/**
* check whether the issuer public key is correct
*
* @return true iff valid
*/
public bool Check()
{
// check formalities of IdemixIssuerPublicKey
if (AttributeNames == null || Hsk == null || HRand == null || HAttrs == null || BarG1 == null || BarG1.IsInfinity() || BarG2 == null || HAttrs.Length < AttributeNames.Length)
{
return(false);
}
for (int i = 0; i < AttributeNames.Length; i++)
{
if (HAttrs[i] == null)
{
return(false);
}
}
// check proofs
ECP2 t1 = IdemixUtils.GenG2.Mul(ProofS);
ECP t2 = BarG1.Mul(ProofS);
t1.Add(W.Mul(BIG.ModNeg(ProofC, IdemixUtils.GROUP_ORDER)));
t2.Add(BarG2.Mul(BIG.ModNeg(ProofC, IdemixUtils.GROUP_ORDER)));
// Generating proofData that will contain 3 elements in G1 (of size 2*FIELD_BYTES+1)and 3 elements in G2 (of size 4 * FIELD_BYTES)
byte[] proofData = new byte[0];
proofData = proofData.Append(t1.ToBytes());
proofData = proofData.Append(t2.ToBytes());
proofData = proofData.Append(IdemixUtils.GenG2.ToBytes());
proofData = proofData.Append(BarG1.ToBytes());
proofData = proofData.Append(W.ToBytes());
proofData = proofData.Append(BarG2.ToBytes());
// Hash proofData to hproofdata and compare with proofC
return(Enumerable.SequenceEqual(proofData.HashModOrder().ToBytes(), ProofC.ToBytes()));
}
/* Multiply P by e in group G2 */
public static ECP2 G2Mul(ECP2 P, BIG e)
{
ECP2 R;
if (USE_GS_G2)
{
ECP2[] Q = new ECP2[4];
FP2 f = new FP2(new BIG(ROM.Fra), new BIG(ROM.Frb));
if (ECP.SEXTIC_TWIST == ECP.M_TYPE)
{
f.Inverse();
f.Norm();
}
BIG q = new BIG(ROM.CURVE_Order);
BIG[] u = GS(e);
BIG t = new BIG(0);
int i, np, nn;
//P.affine();
Q[0] = new ECP2();
Q[0].Copy(P);
for (i = 1; i < 4; i++)
{
Q[i] = new ECP2();
Q[i].Copy(Q[i - 1]);
Q[i].Frob(f);
}
for (i = 0; i < 4; i++)
{
np = u[i].NBits();
t.Copy(BIG.ModNeg(u[i], q));
nn = t.NBits();
if (nn < np)
{
u[i].Copy(t);
Q[i].Neg();
}
u[i].Norm();
//Q[i].affine();
}
R = ECP2.Mul4(Q, u);
}
else
{
R = P.Mul(e);
}
return(R);
}
/* Galbraith & Scott Method */
public static BIG[] GS(BIG e)
{
BIG[] u = new BIG[4];
if (ECP.CURVE_PAIRING_TYPE == ECP.BN)
{
int i, j;
BIG t = new BIG(0);
BIG q = new BIG(ROM.CURVE_Order);
BIG[] v = new BIG[4];
for (i = 0; i < 4; i++)
{
t.Copy(new BIG(ROM.CURVE_WB[i]));
DBIG d = BIG.Mul(t, e);
v[i] = new BIG(d.Div(q));
u[i] = new BIG(0);
}
u[0].Copy(e);
for (i = 0; i < 4; i++)
{
for (j = 0; j < 4; j++)
{
t.Copy(new BIG(ROM.CURVE_BB[j][i]));
t.Copy(BIG.ModMul(v[j], t, q));
u[i].Add(q);
u[i].Sub(t);
u[i].Mod(q);
}
}
}
else
{
BIG q = new BIG(ROM.CURVE_Order);
BIG x = new BIG(ROM.CURVE_Bnx);
BIG w = new BIG(e);
for (int i = 0; i < 3; i++)
{
u[i] = new BIG(w);
u[i].Mod(x);
w.Div(x);
}
u[3] = new BIG(w);
if (ECP.SIGN_OF_X == ECP.NEGATIVEX)
{
u[1].Copy(BIG.ModNeg(u[1], q));
u[3].Copy(BIG.ModNeg(u[3], q));
}
}
return(u);
}
/* Multiply P by e in group G1 */
public static ECP G1Mul(ECP P, BIG e)
{
ECP R;
if (USE_GLV)
{
//P.affine();
R = new ECP();
R.Copy(P);
int np, nn;
ECP Q = new ECP();
Q.Copy(P);
Q.Affine();
