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https://github.com/golang/go
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crypto/elliptic: add constant-time P224.
(Sending to r because of the API change.) This change alters the API for crypto/elliptic to permit different implementations in the future. This will allow us to add faster, constant-time implementations of the standard curves without any more API changes. As a demonstration, it also adds a constant-time implementation of P224. Since it's only 32-bit, it's actually only about 40% the speed of the generic code on a 64-bit system. R=r, rsc CC=golang-dev https://golang.org/cl/5528088
This commit is contained in:
Adam Langley
parent
f2f0059307
commit
247799ce8a
19
doc/go1.tmpl
19
doc/go1.tmpl
@ -592,6 +592,25 @@ the correct function or method for the old functionality, but
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may have the wrong type or require further analysis.
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</p>
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<h3 id="hash">The crypto/elliptic package</h3>
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<p>
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In Go 1, <a href="/pkg/crypto/elliptic/#Curve"><code>elliptic.Curve</code></a>
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has been made an interface to permit alternative implementations. The curve
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parameters have been moved to the
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<a href="/pkg/crypto/elliptic/#CurveParams"><code>elliptic.CurveParams</code></a>
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structure.
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</p>
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<p>
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<em>Updating</em>:
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Existing users of <code>*elliptic.Curve</code> will need to change to
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simply <code>elliptic.Curve</code>. Calls to <code>Marshal</code>,
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<code>Unmarshal</code> and <code>GenerateKey</code> are now functions
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in <code>crypto.elliptic</code> that take an <code>elliptic.Curve</code>
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as their first argument.
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</p>
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<h3 id="hash">The hash package</h3>
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<p>
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@ -20,7 +20,7 @@ import (
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// PublicKey represents an ECDSA public key.
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type PublicKey struct {
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*elliptic.Curve
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elliptic.Curve
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X, Y *big.Int
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}
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@ -34,22 +34,23 @@ var one = new(big.Int).SetInt64(1)
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// randFieldElement returns a random element of the field underlying the given
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// curve using the procedure given in [NSA] A.2.1.
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func randFieldElement(c *elliptic.Curve, rand io.Reader) (k *big.Int, err error) {
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b := make([]byte, c.BitSize/8+8)
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func randFieldElement(c elliptic.Curve, rand io.Reader) (k *big.Int, err error) {
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params := c.Params()
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b := make([]byte, params.BitSize/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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}
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k = new(big.Int).SetBytes(b)
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n := new(big.Int).Sub(c.N, one)
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n := new(big.Int).Sub(params.N, one)
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k.Mod(k, n)
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k.Add(k, one)
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return
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}
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// GenerateKey generates a public&private key pair.
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func GenerateKey(c *elliptic.Curve, rand io.Reader) (priv *PrivateKey, err error) {
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func GenerateKey(c elliptic.Curve, rand io.Reader) (priv *PrivateKey, err error) {
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k, err := randFieldElement(c, rand)
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if err != nil {
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return
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@ -66,8 +67,8 @@ func GenerateKey(c *elliptic.Curve, rand io.Reader) (priv *PrivateKey, err error
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// about how this is done. [NSA] suggests that this is done in the obvious
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// manner, but [SECG] truncates the hash to the bit-length of the curve order
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// first. We follow [SECG] because that's what OpenSSL does.
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func hashToInt(hash []byte, c *elliptic.Curve) *big.Int {
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orderBits := c.N.BitLen()
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func hashToInt(hash []byte, c elliptic.Curve) *big.Int {
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orderBits := c.Params().N.BitLen()
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orderBytes := (orderBits + 7) / 8
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if len(hash) > orderBytes {
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hash = hash[:orderBytes]
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@ -88,6 +89,7 @@ func hashToInt(hash []byte, c *elliptic.Curve) *big.Int {
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func Sign(rand io.Reader, priv *PrivateKey, hash []byte) (r, s *big.Int, err error) {
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// See [NSA] 3.4.1
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c := priv.PublicKey.Curve
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N := c.Params().N
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var k, kInv *big.Int
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for {
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@ -98,9 +100,9 @@ func Sign(rand io.Reader, priv *PrivateKey, hash []byte) (r, s *big.Int, err err
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return
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}
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kInv = new(big.Int).ModInverse(k, c.N)
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kInv = new(big.Int).ModInverse(k, N)
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r, _ = priv.Curve.ScalarBaseMult(k.Bytes())
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r.Mod(r, priv.Curve.N)
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r.Mod(r, N)
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if r.Sign() != 0 {
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break
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}
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@ -110,7 +112,7 @@ func Sign(rand io.Reader, priv *PrivateKey, hash []byte) (r, s *big.Int, err err
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s = new(big.Int).Mul(priv.D, r)
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s.Add(s, e)
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s.Mul(s, kInv)
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s.Mod(s, priv.PublicKey.Curve.N)
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s.Mod(s, N)
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if s.Sign() != 0 {
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break
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}
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@ -124,15 +126,16 @@ func Sign(rand io.Reader, priv *PrivateKey, hash []byte) (r, s *big.Int, err err
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func Verify(pub *PublicKey, hash []byte, r, s *big.Int) bool {
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// See [NSA] 3.4.2
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c := pub.Curve
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N := c.Params().N
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if r.Sign() == 0 || s.Sign() == 0 {
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return false
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}
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if r.Cmp(c.N) >= 0 || s.Cmp(c.N) >= 0 {
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if r.Cmp(N) >= 0 || s.Cmp(N) >= 0 {
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return false
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}
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e := hashToInt(hash, c)
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w := new(big.Int).ModInverse(s, c.N)
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w := new(big.Int).ModInverse(s, N)
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u1 := e.Mul(e, w)
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u2 := w.Mul(r, w)
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@ -143,6 +146,6 @@ func Verify(pub *PublicKey, hash []byte, r, s *big.Int) bool {
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return false
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}
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x, _ := c.Add(x1, y1, x2, y2)
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x.Mod(x, c.N)
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x.Mod(x, N)
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return x.Cmp(r) == 0
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}
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@ -13,7 +13,7 @@ import (
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"testing"
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)
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func testKeyGeneration(t *testing.T, c *elliptic.Curve, tag string) {
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func testKeyGeneration(t *testing.T, c elliptic.Curve, tag string) {
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priv, err := GenerateKey(c, rand.Reader)
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if err != nil {
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t.Errorf("%s: error: %s", tag, err)
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@ -34,7 +34,7 @@ func TestKeyGeneration(t *testing.T) {
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testKeyGeneration(t, elliptic.P521(), "p521")
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}
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func testSignAndVerify(t *testing.T, c *elliptic.Curve, tag string) {
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func testSignAndVerify(t *testing.T, c elliptic.Curve, tag string) {
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priv, _ := GenerateKey(c, rand.Reader)
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hashed := []byte("testing")
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@ -7,5 +7,6 @@ include ../../../Make.inc
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TARG=crypto/elliptic
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GOFILES=\
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elliptic.go\
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p224.go\
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include ../../../Make.pkg
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@ -21,7 +21,25 @@ import (
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// A Curve represents a short-form Weierstrass curve with a=-3.
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// See http://www.hyperelliptic.org/EFD/g1p/auto-shortw.html
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type Curve struct {
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type Curve interface {
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// Params returns the parameters for the curve.
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Params() *CurveParams
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// IsOnCurve returns true if the given (x,y) lies on the curve.
