2 := new(big.Int).Mul(x2, z1z1)
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u2.Mod(u2, curve.P)
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h := new(big.Int).Sub(u2, u1)
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xEqual := h.Sign() == 0
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if h.Sign() == -1 {
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h.Add(h, curve.P)
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}
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i := new(big.Int).Lsh(h, 1)
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i.Mul(i, i)
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j := new(big.Int).Mul(h, i)
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s1 := new(big.Int).Mul(y1, z2)
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s1.Mul(s1, z2z2)
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s1.Mod(s1, curve.P)
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s2 := new(big.Int).Mul(y2, z1)
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s2.Mul(s2, z1z1)
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s2.Mod(s2, curve.P)
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r := new(big.Int).Sub(s2, s1)
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if r.Sign() == -1 {
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r.Add(r, curve.P)
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}
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yEqual := r.Sign() == 0
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if xEqual && yEqual {
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return curve.doubleJacobian(x1, y1, z1)
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}
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r.Lsh(r, 1)
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v := new(big.Int).Mul(u1, i)
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x3.Set(r)
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x3.Mul(x3, x3)
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x3.Sub(x3, j)
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x3.Sub(x3, v)
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x3.Sub(x3, v)
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x3.Mod(x3, curve.P)
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y3.Set(r)
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v.Sub(v, x3)
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y3.Mul(y3, v)
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s1.Mul(s1, j)
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s1.Lsh(s1, 1)
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y3.Sub(y3, s1)
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y3.Mod(y3, curve.P)
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z3.Add(z1, z2)
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z3.Mul(z3, z3)
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z3.Sub(z3, z1z1)
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z3.Sub(z3, z2z2)
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z3.Mul(z3, h)
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z3.Mod(z3, curve.P)
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return x3, y3, z3
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}
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func (curve *CurveParams) Double(x1, y1 *big.Int) (*big.Int, *big.Int) {
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// If there is a dedicated constant-time implementation for this curve operation,
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// use that instead of the generic one.
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if specific, ok := matchesSpecificCurve(curve, p224, p384, p521); ok {
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return specific.Double(x1, y1)
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}
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z1 := zForAffine(x1, y1)
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return curve.affineFromJacobian(curve.doubleJacobian(x1, y1, z1))
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}
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// doubleJacobian takes a point in Jacobian coordinates, (x, y, z), and
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// returns its double, also in Jacobian form.
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func (curve *CurveParams) doubleJacobian(x, y, z *big.Int) (*big.Int, *big.Int, *big.Int) {
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// See https://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#doubling-dbl-2001-b
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delta := new(big.Int).Mul(z, z)
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delta.Mod(delta, curve.P)
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gamma := new(big.Int).Mul(y, y)
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gamma.Mod(gamma, curve.P)
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alpha := new(big.Int).Sub(x, delta)
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if alpha.Sign() == -1 {
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alpha.Add(alpha, curve.P)
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}
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alpha2 := new(big.Int).Add(x, delta)
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alpha.Mul(alpha, alpha2)
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alpha2.Set(alpha)
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alpha.Lsh(alpha, 1)
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alpha.Add(alpha, alpha2)
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beta := alpha2.Mul(x, gamma)
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x3 := new(big.Int).Mul(alpha, alpha)
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beta8 := new(big.Int).Lsh(beta, 3)
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beta8.Mod(beta8, curve.P)
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x3.Sub(x3, beta8)
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if x3.Sign() == -1 {
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x3.Add(x3, curve.P)
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}
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x3.Mod(x3, curve.P)
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z3 := new(big.Int).Add(y, z)
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z3.Mul(z3, z3)
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z3.Sub(z3, gamma)
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if z3.Sign() == -1 {
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z3.Add(z3, curve.P)
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}
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z3.Sub(z3, delta)
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if z3.Sign() == -1 {
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z3.Add(z3, curve.P)
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}
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z3.Mod(z3, curve.P)
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beta.Lsh(beta, 2)
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beta.Sub(beta, x3)
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if beta.Sign() == -1 {
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beta.Add(beta, curve.P)
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}
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y3 := alpha.Mul(alpha, beta)
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gamma.Mul(gamma, gamma)
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gamma.Lsh(gamma, 3)
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gamma.Mod(gamma, curve.P)
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y3.Sub(y3, gamma)
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if y3.Sign() == -1 {
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y3.Add(y3, curve.P)
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}
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y3.Mod(y3, curve.P)
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return x3, y3, z3
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}
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func (curve *CurveParams) ScalarMult(Bx, By *big.Int, k []byte) (*big.Int, *big.Int) {
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// If there is a dedicated constant-time implementation for this curve operation,
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// use that instead of the generic one.
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if specific, ok := matchesSpecificCurve(curve, p224, p256, p384, p521); ok {
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return specific.ScalarMult(Bx, By, k)
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}
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Bz := new(big.Int).SetInt64(1)
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x, y, z := new(big.Int), new(big.Int), new(big.Int)
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for _, byte := range k {
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for bitNum := 0; bitNum < 8; bitNum++ {
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x, y, z = curve.doubleJacobian(x, y, z)
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if byte&0x80 == 0x80 {
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x, y, z = curve.addJacobian(Bx, By, Bz, x, y, z)
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}
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byte <<= 1
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}
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}
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return curve.affineFromJacobian(x, y, z)
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}
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func (curve *CurveParams) ScalarBaseMult(k []byte) (*big.Int, *big.Int) {
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// If there is a dedicated constant-time implementation for this curve operation,
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// use that instead of the generic one.
