--- /dev/null
+package ecmath
+
+import (
+ "crypto/subtle"
+
+ "github.com/bytom/crypto/ed25519/internal/edwards25519"
+)
+
+// Point is a point on the ed25519 curve.
+type Point edwards25519.ExtendedGroupElement
+
+// ZeroPoint is the zero point on the ed25519 curve (not the zero value of Point).
+var ZeroPoint Point
+
+// Add adds the points in x and y, storing the result in z and
+// returning that. Any or all of x, y, and z may be the same pointers.
+func (z *Point) Add(x, y *Point) *Point {
+ var y2 edwards25519.CachedGroupElement
+ (*edwards25519.ExtendedGroupElement)(y).ToCached(&y2)
+
+ var z2 edwards25519.CompletedGroupElement
+ edwards25519.GeAdd(&z2, (*edwards25519.ExtendedGroupElement)(x), &y2)
+
+ z2.ToExtended((*edwards25519.ExtendedGroupElement)(z))
+ return z
+}
+
+// Sub subtracts y from x, storing the result in z and
+// returning that. Any or all of x, y, and z may be the same pointers.
+func (z *Point) Sub(x, y *Point) *Point {
+ var y2 edwards25519.CachedGroupElement
+ (*edwards25519.ExtendedGroupElement)(y).ToCached(&y2)
+
+ var z2 edwards25519.CompletedGroupElement
+ edwards25519.GeSub(&z2, (*edwards25519.ExtendedGroupElement)(x), &y2)
+
+ z2.ToExtended((*edwards25519.ExtendedGroupElement)(z))
+ return z
+}
+
+// ScMul multiplies the EC point x by the scalar y, placing the result
+// in z and returning that. X and z may be the same pointer.
+func (z *Point) ScMul(x *Point, y *Scalar) *Point {
+ return z.ScMulAdd(x, y, &Zero)
+}
+
+// ScMulBase multiplies the ed25519 base point by x and places the
+// result in z, returning that.
+func (z *Point) ScMulBase(x *Scalar) *Point {
+ edwards25519.GeScalarMultBase((*edwards25519.ExtendedGroupElement)(z), (*[32]byte)(x))
+ return z
+}
+
+// ScMulAdd computes xa+yB, where B is the ed25519 base point, and
+// places the result in z, returning that.
+func (z *Point) ScMulAdd(a *Point, x, y *Scalar) *Point {
+ // TODO: replace with constant-time implementation to avoid
+ // sidechannel attacks
+
+ var p edwards25519.ProjectiveGroupElement
+ edwards25519.GeDoubleScalarMultVartime(&p, (*[32]byte)(x), (*edwards25519.ExtendedGroupElement)(a), (*[32]byte)(y))
+
+ var buf [32]byte
+ p.ToBytes(&buf)
+ // TODO(bobg): double-check that it's OK to ignore the return value
+ // from ExtendedGroupElement.FromBytes here. (It's a bool indicating
+ // that its input represented a legal value.)
+ (*edwards25519.ExtendedGroupElement)(z).FromBytes(&buf)
+ return z
+}
+
+func (z *Point) Encode() [32]byte {
+ var e [32]byte
+ (*edwards25519.ExtendedGroupElement)(z).ToBytes(&e)
+ return e
+}
+
+func (z *Point) Decode(e [32]byte) (*Point, bool) {
+ ok := (*edwards25519.ExtendedGroupElement)(z).FromBytes(&e)
+ return z, ok
+}
+
+func (z *Point) ConstTimeEqual(x *Point) bool {
+ xe := x.Encode()
+ ze := z.Encode()
+ return subtle.ConstantTimeCompare(xe[:], ze[:]) == 1
+}
+
+func init() {
+ (*edwards25519.ExtendedGroupElement)(&ZeroPoint).Zero()
+}