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IsOnCurve(x, y *big.Int) bool
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// Add returns the sum of (x1,y1) and (x2,y2)
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Add(x1, y1, x2, y2 *big.Int) (x, y *big.Int)
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// Double returns 2*(x,y)
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Double(x1, y1 *big.Int) (x, y *big.Int)
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// ScalarMult returns k*(Bx,By) where k is a number in big-endian form.
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ScalarMult(x1, y1 *big.Int, scalar []byte) (x, y *big.Int)
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// ScalarBaseMult returns k*G, where G is the base point of the group and k
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// is an integer in big-endian form.
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ScalarBaseMult(scalar []byte) (x, y *big.Int)
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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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@ -29,8 +47,11 @@ type Curve struct {
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BitSize int // the size of the underlying field
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}
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// IsOnCurve returns true if the given (x,y) lies on the curve.
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func (curve *Curve) IsOnCurve(x, y *big.Int) bool {
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func (curve *CurveParams) Params() *CurveParams {
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return curve
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}
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func (curve *CurveParams) IsOnCurve(x, y *big.Int) bool {
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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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@ -50,7 +71,7 @@ func (curve *Curve) IsOnCurve(x, y *big.Int) bool {
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// affineFromJacobian reverses the Jacobian transform. See the comment at the
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// top of the file.
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func (curve *Curve) affineFromJacobian(x, y, z *big.Int) (xOut, yOut *big.Int) {
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func (curve *CurveParams) affineFromJacobian(x, y, z *big.Int) (xOut, yOut *big.Int) {
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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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@ -62,15 +83,14 @@ func (curve *Curve) affineFromJacobian(x, y, z *big.Int) (xOut, yOut *big.Int) {
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return
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}
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// Add returns the sum of (x1,y1) and (x2,y2)
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func (curve *Curve) Add(x1, y1, x2, y2 *big.Int) (*big.Int, *big.Int) {
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func (curve *CurveParams) Add(x1, y1, x2, y2 *big.Int) (*big.Int, *big.Int) {
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z := new(big.Int).SetInt64(1)
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return curve.affineFromJacobian(curve.addJacobian(x1, y1, z, x2, y2, z))
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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 *Curve) addJacobian(x1, y1, z1, x2, y2, z2 *big.Int) (*big.Int, *big.Int, *big.Int) {
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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 http://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#addition-add-2007-bl
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z1z1 := new(big.Int).Mul(z1, z1)
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z1z1.Mod(z1z1, curve.P)
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@ -133,15 +153,14 @@ func (curve *Curve) addJacobian(x1, y1, z1, x2, y2, z2 *big.Int) (*big.Int, *big
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return x3, y3, z3
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}
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// Double returns 2*(x,y)
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func (curve *Curve) Double(x1, y1 *big.Int) (*big.Int, *big.Int) {
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func (curve *CurveParams) Double(x1, y1 *big.Int) (*big.Int, *big.Int) {
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z1 := new(big.Int).SetInt64(1)
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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 *Curve) doubleJacobian(x, y, z *big.Int) (*big.Int, *big.Int, *big.Int) {
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func (curve *CurveParams) doubleJacobian(x, y, z *big.Int) (*big.Int, *big.Int, *big.Int) {
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// See http://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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@ -199,8 +218,7 @@ func (curve *Curve) doubleJacobian(x, y, z *big.Int) (*big.Int, *big.Int, *big.I
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return x3, y3, z3
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}
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// ScalarMult returns k*(Bx,By) where k is a number in big-endian form.
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func (curve *Curve) ScalarMult(Bx, By *big.Int, k []byte) (*big.Int, *big.Int) {
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func (curve *CurveParams) ScalarMult(Bx, By *big.Int, k []byte) (*big.Int, *big.Int) {
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// We have a slight problem in that the identity of the group (the
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// point at infinity) cannot be represented in (x, y) form on a finite
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// machine. Thus the standard add/double algorithm has to be tweaked
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@ -238,18 +256,17 @@ func (curve *Curve) ScalarMult(Bx, By *big.Int, k []byte) (*big.Int, *big.Int) {
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return curve.affineFromJacobian(x, y, z)
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}
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// ScalarBaseMult returns k*G, where G is the base point of the group and k is
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// an integer in big-endian form.
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func (curve *Curve) ScalarBaseMult(k []byte) (*big.Int, *big.Int) {
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func (curve *CurveParams) ScalarBaseMult(k []byte) (*big.Int, *big.Int) {
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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 generated
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// using the given reader, which must return random data.
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func (curve *Curve) GenerateKey(rand io.Reader) (priv []byte, x, y *big.Int, err error) {
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byteLen := (curve.BitSize + 7) >> 3
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// GenerateKey returns a public/private key pair. The private key is
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// generated using the given reader, which must return random data.
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func GenerateKey(curve Curve, rand io.Reader) (priv []byte, x, y *big.Int, err error) {
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bitSize := curve.Params().BitSize
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byteLen := (bitSize + 7) >> 3
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priv = make([]byte, byteLen)
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for x == nil {
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@ -259,7 +276,7 @@ func (curve *Curve) GenerateKey(rand io.Reader) (priv []byte, x, y *big.Int, err
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}
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// We have to mask off any excess bits in the case that the size of the
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// underlying field is not a whole number of bytes.
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priv[0] &= mask[curve.BitSize%8]
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priv[0] &= mask[bitSize%8]
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// This is because, in tests, rand will return all zeros and we don't
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// want to get the point at infinity and loop forever.
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priv[1] ^= 0x42
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@ -268,10 +285,9 @@ func (curve *Curve) GenerateKey(rand io.Reader) (priv []byte, x, y *big.Int, err
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return
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}
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// Marshal converts a point into the form specified in section 4.3.6 of ANSI
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// X9.62.
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func (curve *Curve) Marshal(x, y *big.Int) []byte {
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byteLen := (curve.BitSize + 7) >> 3
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// Marshal converts a point into the form specified in section 4.3.6 of ANSI X9.62.
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func Marshal(curve Curve, x, y *big.Int) []byte {
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byteLen := (curve.Params().BitSize + 7) >> 3
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ret := make([]byte, 1+2*byteLen)
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ret[0] = 4 // uncompressed point
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@ -283,10 +299,9 @@ func (curve *Curve) Marshal(x, y *big.Int) []byte {
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return ret
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}
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// Unmarshal converts a point, serialized by Marshal, into an x, y pair. On
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// error, x = nil.
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func (curve *Curve) Unmarshal(data []byte) (x, y *big.Int) {
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byteLen := (curve.BitSize + 7) >> 3
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// Unmarshal converts a point, serialized by Marshal, into an x, y pair. On error, x = nil.
