优化

elliptic/bitcurves/bitcurve.go

@@ -16,281 +16,10 @@ package bitcurves
 // reverse the transform than to operate in affine coordinates.
 
 import (
-    "io"
     "sync"
     "math/big"
-    "crypto/elliptic"
 )
 
-// A BitCurve represents a Koblitz Curve with a=0.
-// See http://www.hyperelliptic.org/EFD/g1p/auto-shortw.html
-type BitCurve struct {
-    Name    string
-    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 BitCurve equation
-    Gx, Gy  *big.Int // (x,y) of the base point
-    BitSize int      // the size of the underlying field
-}
-
-// Params returns the parameters of the given BitCurve (see BitCurve struct)
-func (bitCurve *BitCurve) Params() (cp *elliptic.CurveParams) {
-    cp = new(elliptic.CurveParams)
-    cp.Name = bitCurve.Name
-    cp.P = bitCurve.P
-    cp.N = bitCurve.N
-    cp.Gx = bitCurve.Gx
-    cp.Gy = bitCurve.Gy
-    cp.BitSize = bitCurve.BitSize
-    return cp
-}
-
-// IsOnCurve returns true if the given (x,y) lies on the BitCurve.
-func (bitCurve *BitCurve) IsOnCurve(x, y *big.Int) bool {
-    // y² = x³ + b
-    y2 := new(big.Int).Mul(y, y) //y²
-    y2.Mod(y2, bitCurve.P)       //y²%P
-
-    x3 := new(big.Int).Mul(x, x) //x²
-    x3.Mul(x3, x)                //x³
-
-    x3.Add(x3, bitCurve.B) //x³+B
-    x3.Mod(x3, bitCurve.P) //(x³+B)%P
-
-    return x3.Cmp(y2) == 0
-}
-
-// affineFromJacobian reverses the Jacobian transform. See the comment at the
-// top of the file.
-func (bitCurve *BitCurve) affineFromJacobian(x, y, z *big.Int) (xOut, yOut *big.Int) {
-    if z.Cmp(big.NewInt(0)) == 0 {
-        panic("bitcurve: Can't convert to affine with Jacobian Z = 0")
-    }
-    // x = YZ^2 mod P
-    zinv := new(big.Int).ModInverse(z, bitCurve.P)
-    zinvsq := new(big.Int).Mul(zinv, zinv)
-
-    xOut = new(big.Int).Mul(x, zinvsq)
-    xOut.Mod(xOut, bitCurve.P)
-    // y = YZ^3 mod P
-    zinvsq.Mul(zinvsq, zinv)
-    yOut = new(big.Int).Mul(y, zinvsq)
-    yOut.Mod(yOut, bitCurve.P)
-    return xOut, yOut
-}
-
-// Add returns the sum of (x1,y1) and (x2,y2)
-func (bitCurve *BitCurve) Add(x1, y1, x2, y2 *big.Int) (*big.Int, *big.Int) {
-    z := new(big.Int).SetInt64(1)
-    x, y, z := bitCurve.addJacobian(x1, y1, z, x2, y2, z)
-    return bitCurve.affineFromJacobian(x, y, z)
-}
-
-// addJacobian takes two points in Jacobian coordinates, (x1, y1, z1) and
-// (x2, y2, z2) and returns their sum, also in Jacobian form.
-func (bitCurve *BitCurve) addJacobian(x1, y1, z1, x2, y2, z2 *big.Int) (*big.Int, *big.Int, *big.Int) {
-    // See http://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-0.html#addition-add-2007-bl
-    z1z1 := new(big.Int).Mul(z1, z1)
-    z1z1.Mod(z1z1, bitCurve.P)
-    z2z2 := new(big.Int).Mul(z2, z2)
-    z2z2.Mod(z2z2, bitCurve.P)
-
-    u1 := new(big.Int).Mul(x1, z2z2)
-    u1.Mod(u1, bitCurve.P)
-    u2 := new(big.Int).Mul(x2, z1z1)
-    u2.Mod(u2, bitCurve.P)
-    h := new(big.Int).Sub(u2, u1)
-    if h.Sign() == -1 {
-        h.Add(h, bitCurve.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, bitCurve.P)
-    s2 := new(big.Int).Mul(y2, z1)
-    s2.Mul(s2, z1z1)
-    s2.Mod(s2, bitCurve.P)
-    r := new(big.Int).Sub(s2, s1)
-    if r.Sign() == -1 {
-        r.Add(r, bitCurve.P)
-    }
-    r.Lsh(r, 1)
-    v := new(big.Int).Mul(u1, i)
-
-    x3 := new(big.Int).Set(r)
-    x3.Mul(x3, x3)
-    x3.Sub(x3, j)
-    x3.Sub(x3, v)
-    x3.Sub(x3, v)
-    x3.Mod(x3, bitCurve.P)
-
-    y3 := new(big.Int).Set(r)
-    v.Sub(v, x3)
-    y3.Mul(y3, v)
-    s1.Mul(s1, j)
-    s1.Lsh(s1, 1)
-    y3.Sub(y3, s1)
-    y3.Mod(y3, bitCurve.P)
-
-    z3 := new(big.Int).Add(z1, z2)
-    z3.Mul(z3, z3)
-    z3.Sub(z3, z1z1)
-    if z3.Sign() == -1 {
-        z3.Add(z3, bitCurve.P)
-    }
-    z3.Sub(z3, z2z2)
-    if z3.Sign() == -1 {
-        z3.Add(z3, bitCurve.P)
-    }
-    z3.Mul(z3, h)
-    z3.Mod(z3, bitCurve.P)
-
-    return x3, y3, z3
-}
-
-// Double returns 2*(x,y)
-func (bitCurve *BitCurve) Double(x1, y1 *big.Int) (*big.Int, *big.Int) {
-    z1 := new(big.Int).SetInt64(1)
-    return bitCurve.affineFromJacobian(bitCurve.doubleJacobian(x1, y1, z1))
-}
-
-// doubleJacobian takes a point in Jacobian coordinates, (x, y, z), and
-// returns its double, also in Jacobian form.
-func (bitCurve *BitCurve) doubleJacobian(x, y, z *big.Int) (*big.Int, *big.Int, *big.Int) {
-    // See http://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-0.html#doubling-dbl-2009-l
-
-    a := new(big.Int).Mul(x, x) //X1²
