ceremonyclient/nekryptology/pkg/accumulator/witness.go

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2023-07-05 05:32:28 +00:00
//
// Copyright Coinbase, Inc. All Rights Reserved.
//
// SPDX-License-Identifier: Apache-2.0
//
package accumulator
import (
"errors"
"fmt"
"git.sr.ht/~sircmpwn/go-bare"
"source.quilibrium.com/quilibrium/monorepo/nekryptology/pkg/core/curves"
)
// MembershipWitness contains the witness c and the value y respect to the accumulator state.
type MembershipWitness struct {
c curves.Point
y curves.Scalar
}
// New creates a new membership witness
func (mw *MembershipWitness) New(y Element, acc *Accumulator, sk *SecretKey) (*MembershipWitness, error) {
if acc.value == nil || acc.value.IsIdentity() {
return nil, fmt.Errorf("value of accumulator should not be nil")
}
if sk.value == nil || sk.value.IsZero() {
return nil, fmt.Errorf("secret key should not be nil")
}
if y == nil || y.IsZero() {
return nil, fmt.Errorf("y should not be nil")
}
newAcc := &Accumulator{acc.value}
_, err := newAcc.Remove(sk, y)
if err != nil {
return nil, err
}
mw.c = newAcc.value
mw.y = y.Add(y.Zero())
return mw, nil
}
// Verify the MembershipWitness mw is a valid witness as per section 4 in
// <https://eprint.iacr.org/2020/777>
func (mw MembershipWitness) Verify(pk *PublicKey, acc *Accumulator) error {
if mw.c == nil || mw.y == nil || mw.c.IsIdentity() || mw.y.IsZero() {
return fmt.Errorf("c and y should not be nil")
}
if pk.value == nil || pk.value.IsIdentity() {
return fmt.Errorf("invalid public key")
}
if acc.value == nil || acc.value.IsIdentity() {
return fmt.Errorf("accumulator value should not be nil")
}
// Set -tildeP
g2, ok := pk.value.Generator().(curves.PairingPoint)
if !ok {
return errors.New("incorrect type conversion")
}
// y*tildeP + tildeQ, tildeP is a G2 generator.
p, ok := g2.Mul(mw.y).Add(pk.value).(curves.PairingPoint)
if !ok {
return errors.New("incorrect type conversion")
}
// Prepare
witness, ok := mw.c.(curves.PairingPoint)
if !ok {
return errors.New("incorrect type conversion")
}
v, ok := acc.value.Neg().(curves.PairingPoint)
if !ok {
return errors.New("incorrect type conversion")
}
// Check e(witness, y*tildeP + tildeQ) * e(-acc, tildeP) == Identity
result := p.MultiPairing(witness, p, v, g2)
if !result.IsOne() {
return fmt.Errorf("invalid result")
}
return nil
}
// ApplyDelta returns C' = dA(y)/dD(y)*C + 1/dD(y) * <Gamma_y, Omega>
// according to the witness update protocol described in section 4 of
// https://eprint.iacr.org/2020/777.pdf
func (mw *MembershipWitness) ApplyDelta(delta *Delta) (*MembershipWitness, error) {
if mw.c == nil || mw.y == nil || delta == nil {
return nil, fmt.Errorf("y, c or delta should not be nil")
}
// C' = dA(y)/dD(y)*C + 1/dD(y) * <Gamma_y, Omega>
mw.c = mw.c.Mul(delta.d).Add(delta.p)
return mw, nil
}
// BatchUpdate performs batch update as described in section 4
func (mw *MembershipWitness) BatchUpdate(additions []Element, deletions []Element, coefficients []Coefficient) (*MembershipWitness, error) {
delta, err := evaluateDelta(mw.y, additions, deletions, coefficients)
if err != nil {
return nil, err
}
mw, err = mw.ApplyDelta(delta)
if err != nil {
return nil, fmt.Errorf("applyDelta fails")
}
return mw, nil
}
// MultiBatchUpdate performs multi-batch update using epoch as described in section 4.2
func (mw *MembershipWitness) MultiBatchUpdate(A [][]Element, D [][]Element, C [][]Coefficient) (*MembershipWitness, error) {
delta, err := evaluateDeltas(mw.y, A, D, C)
if err != nil {
return nil, fmt.Errorf("evaluateDeltas fails")
}
mw, err = mw.ApplyDelta(delta)
if err != nil {
return nil, err
}
return mw, nil
}
// MarshalBinary converts a membership witness to bytes
func (mw MembershipWitness) MarshalBinary() ([]byte, error) {
if mw.c == nil || mw.y == nil {
return nil, fmt.Errorf("c and y value should not be nil")
}
result := append(mw.c.ToAffineCompressed(), mw.y.Bytes()...)
