/
simple.go
256 lines (227 loc) · 5.96 KB
/
simple.go
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package shuffle
import (
"crypto/cipher"
"errors"
"github.com/MarconiProtocol/kyber"
"github.com/MarconiProtocol/kyber/proof"
)
// XX the Zs in front of some field names are a kludge to make them
// accessible via the reflection API,
// which refuses to touch unexported fields in a struct.
// P (Prover) step 0: public inputs to the simple k-shuffle.
type ssa0 struct {
X []kyber.Point
Y []kyber.Point
}
// V (Verifier) step 1: random challenge t
type ssa1 struct {
Zt kyber.Scalar
}
// P step 2: Theta vectors
type ssa2 struct {
Theta []kyber.Point
}
// V step 3: random challenge c
type ssa3 struct {
Zc kyber.Scalar
}
// P step 4: alpha vector
type ssa4 struct {
Zalpha []kyber.Scalar
}
// SimpleShuffle is the "Simple k-shuffle" defined in section 3 of
// Neff, "Verifiable Mixing (Shuffling) of ElGamal Pairs", 2004.
type SimpleShuffle struct {
grp kyber.Group
p0 ssa0
v1 ssa1
p2 ssa2
v3 ssa3
p4 ssa4
}
// Simple helper to compute G^{ab-cd} for Theta vector computation.
func thenc(grp kyber.Group, G kyber.Point,
a, b, c, d kyber.Scalar) kyber.Point {
var ab, cd kyber.Scalar
if a != nil {
ab = grp.Scalar().Mul(a, b)
} else {
ab = grp.Scalar().Zero()
}
if c != nil {
if d != nil {
cd = grp.Scalar().Mul(c, d)
} else {
cd = c
}
} else {
cd = grp.Scalar().Zero()
}
return grp.Point().Mul(ab.Sub(ab, cd), G)
}
// Init initializes the simple shuffle with the given group and the k parameter
// from the paper.
func (ss *SimpleShuffle) Init(grp kyber.Group, k int) *SimpleShuffle {
ss.grp = grp
ss.p0.X = make([]kyber.Point, k)
ss.p0.Y = make([]kyber.Point, k)
ss.p2.Theta = make([]kyber.Point, 2*k)
ss.p4.Zalpha = make([]kyber.Scalar, 2*k-1)
return ss
}
// Prove the "Simple k-shuffle" defined in section 3 of
// Neff, "Verifiable Mixing (Shuffling) of ElGamal Pairs", 2004.
// The Scalar vector y must be a permutation of Scalar vector x
// but with all elements multiplied by common Scalar gamma.
func (ss *SimpleShuffle) Prove(G kyber.Point, gamma kyber.Scalar,
x, y []kyber.Scalar, rand cipher.Stream,
ctx proof.ProverContext) error {
grp := ss.grp
k := len(x)
if k <= 1 {
panic("can't shuffle length 1 vector")
}
if k != len(y) {
panic("mismatched vector lengths")
}
// // Dump input vectors to show their correspondences
// for i := 0; i < k; i++ {
// println("x",grp.Scalar().Mul(gamma,x[i]).String())
// }
// for i := 0; i < k; i++ {
// println("y",y[i].String())
// }
// Step 0: inputs
for i := 0; i < k; i++ { // (4)
ss.p0.X[i] = grp.Point().Mul(x[i], G)
ss.p0.Y[i] = grp.Point().Mul(y[i], G)
}
if err := ctx.Put(ss.p0); err != nil {
return err
}
// V step 1
if err := ctx.PubRand(&ss.v1); err != nil {
return err
}
t := ss.v1.Zt
// P step 2
gammaT := grp.Scalar().Mul(gamma, t)
xhat := make([]kyber.Scalar, k)
yhat := make([]kyber.Scalar, k)
for i := 0; i < k; i++ { // (5) and (6) xhat,yhat vectors
xhat[i] = grp.Scalar().Sub(x[i], t)