-    b := new(big.Int).Mul(y, y) //Y1²
-    c := new(big.Int).Mul(b, b) //B²
-
-    d := new(big.Int).Add(x, b) //X1+B
-    d.Mul(d, d)                 //(X1+B)²
-    d.Sub(d, a)                 //(X1+B)²-A
-    d.Sub(d, c)                 //(X1+B)²-A-C
-    d.Mul(d, big.NewInt(2))     //2*((X1+B)²-A-C)
-
-    e := new(big.Int).Mul(big.NewInt(3), a) //3*A
-    f := new(big.Int).Mul(e, e)             //E²
-
-    x3 := new(big.Int).Mul(big.NewInt(2), d) //2*D
-    x3.Sub(f, x3)                            //F-2*D
-    x3.Mod(x3, bitCurve.P)
-
-    y3 := new(big.Int).Sub(d, x3)                  //D-X3
-    y3.Mul(e, y3)                                  //E*(D-X3)
-    y3.Sub(y3, new(big.Int).Mul(big.NewInt(8), c)) //E*(D-X3)-8*C
-    y3.Mod(y3, bitCurve.P)
-
-    z3 := new(big.Int).Mul(y, z) //Y1*Z1
-    z3.Mul(big.NewInt(2), z3)    //3*Y1*Z1
-    z3.Mod(z3, bitCurve.P)
-
-    return x3, y3, z3
-}
-
-// ScalarMult returns k*(Bx,By) where k is a number in big-endian form.
-func (bitCurve *BitCurve) ScalarMult(Bx, By *big.Int, k []byte) (*big.Int, *big.Int) {
-    // We have a slight problem in that the identity of the group (the
-    // point at infinity) cannot be represented in (x, y) form on a finite
-    // machine. Thus the standard add/double algorithm has to be tweaked
-    // slightly: our initial state is not the identity, but x, and we
-    // ignore the first true bit in |k|.  If we don't find any true bits in
-    // |k|, then we return nil, nil, because we cannot return the identity
-    // element.
-
-    Bz := new(big.Int).SetInt64(1)
-    x := Bx
-    y := By
-    z := Bz
-
-    seenFirstTrue := false
-    for _, byte := range k {
-        for bitNum := 0; bitNum < 8; bitNum++ {
-            if seenFirstTrue {
-                x, y, z = bitCurve.doubleJacobian(x, y, z)
-            }
-            if byte&0x80 == 0x80 {
-                if !seenFirstTrue {
-                    seenFirstTrue = true
-                } else {
-                    x, y, z = bitCurve.addJacobian(Bx, By, Bz, x, y, z)
-                }
-            }
-            byte <<= 1
-        }
-    }
-
-    if !seenFirstTrue {
-        return nil, nil
-    }
-
-    return bitCurve.affineFromJacobian(x, y, z)
-}
-
-// ScalarBaseMult returns k*G, where G is the base point of the group and k is
-// an integer in big-endian form.
-func (bitCurve *BitCurve) ScalarBaseMult(k []byte) (*big.Int, *big.Int) {
-    return bitCurve.ScalarMult(bitCurve.Gx, bitCurve.Gy, k)
-}
-
-var mask = []byte{0xff, 0x1, 0x3, 0x7, 0xf, 0x1f, 0x3f, 0x7f}
-
-// TODO: double check if it is okay
-// GenerateKey returns a public/private key pair. The private key is generated
-// using the given reader, which must return random data.
-func (bitCurve *BitCurve) GenerateKey(rand io.Reader) (priv []byte, x, y *big.Int, err error) {
-    byteLen := (bitCurve.BitSize + 7) >> 3
-    priv = make([]byte, byteLen)
-
-    for x == nil {
-        _, err = io.ReadFull(rand, priv)
-        if err != nil {
-            return
-        }
-        // We have to mask off any excess bits in the case that the size of the
-        // underlying field is not a whole number of bytes.
-        priv[0] &= mask[bitCurve.BitSize%8]
-        // This is because, in tests, rand will return all zeros and we don't
-        // want to get the point at infinity and loop forever.
-        priv[1] ^= 0x42
-        x, y = bitCurve.ScalarBaseMult(priv)
-    }
-    return
-}
-
-// Marshal converts a point into the form specified in section 4.3.6 of ANSI
-// X9.62.
-func (bitCurve *BitCurve) Marshal(x, y *big.Int) []byte {
-    byteLen := (bitCurve.BitSize + 7) >> 3
-
-    ret := make([]byte, 1+2*byteLen)
-    ret[0] = 4 // uncompressed point
-
-    xBytes := x.Bytes()
-    copy(ret[1+byteLen-len(xBytes):], xBytes)
-    yBytes := y.Bytes()
-    copy(ret[1+2*byteLen-len(yBytes):], yBytes)
-    return ret
-}
-
-// Unmarshal converts a point, serialised by Marshal, into an x, y pair. On
-// error, x = nil.
-func (bitCurve *BitCurve) Unmarshal(data []byte) (x, y *big.Int) {
-    byteLen := (bitCurve.BitSize + 7) >> 3
-    if len(data) != 1+2*byteLen {
-        return
-    }
-    if data[0] != 4 { // uncompressed form
-        return
-    }
-    x = new(big.Int).SetBytes(data[1 : 1+byteLen])
-    y = new(big.Int).SetBytes(data[1+byteLen:])
-    return
-}
-
 //curve parameters taken from:
 //http://www.secg.org/collateral/sec2_final.pdf
 