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if specific, ok := matchesSpecificCurve(curve, p224, p256, p384, p521); ok {
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return specific.ScalarBaseMult(k)
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}
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return curve.ScalarMult(curve.Gx, curve.Gy, k)
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}
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var mask = []byte{0xff, 0x1, 0x3, 0x7, 0xf, 0x1f, 0x3f, 0x7f}
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// GenerateKey returns a public/private key pair. The private key is
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File diff suppressed because it is too large
Load Diff
@ -24,27 +24,18 @@ import (
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//go:embed p256_asm_table.bin
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var p256Precomputed string
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type (
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p256Curve struct {
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*CurveParams
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}
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type p256Curve struct {
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*CurveParams
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}
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p256Point struct {
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xyz [12]uint64
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}
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)
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type p256Point struct {
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xyz [12]uint64
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}
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var p256 p256Curve
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func initP256() {
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// See FIPS 186-3, section D.2.3
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p256.CurveParams = &CurveParams{Name: "P-256"}
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p256.P, _ = new(big.Int).SetString("115792089210356248762697446949407573530086143415290314195533631308867097853951", 10)
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p256.N, _ = new(big.Int).SetString("115792089210356248762697446949407573529996955224135760342422259061068512044369", 10)
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p256.B, _ = new(big.Int).SetString("5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b", 16)
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p256.Gx, _ = new(big.Int).SetString("6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296", 16)
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p256.Gy, _ = new(big.Int).SetString("4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5", 16)
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p256.BitSize = 256
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func initP256Arch() {
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p256 = p256Curve{p256Params}
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}
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func (curve p256Curve) Params() *CurveParams {
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File diff suppressed because it is too large
Load Diff
15
src/crypto/elliptic/p256_noasm.go
Normal file
15
src/crypto/elliptic/p256_noasm.go
Normal file
@ -0,0 +1,15 @@
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// Copyright 2016 The Go Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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//go:build !amd64 && !s390x && !arm64 && !ppc64le
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// +build !amd64,!s390x,!arm64,!ppc64le
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package elliptic
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var p256 p256Curve
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func initP256Arch() {
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// Use pure Go constant-time implementation.
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p256 = p256Curve{p256Params}
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}
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@ -35,7 +35,6 @@ var (
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func initP256Arch() {
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p256 = p256CurveFast{p256Params}
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initTable()
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return
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}
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func (curve p256CurveFast) Params() *CurveParams {
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@ -73,7 +72,6 @@ func p256MovCond(res, a, b *p256Point, cond int)
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//go:noescape
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func p256Select(point *p256Point, table []p256Point, idx int)
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|
||||
//
|
||||
//go:noescape
|
||||
func p256SelectBase(point *p256Point, table []p256Point, idx int)
|
||||
|
||||
@ -85,12 +83,9 @@ func p256SelectBase(point *p256Point, table []p256Point, idx int)
|
||||
//go:noescape
|
||||
func p256PointAddAffineAsm(res, in1, in2 *p256Point, sign, sel, zero int)
|
||||
|
||||
// Point add
|
||||
//
|
||||
//go:noescape
|
||||
func p256PointAddAsm(res, in1, in2 *p256Point) int
|
||||
|
||||
//
|
||||
//go:noescape
|
||||
func p256PointDoubleAsm(res, in *p256Point)
|
||||
|
||||
@ -340,7 +335,6 @@ func boothW7(in uint) (int, int) {
|
||||
}
|
||||
|
||||
func initTable() {
|
||||
|
||||
p256PreFast = new([37][64]p256Point)
|
||||
|
||||
// TODO: For big endian, these slices should be in reverse byte order,
|
||||
@ -352,7 +346,6 @@ func initTable() {
|
||||
0x25, 0xf3, 0x21, 0xdd, 0x88, 0x86, 0xe8, 0xd2, 0x85, 0x5d, 0x88, 0x25, 0x18, 0xff, 0x71, 0x85}, //(p256.y*2^256)%p
|
||||
z: [32]byte{0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xff, 0xff, 0xff, 0xff,
|
||||
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00}, //(p256.z*2^256)%p
|
||||
|
||||
}
|
||||
|
||||
t1 := new(p256Point)
|
||||
|
||||
@ -60,7 +60,6 @@ func initP256Arch() {
|
||||
|
||||
// No vector support, use pure Go implementation.
|
||||
p256 = p256Curve{p256Params}
|
||||
return
|
||||
}
|
||||
|
||||
func (curve p256CurveFast) Params() *CurveParams {
|
||||
|
||||
296
src/crypto/elliptic/params.go
Normal file
296
src/crypto/elliptic/params.go
Normal file
@ -0,0 +1,296 @@
|
||||
// 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.
|
||||
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
|
||||
}
|
||||
|
||||
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, p224, p384, p521); 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
|
||||
}
|
||||
|
||||
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, p224, p384, p521); ok {
|
||||
return specific.Add(x1, y1, 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
|
||||
}
|
||||
|
||||
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, p224, p384, p521); ok {
|
||||
return specific.Double(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
|
||||
}
|
||||
|
||||
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, p224, p256, p384, p521); ok {
|
||||
return specific.ScalarMult(Bx, By, k)
|
||||
}
|
||||
|
||||
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)
|
||||
}
|
||||
|
||||
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, p224, p256, p384, p521); ok {
|
||||
return specific.ScalarBaseMult(k)
|
||||
}
|
||||
|
||||
return curve.ScalarMult(curve.Gx, curve.Gy, k)
|
||||
}
|
||||
|
||||
func matchesSpecificCurve(params *CurveParams, available ...Curve) (Curve, bool) {
|
||||
for _, c := range available {
|
||||
if params == c.Params() {
|
||||
return c, true
|
||||
}
|
||||
}
|
||||
return nil, false
|
||||
}
|
||||
Loading…
Reference in New Issue
Block a user