// 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
}