elliptic/bitcurves/bitcurve_test.go

@@ -0,0 +1,48 @@
+package bitcurves
+
+import (
+    "testing"
+    "encoding/hex"
+    "crypto/rand"
+    "crypto/ecdsa"
+    "crypto/elliptic"
+)
+
+func fromHex(s string) []byte {
+    h, _ := hex.DecodeString(s)
+    return h
+}
+
+func testCurve(t *testing.T, curve elliptic.Curve) {
+    priv, err := ecdsa.GenerateKey(curve, rand.Reader)
+    if err != nil {
+        t.Fatal(err)
+    }
+
+    msg := []byte("test-data test-data test-data test-data test-data test-data test-data test-data")
+
+    r, s, err := ecdsa.Sign(rand.Reader, priv, msg)
+    if err != nil {
+        t.Fatal(err)
+    }
+
+    if !ecdsa.Verify(&priv.PublicKey, msg, r, s) {
+        t.Fatal("signature didn't verify.")
+    }
+}
+
+func Test_All(t *testing.T) {
+    t.Run("S160", func(t *testing.T) {
+        testCurve(t, S160())
+    })
+    t.Run("S192", func(t *testing.T) {
+        testCurve(t, S192())
+    })
+
+    t.Run("S224", func(t *testing.T) {
+        testCurve(t, S224())
+    })
+    t.Run("S256", func(t *testing.T) {
+        testCurve(t, S256())
+    })
+}