package nizk

import (
	. "kesim.org/seal/common"
	"kesim.org/seal/nizk/schnorr"
)

// This is a construction of a proof of a statement of the form
//    [(C = g^(αβ))   && (A = g^α) && (Β = g^β)]
// || [(C = g^(αβ+1)) && (A = g^α) && (Β = g^β)]
//
// for given C, A and B

type Bit struct {
	bitSet bool
	α      *Scalar
	β      *Scalar
}

type Commitment struct {
	A *Point // g^α
	B *Point // g^β
	C *Point // g^(ab)g^(bitSet)
}

func NewBit(bitSet bool) *Bit {
	α, β := Curve.RandomScalar(), Curve.RandomScalar()
	return NewBitFromScalars(bitSet, α, β)
}

func NewBitFromScalars(bitSet bool, α, β *Scalar) *Bit {
	return &Bit{
		α:      α,
		β:      β,
		bitSet: bitSet,
	}
}

func (b *Bit) commitment() *Commitment {
	var C *Point
	c := b.α.Mul(b.β)

	if b.bitSet {
		C = G.Exp(c.Add(One))
	} else {
		C = G.Exp(c)
	}
	return &Commitment{
		C: C,
		A: G.Exp(b.α),
		B: G.Exp(b.β),
	}
}

type Proof struct {
	Id Bytes
	A  *schnorr.Proof // Proof for knowledge of α in A = G^α
	B  *schnorr.Proof // Proof for knowledge of β in B = G^β
	C  struct {       // Proof for knowledge of statement above
		Ch [2]*Scalar
		R  [2]*Scalar
	}
}

func (s *Bit) proof(id Bytes, c *Commitment) *Proof {
	var e [2][2]*Point
	var r1, r2, w *Scalar
	r1 = Curve.RandomScalar()
	r2 = Curve.RandomScalar()
	w = Curve.RandomScalar()

	if s.bitSet {
		e[0][0] = G.Exp(r1)
		e[0][1] = c.B.Exp(r1).Mul(G.Exp(w))
		e[1][0] = G.Exp(r2)
		e[1][1] = c.B.Exp(r2)
	} else {
		e[0][0] = G.Exp(r1)
		e[0][1] = c.B.Exp(r1)
		e[1][0] = G.Exp(r2).Mul(c.A.Exp(w))
		e[1][1] = c.B.Exp(r2).Mul(c.C.Div(G).Exp(w))
	}

	ch := Challenge(G, c.C, c.A, c.B, e[0][0], e[0][1], e[1][0], e[1][1], id)
	pr := &Proof{Id: id}

	if s.bitSet {
		pr.C.Ch[0] = w
		pr.C.Ch[1] = ch.Sub(w)
		pr.C.R[0] = r1.Sub(s.α.Mul(pr.C.Ch[0]))
		pr.C.R[1] = r2.Sub(s.α.Mul(pr.C.Ch[1]))
	} else {
		pr.C.Ch[0] = ch.Sub(w)
		pr.C.Ch[1] = w
		pr.C.R[0] = r1.Sub(s.α.Mul(pr.C.Ch[0]))
		pr.C.R[1] = r2
	}
	pr.A = (*schnorr.Statement)(s.α).Proof(id)
	pr.B = (*schnorr.Statement)(s.β).Proof(id)

	return pr
}

func (s *Bit) Commit(id Bytes) (*Commitment, *Proof) {
	c := s.commitment()
	return c, s.proof(id, c)
}

func (c *Commitment) Verify(p *Proof) bool {
	var e [2][2]*Point

	e[0][0] = G.Exp(p.C.R[0]).Mul(c.A.Exp(p.C.Ch[0]))
	e[0][1] = c.B.Exp(p.C.R[0]).Mul(c.C.Exp(p.C.Ch[0]))
	e[1][0] = G.Exp(p.C.R[1]).Mul(c.A.Exp(p.C.Ch[1]))
	e[1][1] = c.B.Exp(p.C.R[1]).Mul(c.C.Div(G).Exp(p.C.Ch[1]))
	ch := Challenge(G, c.C, c.A, c.B, e[0][0], e[0][1], e[1][0], e[1][1], p.Id)
	return p.C.Ch[0].Add(p.C.Ch[1]).Equal(ch) &&
		(*schnorr.Commitment)(c.A).Verify(p.A, p.Id) &&
		(*schnorr.Commitment)(c.B).Verify(p.B, p.Id)
}