tv := &structMarshal{
Value: result,
Curve: mw.c.CurveName(),
}
return bare.Marshal(tv)
}
// UnmarshalBinary converts bytes into MembershipWitness
func (mw *MembershipWitness) UnmarshalBinary(data []byte) error {
if data == nil {
return fmt.Errorf("input data should not be nil")
}
tv := new(structMarshal)
err := bare.Unmarshal(data, tv)
if err != nil {
return err
}
curve := curves.GetCurveByName(tv.Curve)
if curve == nil {
return fmt.Errorf("invalid curve")
}
ptLength := len(curve.Point.ToAffineCompressed())
scLength := len(curve.Scalar.Bytes())
expectedLength := ptLength + scLength
if len(tv.Value) != expectedLength {
return fmt.Errorf("invalid byte sequence")
}
cValue, err := curve.Point.FromAffineCompressed(tv.Value[:ptLength])
if err != nil {
return err
}
yValue, err := curve.Scalar.SetBytes(tv.Value[ptLength:])
if err != nil {
return err
}
mw.c = cValue
mw.y = yValue
return nil
}
// Delta contains values d and p, where d should be the division dA(y)/dD(y) on some value y
// p should be equal to 1/dD * <Gamma_y, Omega>
type Delta struct {
d curves.Scalar
p curves.Point
}
// MarshalBinary converts Delta into bytes
func (d *Delta) MarshalBinary() ([]byte, error) {
if d.d == nil || d.p == nil {
return nil, fmt.Errorf("d and p should not be nil")
}
var result []byte
result = append(result, d.p.ToAffineCompressed()...)
result = append(result, d.d.Bytes()...)
tv := &structMarshal{
Value: result,
Curve: d.p.CurveName(),
}
return bare.Marshal(tv)
}
// UnmarshalBinary converts data into Delta
func (d *Delta) UnmarshalBinary(data []byte) error {
if data == nil {
return fmt.Errorf("expected non-zero byte sequence")
}
tv := new(structMarshal)
err := bare.Unmarshal(data, tv)
if err != nil {
return err
}
curve := curves.GetCurveByName(tv.Curve)
if curve == nil {
return fmt.Errorf("invalid curve")
}
ptLength := len(curve.Point.ToAffineCompressed())
scLength := len(curve.Scalar.Bytes())
expectedLength := ptLength + scLength
if len(tv.Value) != expectedLength {
return fmt.Errorf("invalid byte sequence")
}
pValue, err := curve.NewIdentityPoint().FromAffineCompressed(tv.Value[:ptLength])
if err != nil {
return err
}
dValue, err := curve.NewScalar().SetBytes(tv.Value[ptLength:])
if err != nil {
return err
}
if err != nil {
return err
}
d.d = dValue
d.p = pValue
return nil
}
// evaluateDeltas compute values used for membership witness batch update with epoch
// as described in section 4.2, page 11 of https://eprint.iacr.org/2020/777.pdf
func evaluateDeltas(y Element, A [][]Element, D [][]Element, C [][]Coefficient) (*Delta, error) {
if len(A) != len(D) || len(A) != len(C) {
return nil, fmt.Errorf("a, d, c should have same length")
}
one := y.One()
size := len(A)
// dA(x) = ∏ 1..n (yA_i - x)
aa := make([]curves.Scalar, 0)
// dD(x) = ∏ 1..m (yD_i - x)
dd := make([]curves.Scalar, 0)
a := one
d := one
// dA_{a->b}(y) = ∏ a..b dAs(y)
// dD_{a->b}(y) = ∏ a..b dDs(y)
for i := 0; i < size; i++ {
adds := A[i]
dels := D[i]
// ta = dAs(y)
ta, err := dad(adds, y)
if err != nil {
return nil, fmt.Errorf("dad on additions fails")
}
// td = dDs(y)
td, err := dad(dels, y)
if err != nil {
return nil, fmt.Errorf("dad on deletions fails")
}
// ∏ a..b dAs(y)
a = a.Mul(ta)
// ∏ a..b dDs(y)
d = d.Mul(td)
aa = append(aa, ta)
dd = append(dd, td)
}
// If this fails, then this value was removed.