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func Unmarshal(curve Curve, data []byte) (x, y *big.Int) {
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byteLen := (curve.Params().BitSize + 7) >> 3
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if len(data) != 1+2*byteLen {
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return
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}
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@ -299,10 +314,9 @@ func (curve *Curve) Unmarshal(data []byte) (x, y *big.Int) {
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}
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var initonce sync.Once
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var p224 *Curve
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var p256 *Curve
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var p384 *Curve
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var p521 *Curve
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var p256 *CurveParams
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var p384 *CurveParams
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var p521 *CurveParams
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func initAll() {
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initP224()
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@ -311,20 +325,9 @@ func initAll() {
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initP521()
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}
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func initP224() {
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// See FIPS 186-3, section D.2.2
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p224 = new(Curve)
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p224.P, _ = new(big.Int).SetString("26959946667150639794667015087019630673557916260026308143510066298881", 10)
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p224.N, _ = new(big.Int).SetString("26959946667150639794667015087019625940457807714424391721682722368061", 10)
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p224.B, _ = new(big.Int).SetString("b4050a850c04b3abf54132565044b0b7d7bfd8ba270b39432355ffb4", 16)
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p224.Gx, _ = new(big.Int).SetString("b70e0cbd6bb4bf7f321390b94a03c1d356c21122343280d6115c1d21", 16)
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p224.Gy, _ = new(big.Int).SetString("bd376388b5f723fb4c22dfe6cd4375a05a07476444d5819985007e34", 16)
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p224.BitSize = 224
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}
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func initP256() {
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// See FIPS 186-3, section D.2.3
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p256 = new(Curve)
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p256 = new(CurveParams)
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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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@ -335,7 +338,7 @@ func initP256() {
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func initP384() {
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// See FIPS 186-3, section D.2.4
|
||||
p384 = new(Curve)
|
||||
p384 = new(CurveParams)
|
||||
p384.P, _ = new(big.Int).SetString("39402006196394479212279040100143613805079739270465446667948293404245721771496870329047266088258938001861606973112319", 10)
|
||||
p384.N, _ = new(big.Int).SetString("39402006196394479212279040100143613805079739270465446667946905279627659399113263569398956308152294913554433653942643", 10)
|
||||
p384.B, _ = new(big.Int).SetString("b3312fa7e23ee7e4988e056be3f82d19181d9c6efe8141120314088f5013875ac656398d8a2ed19d2a85c8edd3ec2aef", 16)
|
||||
@ -346,7 +349,7 @@ func initP384() {
|
||||
|
||||
func initP521() {
|
||||
// See FIPS 186-3, section D.2.5
|
||||
p521 = new(Curve)
|
||||
p521 = new(CurveParams)
|
||||
p521.P, _ = new(big.Int).SetString("6864797660130609714981900799081393217269435300143305409394463459185543183397656052122559640661454554977296311391480858037121987999716643812574028291115057151", 10)
|
||||
p521.N, _ = new(big.Int).SetString("6864797660130609714981900799081393217269435300143305409394463459185543183397655394245057746333217197532963996371363321113864768612440380340372808892707005449", 10)
|
||||
p521.B, _ = new(big.Int).SetString("051953eb9618e1c9a1f929a21a0b68540eea2da725b99b315f3b8b489918ef109e156193951ec7e937b1652c0bd3bb1bf073573df883d2c34f1ef451fd46b503f00", 16)
|
||||
@ -355,26 +358,20 @@ func initP521() {
|
||||
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 {
|
||||
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 {
|
||||
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 {
|
||||
func P521() Curve {
|
||||
initonce.Do(initAll)
|
||||
return p521
|
||||
}
|
||||
|
||||
@ -13,7 +13,7 @@ import (
|
||||
|
||||
func TestOnCurve(t *testing.T) {
|
||||
p224 := P224()
|
||||
if !p224.IsOnCurve(p224.Gx, p224.Gy) {
|
||||
if !p224.IsOnCurve(p224.Params().Gx, p224.Params().Gy) {
|
||||
t.Errorf("FAIL")
|
||||
}
|
||||
}
|
||||
@ -295,7 +295,25 @@ func TestBaseMult(t *testing.T) {
|
||||
}
|
||||
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, %s), want (%x, %s)", i, e.k, x, y, e.x, 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 TestGenericBaseMult(t *testing.T) {
|
||||
// We use the P224 CurveParams directly in order to test the generic implementation.
|
||||
p224 := P224().Params()
|
||||
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
|
||||
@ -316,13 +334,13 @@ func BenchmarkBaseMult(b *testing.B) {
|
||||
|
||||
func TestMarshal(t *testing.T) {
|
||||
p224 := P224()
|
||||
_, x, y, err := p224.GenerateKey(rand.Reader)
|
||||
_, x, y, err := GenerateKey(p224, rand.Reader)
|
||||
if err != nil {
|
||||
t.Error(err)
|
||||
return
|
||||
}
|
||||
serialized := p224.Marshal(x, y)
|
||||
xx, yy := p224.Unmarshal(serialized)
|
||||
serialized := Marshal(p224, x, y)
|
||||
xx, yy := Unmarshal(p224, serialized)
|
||||
if xx == nil {
|
||||
t.Error("failed to unmarshal")
|
||||
return
|
||||
|
||||
685
src/pkg/crypto/elliptic/p224.go
Normal file
685
src/pkg/crypto/elliptic/p224.go
Normal file
@ -0,0 +1,685 @@
|
||||
// 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
|
||||
|
||||
// This is a constant-time, 32-bit implementation of P224. See FIPS 186-3,
|
||||
// section D.2.2.
|
||||
//
|
||||
