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crypto/zkproof: Implement a proof of consistency two points #113

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180 changes: 180 additions & 0 deletions crypto/zkproof/consistencytwopoints.go
Original file line number Diff line number Diff line change
@@ -0,0 +1,180 @@
// Copyright © 2020 AMIS Technologies
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.

package zkproof

import (
"math/big"

ecpointgrouplaw "github.com/getamis/alice/crypto/ecpointgrouplaw"
pt "github.com/getamis/alice/crypto/ecpointgrouplaw"
"github.com/getamis/alice/crypto/utils"
)

/*
Notations:
- secret keys: σ,l
- public points: R and H
- field Order: p

Alice(i.e. Prover) has two secret integers σ and l and two public points R and H .
1. Check σ,l ∈ [0, p−1].
2. Randomly choose a,b ∈ [1, p−1] and compute A := a·R and B := a·G + b·H.
3. Compute c = H(G,A,B,R,H).
4. Compute u := a + cσ mod p and t := b + c·l mod p.
The proof includes u, t, A, B.

Step 2: The verifier verifies
1. Check u,t ∈ [0, p-1].
2: Compute c = H(G,A,B,R,H).
3: Check t·R = A + c·S and t·G + u·H = B + c·T.
If the result true accept, otherwise reject.
*/
type consistencyTwoPointsMessage struct {
u []byte
t []byte
A *ecpointgrouplaw.EcPointMessage
B *ecpointgrouplaw.EcPointMessage
S *ecpointgrouplaw.EcPointMessage
T *ecpointgrouplaw.EcPointMessage
}

func NewConsistencyTwoPoints(sigma, ell *big.Int, R, H *pt.ECPoint) (*consistencyTwoPointsMessage, error) {
fieldOrder := R.GetCurve().Params().N
// Check σ,l ∈ [0, p−1].
err := utils.InRange(sigma, big0, fieldOrder)
if err != nil {
return nil, err
}
err = utils.InRange(ell, big0, fieldOrder)
if err != nil {
return nil, err
}

// Randomly choose a,b ∈ [1, p−1] and compute A := a·R and B := a·G + b·H.
a, err := utils.RandomPositiveInt(fieldOrder)
if err != nil {
return nil, err
}
b, err := utils.RandomPositiveInt(fieldOrder)
if err != nil {
return nil, err
}
A := R.ScalarMult(a)
B := pt.ScalarBaseMult(R.GetCurve(), a)
bH := H.ScalarMult(b)
B, err = B.Add(bH)
if err != nil {
return nil, err
}

msgA, err := A.ToEcPointMessage()
if err != nil {
return nil, err
}
msgB, err := B.ToEcPointMessage()
if err != nil {
return nil, err
}

// Compute c = H(G,A,B,R,H).
c := big.NewInt(1)

// Compute u := a + cσ mod p and t := b + c·l mod p.
u := new(big.Int).Mul(c, sigma)
u = u.Add(u, a)

t := new(big.Int).Mul(c, ell)
t = t.Add(t, b)

proof := &consistencyTwoPointsMessage{
u: u.Bytes(),
t: t.Bytes(),
A: msgA,
B: msgB,
}
err = proof.Verify(R, H)
if err != nil {
return nil, err
}
return proof, nil
}

func (s *consistencyTwoPointsMessage) Verify(R, H *pt.ECPoint) error {
A, err := s.A.ToPoint()
if err != nil {
return err
}
fieldOrder := A.GetCurve().Params().N

// Check u,t ∈ [0, p-1].
u := new(big.Int).SetBytes(s.u)
err = utils.InRange(u, big0, fieldOrder)
if err != nil {
return err
}
t := new(big.Int).SetBytes(s.t)
err = utils.InRange(t, big0, fieldOrder)
if err != nil {
return err
}

// Compute c = H(G,A,B,R,H).
c := big.NewInt(1)
// Check t·R = A + c·S and t·G + u·H = B + c·T.
S, err := s.S.ToPoint()
if err != nil {
return err
}
if !S.IsSameCurve(A) {
return ErrDifferentCurves
}
if !S.IsSameCurve(R) {
return ErrDifferentCurves
}
aAddcS := S.ScalarMult(c)
aAddcS, err = A.Add(aAddcS)
if err != nil {
return err
}
tR := R.ScalarMult(t)
if !tR.Equal(aAddcS) {
return ErrVerifyFailure
}

T, err := s.T.ToPoint()
if err != nil {
return err
}
B, err := s.B.ToPoint()
if err != nil {
return err
}
if !T.IsSameCurve(B) {
return ErrDifferentCurves
}
if !T.IsSameCurve(H) {
return ErrDifferentCurves
}

BaddCT := T.ScalarMult(c)
BaddCT, err = BaddCT.Add(B)
tGAdduH := H.ScalarMult(u)
tG := pt.ScalarBaseMult(T.GetCurve(), t)
tGAdduH, err = tGAdduH.Add(tG)
if !tGAdduH.IsSameCurve(BaddCT) {
return ErrDifferentCurves
}
return nil
}