d, err := d.Invert()
if err != nil {
return nil, fmt.Errorf("no inverse exists")
}
// <Gamma_y, Omega>
p := make(polynomialPoint, 0, size)
// Ωi->j+1 = ∑ 1..t (dAt * dDt-1) · Ω
for i := 0; i < size; i++ {
// t = i+1
// ∏^(t-1)_(h=i+1)
ddh := one
// dDi→t1 (y)
for h := 0; h < i; h++ {
ddh = ddh.Mul(dd[h])
}
// ∏^(j+1)_(k=t+1)
dak := one
// dAt->j(y)
for k := i + 1; k < size; k++ {
dak = dak.Mul(aa[k])
}
// dDi->t-1(y) * dAt->j(y)
dak = dak.Mul(ddh)
pp := make(polynomialPoint, len(C[i]))
for j := 0; j < len(pp); j++ {
pp[j] = C[i][j]
}
// dDi->t-1(y) * dAt->j(y) · Ω
pp, err := pp.Mul(dak)
if err != nil {
return nil, fmt.Errorf("pp.Mul fails")
}
p, err = p.Add(pp)
if err != nil {
return nil, fmt.Errorf("pp.Add fails")
}
}
// dAi->j(y)/dDi->j(y)
a = a.Mul(d)
// Ωi->j(y)
v, err := p.evaluate(y)
if err != nil {
return nil, fmt.Errorf("p.evaluate fails")
}
// (1/dDi->j(y)) * Ωi->j(y)
v = v.Mul(d)
// return
return &Delta{d: a, p: v}, nil
}
// evaluateDelta computes values used for membership witness batch update
// as described in section 4.1 of https://eprint.iacr.org/2020/777.pdf
func evaluateDelta(y Element, additions []Element, deletions []Element, coefficients []Coefficient) (*Delta, error) {
// dD(y) = ∏ 1..m (yD_i - y), d = 1/dD(y)
var err error
d, err := dad(deletions, y)
if err != nil {
return nil, fmt.Errorf("dad fails on deletions")
}
d, err = d.Invert()
if err != nil {
return nil, fmt.Errorf("no inverse exists")
}
//dA(y) = ∏ 1..n (yA_i - y)
a, err := dad(additions, y)
if err != nil {
return nil, fmt.Errorf("dad fails on additions")
}
// dA(y)/dD(y)
a = a.Mul(d)
// Create a PolynomialG1 from coefficients
p := make(polynomialPoint, len(coefficients))
for i := 0; i < len(coefficients); i++ {
p[i] = coefficients[i]
}
// <Gamma_y, Omega>
v, err := p.evaluate(y)
if err != nil {
return nil, fmt.Errorf("p.evaluate fails")
}
// 1/dD * <Gamma_y, Omega>
v = v.Mul(d)
return &Delta{d: a, p: v}, nil
}