// See http://www.imperialviolet.org/2010/12/04/ecc.html ([1]) for background.
|
||||
|
||||
import (
|
||||
"math/big"
|
||||
)
|
||||
|
||||
var p224 p224Curve
|
||||
|
||||
type p224Curve struct {
|
||||
*CurveParams
|
||||
gx, gy, b p224FieldElement
|
||||
}
|
||||
|
||||
func initP224() {
|
||||
// See FIPS 186-3, section D.2.2
|
||||
p224.CurveParams = new(CurveParams)
|
||||
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
|
||||
|
||||
p224FromBig(&p224.gx, p224.Gx)
|
||||
p224FromBig(&p224.gy, p224.Gy)
|
||||
p224FromBig(&p224.b, p224.B)
|
||||
}
|
||||
|
||||
// P224 returns a Curve which implements P-224 (see FIPS 186-3, section D.2.2)
|
||||
func P224() Curve {
|
||||
initonce.Do(initAll)
|
||||
return p224
|
||||
}
|
||||
|
||||
func (curve p224Curve) Params() *CurveParams {
|
||||
return curve.CurveParams
|
||||
}
|
||||
|
||||
func (curve p224Curve) IsOnCurve(bigX, bigY *big.Int) bool {
|
||||
var x, y p224FieldElement
|
||||
p224FromBig(&x, bigX)
|
||||
p224FromBig(&y, bigY)
|
||||
|
||||
// y² = x³ - 3x + b
|
||||
var tmp p224LargeFieldElement
|
||||
var x3 p224FieldElement
|
||||
p224Square(&x3, &x, &tmp)
|
||||
p224Mul(&x3, &x3, &x, &tmp)
|
||||
|
||||
for i := 0; i < 8; i++ {
|
||||
x[i] *= 3
|
||||
}
|
||||
p224Sub(&x3, &x3, &x)
|
||||
p224Reduce(&x3)
|
||||
p224Add(&x3, &x3, &curve.b)
|
||||
p224Contract(&x3, &x3)
|
||||
|
||||
p224Square(&y, &y, &tmp)
|
||||
p224Contract(&y, &y)
|
||||
|
||||
for i := 0; i < 8; i++ {
|
||||
if y[i] != x3[i] {
|
||||
return false
|
||||
}
|
||||
}
|
||||
return true
|
||||
}
|
||||
|
||||
func (p224Curve) Add(bigX1, bigY1, bigX2, bigY2 *big.Int) (x, y *big.Int) {
|
||||
var x1, y1, z1, x2, y2, z2, x3, y3, z3 p224FieldElement
|
||||
|
||||
p224FromBig(&x1, bigX1)
|
||||
p224FromBig(&y1, bigY1)
|
||||
z1[0] = 1
|
||||
p224FromBig(&x2, bigX2)
|
||||
p224FromBig(&y2, bigY2)
|
||||
z2[0] = 1
|
||||
|
||||
p224AddJacobian(&x3, &y3, &z3, &x1, &y1, &z1, &x2, &y2, &z2)
|
||||
return p224ToAffine(&x3, &y3, &z3)
|
||||
}
|
||||
|
||||
func (p224Curve) Double(bigX1, bigY1 *big.Int) (x, y *big.Int) {
|
||||
var x1, y1, z1, x2, y2, z2 p224FieldElement
|
||||
|
||||
p224FromBig(&x1, bigX1)
|
||||
p224FromBig(&y1, bigY1)
|
||||
z1[0] = 1
|
||||
|
||||
p224DoubleJacobian(&x2, &y2, &z2, &x1, &y1, &z1)
|
||||
return p224ToAffine(&x2, &y2, &z2)
|
||||
}
|
||||
|
||||
func (p224Curve) ScalarMult(bigX1, bigY1 *big.Int, scalar []byte) (x, y *big.Int) {
|
||||
var x1, y1, z1, x2, y2, z2 p224FieldElement
|
||||
|
||||
p224FromBig(&x1, bigX1)
|
||||
p224FromBig(&y1, bigY1)
|
||||
z1[0] = 1
|
||||
|
||||
p224ScalarMult(&x2, &y2, &z2, &x1, &y1, &z1, scalar)
|
||||
return p224ToAffine(&x2, &y2, &z2)
|
||||
}
|
||||
|
||||
func (curve p224Curve) ScalarBaseMult(scalar []byte) (x, y *big.Int) {
|
||||
var z1, x2, y2, z2 p224FieldElement
|
||||
|
||||
z1[0] = 1
|
||||
p224ScalarMult(&x2, &y2, &z2, &curve.gx, &curve.gy, &z1, scalar)
|
||||
return p224ToAffine(&x2, &y2, &z2)
|
||||
}
|
||||
|
||||
// Field element functions.
|
||||
//
|
||||
// The field that we're dealing with is ℤ/pℤ where p = 2**224 - 2**96 + 1.
|
||||
//
|
||||
// Field elements are represented by a FieldElement, which is a typedef to an
|
||||
// array of 8 uint32's. The value of a FieldElement, a, is:
|
||||
// a[0] + 2**28·a[1] + 2**56·a[1] + ... + 2**196·a[7]
|
||||
//
|
||||
// Using 28-bit limbs means that there's only 4 bits of headroom, which is less
|
||||
// than we would really like. But it has the useful feature that we hit 2**224
|
||||
// exactly, making the reflections during a reduce much nicer.
|
||||
type p224FieldElement [8]uint32
|
||||
|
||||
// p224Add computes *out = a+b
|
||||
//
|
||||
// a[i] + b[i] < 2**32
|
||||
func p224Add(out, a, b *p224FieldElement) {
|
||||
for i := 0; i < 8; i++ {
|
||||
out[i] = a[i] + b[i]
|
||||
}
|
||||
}
|
||||
|
||||
const two31p3 = 1<<31 + 1<<3
|
||||
const two31m3 = 1<<31 - 1<<3
|
||||
const two31m15m3 = 1<<31 - 1<<15 - 1<<3
|
||||
|
||||
// p224ZeroModP31 is 0 mod p where bit 31 is set in all limbs so that we can
|
||||
// subtract smaller amounts without underflow. See the section "Subtraction" in
|
||||
// [1] for reasoning.
|
||||
var p224ZeroModP31 = []uint32{two31p3, two31m3, two31m3, two31m15m3, two31m3, two31m3, two31m3, two31m3}
|
||||
|
||||
// p224Sub computes *out = a-b
|
||||
//
|
||||
// a[i], b[i] < 2**30
|
||||
// out[i] < 2**32
|
||||
func p224Sub(out, a, b *p224FieldElement) {
|
||||
for i := 0; i < 8; i++ {
|
||||
out[i] = a[i] + p224ZeroModP31[i] - b[i]
|
||||
}
|
||||
}
|
||||
|
||||
// LargeFieldElement also represents an element of the field. The limbs are
|
||||
// still spaced 28-bits apart and in little-endian order. So the limbs are at
|
||||
// 0, 28, 56, ..., 392 bits, each 64-bits wide.
|
||||
type p224LargeFieldElement [15]uint64
|
||||
|
||||
const two63p35 = 1<<63 + 1<<35
|
||||
const two63m35 = 1<<63 - 1<<35
|
||||
const two63m35m19 = 1<<63 - 1<<35 - 1<<19
|
||||
|
||||
// p224ZeroModP63 is 0 mod p where bit 63 is set in all limbs. See the section
|
||||
// "Subtraction" in [1] for why.
|
||||
var p224ZeroModP63 = [8]uint64{two63p35, two63m35, two63m35, two63m35, two63m35m19, two63m35, two63m35, two63m35}
|
||||
|
||||
const bottom12Bits = 0xfff
|
||||
const bottom28Bits = 0xfffffff
|
||||
|
||||
// p224Mul computes *out = a*b
|
||||
//
|
||||
// a[i] < 2**29, b[i] < 2**30 (or vice versa)
|
||||
// out[i] < 2**29
|
||||
func p224Mul(out, a, b *p224FieldElement, tmp *p224LargeFieldElement) {
|
||||
for i := 0; i < 15; i++ {
|
||||
tmp[i] = 0
|
||||
}
|
||||
|
||||
for i := 0; i < 8; i++ {
|
||||
for j := 0; j < 8; j++ {
|
||||
tmp[i+j] += uint64(a[i]) * uint64(b[j])
|
||||
}
|
||||
}
|
||||
|
||||
p224ReduceLarge(out, tmp)
|
||||
}
|
||||
|
||||
// Square computes *out = a*a
|
||||
//
|
||||
// a[i] < 2**29
|
||||
// out[i] < 2**29
|
||||
func p224Square(out, a *p224FieldElement, tmp *p224LargeFieldElement) {
|
||||
for i := 0; i < 15; i++ {
|
||||
tmp[i] = 0
|
||||
}
|
||||
|
||||
for i := 0; i < 8; i++ {
|
||||
for j := 0; j <= i; j++ {
|
||||
r := uint64(a[i]) * uint64(a[j])
|
||||
if i == j {
|
||||
tmp[i+j] += r
|
||||
} else {
|
||||
tmp[i+j] += r << 1
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
p224ReduceLarge(out, tmp)
|
||||
}
|
||||
|
||||
// ReduceLarge converts a p224LargeFieldElement to a p224FieldElement.
|
||||
//
|
||||
// in[i] < 2**62
|
||||
func p224ReduceLarge(out *p224FieldElement, in *p224LargeFieldElement) {
|
||||
for i := 0; i < 8; i++ {
|
||||
in[i] += p224ZeroModP63[i]
|
||||
}
|
||||
|
||||
// Elimintate the coefficients at 2**224 and greater.