yhat[i] = grp.Scalar().Sub(y[i], gammaT)
}
thlen := 2*k - 1 // (7) theta and Theta vectors
theta := make([]kyber.Scalar, thlen)
ctx.PriRand(theta)
Theta := make([]kyber.Point, thlen+1)
Theta[0] = thenc(grp, G, nil, nil, theta[0], yhat[0])
for i := 1; i < k; i++ {
Theta[i] = thenc(grp, G, theta[i-1], xhat[i],
theta[i], yhat[i])
}
for i := k; i < thlen; i++ {
Theta[i] = thenc(grp, G, theta[i-1], gamma,
theta[i], nil)
}
Theta[thlen] = thenc(grp, G, theta[thlen-1], gamma, nil, nil)
ss.p2.Theta = Theta
if err := ctx.Put(ss.p2); err != nil {
return err
}
// V step 3
if err := ctx.PubRand(&ss.v3); err != nil {
return err
}
c := ss.v3.Zc
// P step 4
alpha := make([]kyber.Scalar, thlen)
runprod := grp.Scalar().Set(c)
for i := 0; i < k; i++ { // (8)
runprod.Mul(runprod, xhat[i])
runprod.Div(runprod, yhat[i])
alpha[i] = grp.Scalar().Add(theta[i], runprod)
}
gammainv := grp.Scalar().Inv(gamma)
rungamma := grp.Scalar().Set(c)
for i := 1; i < k; i++ {
rungamma.Mul(rungamma, gammainv)
alpha[thlen-i] = grp.Scalar().Add(theta[thlen-i], rungamma)
}
ss.p4.Zalpha = alpha
return ctx.Put(ss.p4)
}
// Simple helper to verify Theta elements,
// by checking whether A^a*B^-b = T.
// P,Q,s are simply "scratch" kyber.Point/Scalars reused for efficiency.
func thver(A, B, T, P, Q kyber.Point, a, b, s kyber.Scalar) bool {
P.Mul(a, A)
Q.Mul(s.Neg(b), B)
P.Add(P, Q)
return P.Equal(T)
}
// Verify for Neff simple k-shuffle proofs.
func (ss *SimpleShuffle) Verify(G, Gamma kyber.Point,
ctx proof.VerifierContext) error {
grp := ss.grp
// extract proof transcript
X := ss.p0.X
Y := ss.p0.Y
Theta := ss.p2.Theta
alpha := ss.p4.Zalpha
// Validate all vector lengths
k := len(Y)
thlen := 2*k - 1
if k <= 1 || len(Y) != k || len(Theta) != thlen+1 ||
len(alpha) != thlen {
return errors.New("malformed SimpleShuffleProof")
}
// check verifiable challenges (usually by reproducing a hash)
if err := ctx.Get(ss.p0); err != nil {
return err
}
if err := ctx.PubRand(&ss.v1); err != nil { // fills in v1
return err
}
t := ss.v1.Zt
if err := ctx.Get(ss.p2); err != nil {
return err
}
if err := ctx.PubRand(&ss.v3); err != nil { // fills in v3
return err
}
c := ss.v3.Zc
if err := ctx.Get(ss.p4); err != nil {
return err
}
// Verifier step 5
negt := grp.Scalar().Neg(t)
U := grp.Point().Mul(negt, G)
W := grp.Point().Mul(negt, Gamma)
Xhat := make([]kyber.Point, k)
Yhat := make([]kyber.Point, k)
for i := 0; i < k; i++ {
Xhat[i] = grp.Point().Add(X[i], U)
Yhat[i] = grp.Point().Add(Y[i], W)
}
P := grp.Point() // scratch variables
Q := grp.Point()
s := grp.Scalar()
good := true
good = good && thver(Xhat[0], Yhat[0], Theta[0], P, Q, c, alpha[0], s)
for i := 1; i < k; i++ {
good = good && thver(Xhat[i], Yhat[i], Theta[i], P, Q,
alpha[i-1], alpha[i], s)
}
for i := k; i < thlen; i++ {
good = good && thver(Gamma, G, Theta[i], P, Q,
alpha[i-1], alpha[i], s)
}
good = good && thver(Gamma, G, Theta[thlen], P, Q,
alpha[thlen-1], c, s)
if !good {
return errors.New("incorrect SimpleShuffleProof")
}
return nil
}