2 files changed, 193 insertions, 0 deletions
diff --git a/curve/curve.go b/curve/curve.go
new file mode 100644
index 0000000..a194cde
--- /dev/null
+++ b/curve/curve.go
@@ -0,0 +1,61 @@
+// This package implements an abstraction for various
+// elliptic curve primitives, as multiplicative group.
+package curve
+
+import "io"
+
+type Data interface {
+	Bytes() []byte
+	String() string
+}
+
+type SomeScalar[S Data] interface {
+	Add(S) S
+	Sub(S) S
+	Mult(S) S
+	Equal(S) bool
+
+	// Maybe later:
+	// Invert(S) S
+	// Negate(S) S
+}
+
+type ScalarReader[S any] interface {
+	RandomScalar() S
+	ScalarFromReader(io.Reader) (S, error)
+	ScalarFromBytes([]byte) (S, error)
+}
+
+type MultiplicativeCurve[S SomeScalar[s], s Data, P MPoint[S, s, p], p Data] interface {
+	ScalarReader[S]
+
+	Identity() P
+	Generator() P
+	Product([]P) P
+	Exp(S) P
+}
+
+type MPoint[S SomeScalar[s], s Data, P Data] interface {
+	Mult(P) P
+	Div(P) P
+	Inv() P
+	Exp(S) P
+	Equal(P) bool
+}
+
+// For additive formulation of the curve, use these interfaces:
+type AdditiveCurve[S SomeScalar[s], s Data, P APoint[S, s, p], p Data] interface {
+	ScalarReader[S]
+	Zero() P
+	Generator() P
+	Sum([]P) P
+	Mul(S) P
+}
+
+type APoint[S SomeScalar[s], s Data, P Data] interface {
+	Add(P) P
+	Sub(P) P
+	Neg(P) P
+	ScalarMult(S) P
+	Equal(P) bool
+}
+\ No newline at end of file
diff --git a/curve/ed25519.go b/curve/ed25519.go
new file mode 100644
index 0000000..e8e380d
--- /dev/null
+++ b/curve/ed25519.go
@@ -0,0 +1,132 @@
+// Implementation of a MultiplicateCurve, using filippo.io/edwards25519.
+// Note that the implementation in edwards25519 uses addition for the group operation,
+// while we are exposing a multiplicative version of it.
+package curve
+
+import (
+	"crypto/rand"
+	"encoding/base64"
+	"io"
+
+	ed "filippo.io/edwards25519"
+)
+
+var Curve25519 = &c25519{}
+
+type Curve25519Scalar = scalar
+type Curve25519Point = point
+
+type c25519 struct{}
+type scalar ed.Scalar
+type point ed.Point
+
+var _ MPoint[*scalar, *scalar, *point] = (*point)(nil)
+var _ MultiplicativeCurve[*scalar, *scalar, *point, *point] = Curve25519
+var _ SomeScalar[*scalar] = (*scalar)(nil)
+
+var b64 = base64.StdEncoding.WithPadding(base64.NoPadding)
+
+func (s *scalar) Bytes() []byte {
+	return ((*ed.Scalar)(s)).Bytes()
+}
+
+func (s *scalar) Equal(t *scalar) bool {
+	return ((*ed.Scalar)(s)).Equal((*ed.Scalar)(t)) == 1
+}
+
+func (s *scalar) String() string {
+	return b64.EncodeToString(s.Bytes())
+}
+
+func (s *scalar) Add(t *scalar) *scalar {
+	return (*scalar)(new(ed.Scalar).Add((*ed.Scalar)(s), (*ed.Scalar)(t)))
+}
+
+func (s *scalar) Sub(t *scalar) *scalar {
+	return (*scalar)(new(ed.Scalar).Subtract((*ed.Scalar)(s), (*ed.Scalar)(t)))
+}
+
+func (s *scalar) Mult(t *scalar) *scalar {
+	return (*scalar)(new(ed.Scalar).Multiply((*ed.Scalar)(s), (*ed.Scalar)(t)))
+}
+
+func (c *c25519) ScalarFromReader(random io.Reader) (*scalar, error) {
+	var buf [64]byte
+	if random == nil {
+		random = rand.Reader
+	}
+	random.Read(buf[:])
+	return c.ScalarFromBytes(buf[:])
+}
+
+func (c *c25519) RandomScalar() *scalar {
+	for i := 0; i < 3; i++ {
+		if s, e := c.ScalarFromReader(nil); e == nil {
+			return s
+		}
+	}
+	panic("couldn't generate scalar")
+}
+
+func (c *c25519) ScalarFromBytes(b []byte) (*scalar, error) {
+	s, e := new(ed.Scalar).SetUniformBytes(b)
+	return (*scalar)(s), e
+}
+
+func (c *c25519) Exp(s *scalar) *point {
+	p := new(ed.Point).ScalarBaseMult((*ed.Scalar)(s))
+	return (*point)(p)
+}
+
+func (c *c25519) Identity() *point {
+	return (*point)(ed.NewIdentityPoint())
+}
+
+func (c *c25519) Generator() *point {
+	return (*point)(ed.NewGeneratorPoint())
+}
+
+func (c *c25519) Product(pts []*point) (product *point) {
+	product = c.Identity()
+	for _, p := range pts {
+		product = product.Mult(p)
+	}
+	return product
+}
+
+// Return P^n , for n Sc, and P Pt
+func (p *point) Exp(s *scalar) *point {
+	r := new(ed.Point).ScalarMult((*ed.Scalar)(s), (*ed.Point)(p))
+	return (*point)(r)
+}
+
+func (p *point) Bytes() []byte {
+	return ((*ed.Point)(p)).Bytes()
+}
+
+// Return p (*) q in group
+func (p *point) Mult(q *point) *point {
+	r := new(ed.Point).Add((*ed.Point)(p), (*ed.Point)(q))
+	return (*point)(r)
+}
+
+// Return p (/) q in group
+func (p *point) Div(q *point) *point {
+	r := new(ed.Point).Subtract((*ed.Point)(p), (*ed.Point)(q))
+	return (*point)(r)
+}
+
+// Return p^(-1)
+func (p *point) Inv() *point {
+	n := new(ed.Point).Negate((*ed.Point)(p))
+	return (*point)(n)
+}
+
+func (p *point) Equal(q *point) bool {
+	return ((*ed.Point)(p)).Equal((*ed.Point)(q)) == 1
+
+}
+
+func (p *point) String() string {
+	return b64.EncodeToString(p.Bytes())
+}