|
||||
for i := 14; i >= 8; i-- {
|
||||
in[i-8] -= in[i]
|
||||
in[i-5] += (in[i] & 0xffff) << 12
|
||||
in[i-4] += in[i] >> 16
|
||||
}
|
||||
in[8] = 0
|
||||
// in[0..8] < 2**64
|
||||
|
||||
// As the values become small enough, we start to store them in |out|
|
||||
// and use 32-bit operations.
|
||||
for i := 1; i < 8; i++ {
|
||||
in[i+1] += in[i] >> 28
|
||||
out[i] = uint32(in[i] & bottom28Bits)
|
||||
}
|
||||
in[0] -= in[8]
|
||||
out[3] += uint32(in[8]&0xffff) << 12
|
||||
out[4] += uint32(in[8] >> 16)
|
||||
// in[0] < 2**64
|
||||
// out[3] < 2**29
|
||||
// out[4] < 2**29
|
||||
// out[1,2,5..7] < 2**28
|
||||
|
||||
out[0] = uint32(in[0] & bottom28Bits)
|
||||
out[1] += uint32((in[0] >> 28) & bottom28Bits)
|
||||
out[2] += uint32(in[0] >> 56)
|
||||
// out[0] < 2**28
|
||||
// out[1..4] < 2**29
|
||||
// out[5..7] < 2**28
|
||||
}
|
||||
|
||||
// Reduce reduces the coefficients of a to smaller bounds.
|
||||
//
|
||||
// On entry: a[i] < 2**31 + 2**30
|
||||
// On exit: a[i] < 2**29
|
||||
func p224Reduce(a *p224FieldElement) {
|
||||
for i := 0; i < 7; i++ {
|
||||
a[i+1] += a[i] >> 28
|
||||
a[i] &= bottom28Bits
|
||||
}
|
||||
top := a[7] >> 28
|
||||
a[7] &= bottom28Bits
|
||||
|
||||
// top < 2**4
|
||||
mask := top
|
||||
mask |= mask >> 2
|
||||
mask |= mask >> 1
|
||||
mask <<= 31
|
||||
mask = uint32(int32(mask) >> 31)
|
||||
// Mask is all ones if top != 0, all zero otherwise
|
||||
|
||||
a[0] -= top
|
||||
a[3] += top << 12
|
||||
|
||||
// We may have just made a[0] negative but, if we did, then we must
|
||||
// have added something to a[3], this it's > 2**12. Therefore we can
|
||||
// carry down to a[0].
|
||||
a[3] -= 1 & mask
|
||||
a[2] += mask & (1<<28 - 1)
|
||||
a[1] += mask & (1<<28 - 1)
|
||||
a[0] += mask & (1 << 28)
|
||||
}
|
||||
|
||||
// p224Invert calcuates *out = in**-1 by computing in**(2**224 - 2**96 - 1),
|
||||
// i.e. Fermat's little theorem.
|
||||
func p224Invert(out, in *p224FieldElement) {
|
||||
var f1, f2, f3, f4 p224FieldElement
|
||||
var c p224LargeFieldElement
|
||||
|
||||
p224Square(&f1, in, &c) // 2
|
||||
p224Mul(&f1, &f1, in, &c) // 2**2 - 1
|
||||
p224Square(&f1, &f1, &c) // 2**3 - 2
|
||||
p224Mul(&f1, &f1, in, &c) // 2**3 - 1
|
||||
p224Square(&f2, &f1, &c) // 2**4 - 2
|
||||
p224Square(&f2, &f2, &c) // 2**5 - 4
|
||||
p224Square(&f2, &f2, &c) // 2**6 - 8
|
||||
p224Mul(&f1, &f1, &f2, &c) // 2**6 - 1
|
||||
p224Square(&f2, &f1, &c) // 2**7 - 2
|
||||
for i := 0; i < 5; i++ { // 2**12 - 2**6
|
||||
p224Square(&f2, &f2, &c)
|
||||
}
|
||||
p224Mul(&f2, &f2, &f1, &c) // 2**12 - 1
|
||||
p224Square(&f3, &f2, &c) // 2**13 - 2
|
||||
for i := 0; i < 11; i++ { // 2**24 - 2**12
|
||||
p224Square(&f3, &f3, &c)
|
||||
}
|
||||
p224Mul(&f2, &f3, &f2, &c) // 2**24 - 1
|
||||
p224Square(&f3, &f2, &c) // 2**25 - 2
|
||||
for i := 0; i < 23; i++ { // 2**48 - 2**24
|
||||
p224Square(&f3, &f3, &c)
|
||||
}
|
||||
p224Mul(&f3, &f3, &f2, &c) // 2**48 - 1
|
||||
p224Square(&f4, &f3, &c) // 2**49 - 2
|
||||
for i := 0; i < 47; i++ { // 2**96 - 2**48
|
||||
p224Square(&f4, &f4, &c)
|
||||
}
|
||||
p224Mul(&f3, &f3, &f4, &c) // 2**96 - 1
|
||||
p224Square(&f4, &f3, &c) // 2**97 - 2
|
||||
for i := 0; i < 23; i++ { // 2**120 - 2**24
|
||||
p224Square(&f4, &f4, &c)
|
||||
}
|
||||
p224Mul(&f2, &f4, &f2, &c) // 2**120 - 1
|
||||
for i := 0; i < 6; i++ { // 2**126 - 2**6
|
||||
p224Square(&f2, &f2, &c)
|
||||
}
|
||||
p224Mul(&f1, &f1, &f2, &c) // 2**126 - 1
|
||||
p224Square(&f1, &f1, &c) // 2**127 - 2
|
||||
p224Mul(&f1, &f1, in, &c) // 2**127 - 1
|
||||
for i := 0; i < 97; i++ { // 2**224 - 2**97
|
||||
p224Square(&f1, &f1, &c)
|
||||
}
|
||||
p224Mul(out, &f1, &f3, &c) // 2**224 - 2**96 - 1
|
||||
}
|
||||
|
||||
// p224Contract converts a FieldElement to its unique, minimal form.
|
||||
//
|
||||
// On entry, in[i] < 2**32
|
||||
// On exit, in[i] < 2**28
|
||||
func p224Contract(out, in *p224FieldElement) {
|
||||
copy(out[:], in[:])
|
||||
|
||||
for i := 0; i < 7; i++ {
|
||||
out[i+1] += out[i] >> 28
|
||||
out[i] &= bottom28Bits
|
||||
}
|
||||
top := out[7] >> 28
|
||||
out[7] &= bottom28Bits
|
||||
|
||||
out[0] -= top
|
||||
out[3] += top << 12
|
||||
|
||||
// We may just have made out[i] negative. So we carry down. If we made
|
||||
// out[0] negative then we know that out[3] is sufficiently positive
|
||||
// because we just added to it.
|
||||
for i := 0; i < 3; i++ {
|
||||
mask := uint32(int32(out[i]) >> 31)
|
||||
out[i] += (1 << 28) & mask
|
||||
out[i+1] -= 1 & mask
|
||||
}
|
||||
|
||||
// Now we see if the value is >= p and, if so, subtract p.
|
||||
|
||||
// First we build a mask from the top four limbs, which must all be
|
||||
// equal to bottom28Bits if the whole value is >= p. If top4AllOnes
|
||||
// ends up with any zero bits in the bottom 28 bits, then this wasn't
|
||||
// true.
|
||||
top4AllOnes := uint32(0xffffffff)
|
||||
for i := 4; i < 8; i++ {
|
||||
top4AllOnes &= (out[i] & bottom28Bits) - 1
|
||||
}
|
||||
top4AllOnes |= 0xf0000000
|
||||
// Now we replicate any zero bits to all the bits in top4AllOnes.
|
||||
top4AllOnes &= top4AllOnes >> 16
|
||||
top4AllOnes &= top4AllOnes >> 8
|
||||
top4AllOnes &= top4AllOnes >> 4
|
||||
top4AllOnes &= top4AllOnes >> 2
|
||||
top4AllOnes &= top4AllOnes >> 1
|
||||
top4AllOnes = uint32(int32(top4AllOnes<<31) >> 31)
|
||||
|
||||
// Now we test whether the bottom three limbs are non-zero.
|
||||
bottom3NonZero := out[0] | out[1] | out[2]
|
||||
bottom3NonZero |= bottom3NonZero >> 16
|
||||
bottom3NonZero |= bottom3NonZero >> 8
|
||||
bottom3NonZero |= bottom3NonZero >> 4
|
||||
bottom3NonZero |= bottom3NonZero >> 2
|
||||
bottom3NonZero |= bottom3NonZero >> 1
|
||||
bottom3NonZero = uint32(int32(bottom3NonZero<<31) >> 31)
|
||||
|
||||
// Everything depends on the value of out[3].
|
||||
// If it's > 0xffff000 and top4AllOnes != 0 then the whole value is >= p
|
||||
// If it's = 0xffff000 and top4AllOnes != 0 and bottom3NonZero != 0,
|
||||
// then the whole value is >= p
|
||||
// If it's < 0xffff000, then the whole value is < p
|
||||
n := out[3] - 0xffff000
|
||||
out3Equal := n
|
||||
out3Equal |= out3Equal >> 16
|
||||
out3Equal |= out3Equal >> 8
|
||||
out3Equal |= out3Equal >> 4
|
||||
out3Equal |= out3Equal >> 2
|
||||
out3Equal |= out3Equal >> 1
|
||||
out3Equal = ^uint32(int32(out3Equal<<31) >> 31)
|
||||
|
||||
// If out[3] > 0xffff000 then n's MSB will be zero.
|
||||
out3GT := ^uint32(int32(n<<31) >> 31)
|
||||
|
||||
mask := top4AllOnes & ((out3Equal & bottom3NonZero) | out3GT)
|
||||
out[0] -= 1 & mask
|
||||
out[3] -= 0xffff000 & mask
|
||||
out[4] -= 0xfffffff & mask
|
||||
out[5] -= 0xfffffff & mask
|
||||
out[6] -= 0xfffffff & mask
|
||||
out[7] -= 0xfffffff & mask
|
||||
}
|
||||
|
||||
// Group element functions.
|
||||
//
|
||||
// These functions deal with group elements. The group is an elliptic curve
|
||||
// group with a = -3 defined in FIPS 186-3, section D.2.2.
|
||||
|
||||
// p224AddJacobian computes *out = a+b where a != b.
|
||||
func p224AddJacobian(x3, y3, z3, x1, y1, z1, x2, y2, z2 *p224FieldElement) {
|
||||
// See http://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#addition-p224Add-2007-bl
|
||||
var z1z1, z2z2, u1, u2, s1, s2, h, i, j, r, v p224FieldElement
|
||||
var c p224LargeFieldElement
|
||||
|
||||
// Z1Z1 = Z1²
|
||||
p224Square(&z1z1, z1, &c)
|
||||
// Z2Z2 = Z2²
|
||||
p224Square(&z2z2, z2, &c)
|
||||
// U1 = X1*Z2Z2
|
||||
p224Mul(&u1, x1, &z2z2, &c)
|
||||
// U2 = X2*Z1Z1
|
||||
p224Mul(&u2, x2, &z1z1, &c)
|
||||
// S1 = Y1*Z2*Z2Z2
|
||||
p224Mul(&s1, z2, &z2z2, &c)
|
||||
p224Mul(&s1, y1, &s1, &c)
|
||||
// S2 = Y2*Z1*Z1Z1
|
||||
p224Mul(&s2, z1, &z1z1, &c)
|
||||
p224Mul(&s2, y2, &s2, &c)
|
||||
// H = U2-U1
|
||||
p224Sub(&h, &u2, &u1)
|
||||
p224Reduce(&h)
|
||||
// I = (2*H)²
|
||||
for j := 0; j < 8; j++ {
|
||||
i[j] = h[j] << 1
|
||||
}
|
||||
p224Reduce(&i)
|
||||
p224Square(&i, &i, &c)
|
||||
// J = H*I
|
||||
p224Mul(&j, &h, &i, &c)
|
||||
// r = 2*(S2-S1)
|
||||
p224Sub(&r, &s2, &s1)
|
||||
p224Reduce(&r)
|
||||
for i := 0; i < 8; i++ {
|
||||
r[i] <<= 1
|
||||
}
|
||||
p224Reduce(&r)
|
||||
// V = U1*I
|
||||
p224Mul(&v, &u1, &i, &c)
|
||||
// Z3 = ((Z1+Z2)²-Z1Z1-Z2Z2)*H
|
||||
p224Add(&z1z1, &z1z1, &z2z2)
|
||||
p224Add(&z2z2, z1, z2)
|
||||
p224Reduce(&z2z2)
|
||||
p224Square(&z2z2, &z2z2, &c)
|
||||
p224Sub(z3, &z2z2, &z1z1)
|
||||
p224Reduce(z3)
|
||||
p224Mul(z3, z3, &h, &c)
|
||||
// X3 = r²-J-2*V
|
||||
for i := 0; i < 8; i++ {
|
||||
z1z1[i] = v[i] << 1
|
||||
}
|
||||
p224Add(&z1z1, &j, &z1z1)
|
||||
p224Reduce(&z1z1)
|
||||
p224Square(x3, &r, &c)
|
||||
p224Sub(x3, x3, &z1z1)
|
||||
p224Reduce(x3)
|
||||
// Y3 = r*(V-X3)-2*S1*J
|
||||
for i := 0; i < 8; i++ {
|
||||
s1[i] <<= 1
|
||||
}
|
||||
p224Mul(&s1, &s1, &j, &c)
|
||||
p224Sub(&z1z1, &v, x3)
|
||||
p224Reduce(&z1z1)
|
||||
p224Mul(&z1z1, &z1z1, &r, &c)
|
||||
p224Sub(y3, &z1z1, &s1)
|
||||
p224Reduce(y3)
|
||||
}
|
||||
|
||||
// p224DoubleJacobian computes *out = a+a.
|
||||
func p224DoubleJacobian(x3, y3, z3, x1, y1, z1 *p224FieldElement) {
|
||||
var delta, gamma, beta, alpha, t p224FieldElement
|
||||
var c p224LargeFieldElement
|
||||
|
||||
p224Square(&delta, z1, &c)
|
||||
p224Square(&gamma, y1, &c)
|
||||
p224Mul(&beta, x1, &gamma, &c)
|
||||
|
||||
// alpha = 3*(X1-delta)*(X1+delta)
|
||||
p224Add(&t, x1, &delta)
|
||||
for i := 0; i < 8; i++ {
|
||||
t[i] += t[i] << 1
|
||||
}
|
||||
p224Reduce(&t)
|
||||
p224Sub(&alpha, x1, &delta)
|
||||
p224Reduce(&alpha)
|
||||
p224Mul(&alpha, &alpha, &t, &c)
|
||||
|
||||
// Z3 = (Y1+Z1)²-gamma-delta
|
||||
p224Add(z3, y1, z1)
|
||||
p224Reduce(z3)
|
||||
p224Square(z3, z3, &c)
|
||||
p224Sub(z3, z3, &gamma)
|
||||
p224Reduce(z3)
|
||||
p224Sub(z3, z3, &delta)
|
||||
p224Reduce(z3)
|
||||
|
||||
// X3 = alpha²-8*beta
|
||||
for i := 0; i < 8; i++ {
|
||||
delta[i] = beta[i] << 3
|
||||
}
|
||||
p224Reduce(&delta)
|
||||
p224Square(x3, &alpha, &c)
|
||||
p224Sub(x3, x3, &delta)
|
||||
p224Reduce(x3)
|
||||
|
||||
// Y3 = alpha*(4*beta-X3)-8*gamma²
|
||||
for i := 0; i < 8; i++ {
|
||||
beta[i] <<= 2
|
||||
}
|
||||
p224Sub(&beta, &beta, x3)
|
||||
p224Reduce(&beta)
|
||||
p224Square(&gamma, &gamma, &c)
|
||||
for i := 0; i < 8; i++ {
|
||||
gamma[i] <<= 3
|
||||
}
|
||||
p224Reduce(&gamma)
|
||||
p224Mul(y3, &alpha, &beta, &c)
|
||||
p224Sub(y3, y3, &gamma)
|
||||
p224Reduce(y3)
|
||||
}
|
||||
|
||||
// p224CopyConditional sets *out = *in iff the least-significant-bit of control
|
||||
// is true, and it runs in constant time.
|
||||
func p224CopyConditional(out, in *p224FieldElement, control uint32) {
|
||||
control <<= 31
|
||||
control = uint32(int32(control) >> 31)
|
||||
|
||||
for i := 0; i < 8; i++ {
|
||||
out[i] ^= (out[i] ^ in[i]) & control
|
||||
}
|
||||
}
|
||||
|
||||
func p224ScalarMult(outX, outY, outZ, inX, inY, inZ *p224FieldElement, scalar []byte) {
|
||||
var xx, yy, zz p224FieldElement
|
||||
for i := 0; i < 8; i++ {
|
||||
outZ[i] = 0
|
||||
}
|
||||
|
||||
firstBit := uint32(1)
|
||||
for _, byte := range scalar {
|
||||
for bitNum := uint(0); bitNum < 8; bitNum++ {
|
||||
p224DoubleJacobian(outX, outY, outZ, outX, outY, outZ)
|
||||
bit := uint32((byte >> (7 - bitNum)) & 1)
|
||||
p224AddJacobian(&xx, &yy, &zz, inX, inY, inZ, outX, outY, outZ)
|
||||
p224CopyConditional(outX, inX, firstBit&bit)
|
||||
p224CopyConditional(outY, inY, firstBit&bit)
|
||||
p224CopyConditional(outZ, inZ, firstBit&bit)
|
||||
p224CopyConditional(outX, &xx, ^firstBit&bit)
|
||||
p224CopyConditional(outY, &yy, ^firstBit&bit)
|
||||
p224CopyConditional(outZ, &zz, ^firstBit&bit)
|
||||
firstBit = firstBit & ^bit
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// p224ToAffine converts from Jacobian to affine form.
|
||||
func p224ToAffine(x, y, z *p224FieldElement) (*big.Int, *big.Int) {
|
||||
var zinv, zinvsq, outx, outy p224FieldElement
|
||||
var tmp p224LargeFieldElement
|
||||
|
||||
isPointAtInfinity := true
|
||||
for i := 0; i < 8; i++ {
|
||||
if z[i] != 0 {
|
||||
isPointAtInfinity = false
|
||||
break
|
||||
}
|
||||
}
|
||||
|
||||
if isPointAtInfinity {
|
||||
return nil, nil
|
||||
}
|
||||
|
||||
p224Invert(&zinv, z)
|
||||
p224Square(&zinvsq, &zinv, &tmp)
|
||||
p224Mul(x, x, &zinvsq, &tmp)
|
||||
p224Mul(&zinvsq, &zinvsq, &zinv, &tmp)
|
||||
p224Mul(y, y, &zinvsq, &tmp)
|
||||
|
||||
p224Contract(&outx, x)
|
||||
p224Contract(&outy, y)
|
||||
return p224ToBig(&outx), p224ToBig(&outy)
|
||||
}
|
||||
|
||||
// get28BitsFromEnd returns the least-significant 28 bits from buf>>shift,
|
||||
// where buf is interpreted as a big-endian number.
|
||||
func get28BitsFromEnd(buf []byte, shift uint) (uint32, []byte) {
|
||||
var ret uint32
|
||||
|
||||
for i := uint(0); i < 4; i++ {
|
||||
var b byte
|
||||
if l := len(buf); l > 0 {
|
||||
b = buf[l-1]
|
||||
// We don't remove the byte if we're about to return and we're not
|
||||
// reading all of it.
|
||||
if i != 3 || shift == 4 {
|
||||
buf = buf[:l-1]
|
||||
}
|
||||
}
|
||||
ret |= uint32(b) << (8 * i) >> shift
|
||||
}
|
||||
ret &= bottom28Bits
|
||||
return ret, buf
|
||||
}
|
||||
|
||||
// p224FromBig sets *out = *in.
|
||||
func p224FromBig(out *p224FieldElement, in *big.Int) {
|
||||
bytes := in.Bytes()
|
||||
out[0], bytes = get28BitsFromEnd(bytes, 0)
|
||||
out[1], bytes = get28BitsFromEnd(bytes, 4)
|
||||
out[2], bytes = get28BitsFromEnd(bytes, 0)
|
||||
out[3], bytes = get28BitsFromEnd(bytes, 4)
|
||||
out[4], bytes = get28BitsFromEnd(bytes, 0)
|
||||
out[5], bytes = get28BitsFromEnd(bytes, 4)
|
||||
out[6], bytes = get28BitsFromEnd(bytes, 0)
|
||||
out[7], bytes = get28BitsFromEnd(bytes, 4)
|
||||
}
|
||||
|
||||
// p224ToBig returns in as a big.Int.
|
||||
func p224ToBig(in *p224FieldElement) *big.Int {
|
||||
var buf [28]byte
|
||||
buf[27] = byte(in[0])
|
||||
buf[26] = byte(in[0] >> 8)
|
||||
buf[25] = byte(in[0] >> 16)
|
||||
buf[24] = byte(((in[0] >> 24) & 0x0f) | (in[1]<<4)&0xf0)
|
||||
|
||||
buf[23] = byte(in[1] >> 4)
|
||||
buf[22] = byte(in[1] >> 12)
|
||||
buf[21] = byte(in[1] >> 20)
|
||||
|
||||
buf[20] = byte(in[2])
|
||||
buf[19] = byte(in[2] >> 8)
|
||||
buf[18] = byte(in[2] >> 16)
|
||||
buf[17] = byte(((in[2] >> 24) & 0x0f) | (in[3]<<4)&0xf0)
|
||||
|
||||
buf[16] = byte(in[3] >> 4)
|
||||
buf[15] = byte(in[3] >> 12)
|
||||
buf[14] = byte(in[3] >> 20)
|
||||
|
||||
buf[13] = byte(in[4])
|
||||
buf[12] = byte(in[4] >> 8)
|
||||
buf[11] = byte(in[4] >> 16)
|
||||
buf[10] = byte(((in[4] >> 24) & 0x0f) | (in[5]<<4)&0xf0)
|
||||
|
||||
buf[9] = byte(in[5] >> 4)
|
||||
buf[8] = byte(in[5] >> 12)
|
||||
buf[7] = byte(in[5] >> 20)
|
||||
|
||||
buf[6] = byte(in[6])
|
||||
buf[5] = byte(in[6] >> 8)
|
||||
buf[4] = byte(in[6] >> 16)
|
||||
buf[3] = byte(((in[6] >> 24) & 0x0f) | (in[7]<<4)&0xf0)
|
||||
|
||||
buf[2] = byte(in[7] >> 4)
|
||||
buf[1] = byte(in[7] >> 12)
|
||||
buf[0] = byte(in[7] >> 20)
|
||||
|
||||
return new(big.Int).SetBytes(buf[:])
|
||||
}
|
||||
47
src/pkg/crypto/elliptic/p224_test.go
Normal file
47
src/pkg/crypto/elliptic/p224_test.go
Normal file
@ -0,0 +1,47 @@
|
||||
// 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 (
|
||||
"math/big"
|
||||
"testing"
|
||||
)
|
||||
|
||||
var toFromBigTests = []string{
|
||||
"0",
|
||||
"1",
|
||||
"23",
|
||||
"b70e0cb46bb4bf7f321390b94a03c1d356c01122343280d6105c1d21",
|
||||
"706a46d476dcb76798e6046d89474788d164c18032d268fd10704fa6",
|
||||
}
|
||||
|
||||
func p224AlternativeToBig(in *p224FieldElement) *big.Int {
|
||||
ret := new(big.Int)
|
||||
tmp := new(big.Int)
|
||||
|
||||
for i := uint(0); i < 8; i++ {
|
||||
tmp.SetInt64(int64(in[i]))
|
||||
tmp.Lsh(tmp, 28*i)
|
||||
ret.Add(ret, tmp)
|
||||
}
|
||||
ret.Mod(ret, p224.P)
|
||||
return ret
|
||||
}
|
||||
|
||||
func TestToFromBig(t *testing.T) {
|
||||
for i, test := range toFromBigTests {
|
||||
n, _ := new(big.Int).SetString(test, 16)
|
||||
var x p224FieldElement
|
||||
p224FromBig(&x, n)
|
||||
m := p224ToBig(&x)
|
||||
if n.Cmp(m) != 0 {
|
||||
t.Errorf("#%d: %x != %x", i, n, m)
|
||||
}
|
||||
q := p224AlternativeToBig(&x)
|
||||
if n.Cmp(q) != 0 {
|
||||
t.Errorf("#%d: %x != %x (alternative)", i, n, m)
|
||||
}
|
||||
}
|
||||
}
|
||||
@ -105,7 +105,7 @@ func md5SHA1Hash(slices ...[]byte) []byte {
|
||||
// pre-master secret is then calculated using ECDH.
|
||||
type ecdheRSAKeyAgreement struct {
|
||||
privateKey []byte
|
||||
curve *elliptic.Curve
|
||||
curve elliptic.Curve
|
||||
x, y *big.Int
|
||||
}
|
||||
|
||||
@ -132,11 +132,11 @@ Curve:
|
||||
|
||||
var x, y *big.Int
|
||||
var err error
|
||||
ka.privateKey, x, y, err = ka.curve.GenerateKey(config.rand())
|
||||
ka.privateKey, x, y, err = elliptic.GenerateKey(ka.curve, config.rand())
|
||||
if err != nil {
|
||||
return nil, err
|
||||
}
|
||||
ecdhePublic := ka.curve.Marshal(x, y)
|
||||
ecdhePublic := elliptic.Marshal(ka.curve, x, y)
|
||||
|
||||
// http://tools.ietf.org/html/rfc4492#section-5.4
|
||||
serverECDHParams := make([]byte, 1+2+1+len(ecdhePublic))
|
||||
@ -167,12 +167,12 @@ func (ka *ecdheRSAKeyAgreement) processClientKeyExchange(config *Config, ckx *cl
|
||||
if len(ckx.ciphertext) == 0 || int(ckx.ciphertext[0]) != len(ckx.ciphertext)-1 {
|
||||
return nil, errors.New("bad ClientKeyExchange")
|
||||
}
|
||||
x, y := ka.curve.Unmarshal(ckx.ciphertext[1:])
|
||||
x, y := elliptic.Unmarshal(ka.curve, ckx.ciphertext[1:])
|
||||
if x == nil {
|
||||
return nil, errors.New("bad ClientKeyExchange")
|
||||
}
|
||||
x, _ = ka.curve.ScalarMult(x, y, ka.privateKey)
|
||||
preMasterSecret := make([]byte, (ka.curve.BitSize+7)>>3)
|
||||
preMasterSecret := make([]byte, (ka.curve.Params().BitSize+7)>>3)
|
||||
xBytes := x.Bytes()
|
||||
copy(preMasterSecret[len(preMasterSecret)-len(xBytes):], xBytes)
|
||||
|
||||
@ -205,7 +205,7 @@ func (ka *ecdheRSAKeyAgreement) processServerKeyExchange(config *Config, clientH
|
||||
if publicLen+4 > len(skx.key) {
|
||||
return errServerKeyExchange
|
||||
}
|
||||
ka.x, ka.y = ka.curve.Unmarshal(skx.key[4 : 4+publicLen])
|
||||
ka.x, ka.y = elliptic.Unmarshal(ka.curve, skx.key[4:4+publicLen])
|
||||
if ka.x == nil {
|
||||
return errServerKeyExchange
|
||||
}
|
||||
@ -229,16 +229,16 @@ func (ka *ecdheRSAKeyAgreement) generateClientKeyExchange(config *Config, client
|
||||
if ka.curve == nil {
|
||||
return nil, nil, errors.New("missing ServerKeyExchange message")
|
||||
}
|
||||
priv, mx, my, err := ka.curve.GenerateKey(config.rand())
|
||||
priv, mx, my, err := elliptic.GenerateKey(ka.curve, config.rand())
|
||||
if err != nil {
|
||||
return nil, nil, err
|
||||
}
|
||||
x, _ := ka.curve.ScalarMult(ka.x, ka.y, priv)
|
||||
preMasterSecret := make([]byte, (ka.curve.BitSize+7)>>3)
|
||||
preMasterSecret := make([]byte, (ka.curve.Params().BitSize+7)>>3)
|
||||
xBytes := x.Bytes()
|
||||
copy(preMasterSecret[len(preMasterSecret)-len(xBytes):], xBytes)
|
||||
|
||||
serialized := ka.curve.Marshal(mx, my)
|
||||
serialized := elliptic.Marshal(ka.curve, mx, my)
|
||||
|
||||
ckx := new(clientKeyExchangeMsg)
|
||||
ckx.ciphertext = make([]byte, 1+len(serialized))
|
||||
|
||||
Loading…
Reference in New Issue
Block a user