BIG q = new BIG(ROM.CURVE_Order);
FP cru = new FP(new BIG(ROM.CURVE_Cru));
BIG t = new BIG(0);
BIG[] u = Glv(e);
Q.GetX().Mul(cru);
np = u[0].NBits();
t.Copy(BIG.ModNeg(u[0], q));
nn = t.NBits();
if (nn < np)
{
u[0].Copy(t);
R.Neg();
}
np = u[1].NBits();
t.Copy(BIG.ModNeg(u[1], q));
nn = t.NBits();
if (nn < np)
{
u[1].Copy(t);
Q.Neg();
}
u[0].Norm();
u[1].Norm();
R = R.Mul2(u[0], Q, u[1]);
}
else
{
R = P.Mul(e);
}
return(R);
}
/* f=f^e */
/* Note that this method requires a lot of RAM! Better to use compressed XTR method, see FP4.java */
public static FP12 GTPow(FP12 d, BIG e)
{
FP12 r;
if (USE_GS_GT)
{
FP12[] g = new FP12[4];
FP2 f = new FP2(new BIG(ROM.Fra), new BIG(ROM.Frb));
BIG q = new BIG(ROM.CURVE_Order);
BIG t = new BIG(0);
int i, np, nn;
BIG[] u = GS(e);
g[0] = new FP12(d);
for (i = 1; i < 4; i++)
{
g[i] = new FP12(0);
g[i].Copy(g[i - 1]);
g[i].Frob(f);
}
for (i = 0; i < 4; i++)
{
np = u[i].NBits();
t.Copy(BIG.ModNeg(u[i], q));
nn = t.NBits();
if (nn < np)
{
u[i].Copy(t);
g[i].Conj();
}
u[i].Norm();
}
r = FP12.Pow4(g, u);
}
else
{
r = d.Pow(e);
}
return(r);
}
/**
* Create a new IdemixSignature by proving knowledge of a credential
*
* @param c the credential used to create an idemix signature
* @param sk the signer's secret key
* @param pseudonym a pseudonym of the signer
* @param ipk the issuer public key
* @param disclosure a bool-array that steers the disclosure of attributes
* @param msg the message to be signed
* @param rhIndex the index of the attribute that represents the revocation handle
* @param cri the credential revocation information that allows the signer to prove non-revocation
*/
public IdemixSignature(IdemixCredential c, BIG sk, IdemixPseudonym pseudonym, IdemixIssuerPublicKey ipk, bool[] disclosure, byte[] msg, int rhIndex, CredentialRevocationInformation cri)
{
if (c == null || sk == null || pseudonym == null || pseudonym.Nym == null || pseudonym.RandNym == null || ipk == null || disclosure == null || msg == null || cri == null)
{
throw new ArgumentException("Cannot construct idemix signature from null input");
}
if (disclosure.Length != c.Attrs.Length)
{
throw new ArgumentException("Disclosure length must be the same as the number of attributes");
}
if (cri.RevocationAlg >= Enum.GetValues(typeof(RevocationAlgorithm)).Length)
{
throw new ArgumentException("CRI specifies unknown revocation algorithm");
}
if (cri.RevocationAlg != (int)RevocationAlgorithm.ALG_NO_REVOCATION && disclosure[rhIndex])
{
throw new ArgumentException("Attribute " + rhIndex + " is disclosed but also used a revocation handle attribute, which should remain hidden");
}
RevocationAlgorithm revocationAlgorithm = (RevocationAlgorithm)cri.RevocationAlg;
int[] hiddenIndices = HiddenIndices(disclosure);
RAND rng = IdemixUtils.GetRand();
// Start signature
BIG r1 = rng.RandModOrder();
BIG r2 = rng.RandModOrder();
BIG r3 = new BIG(r1);
r3.InvModp(IdemixUtils.GROUP_ORDER);
nonce = rng.RandModOrder();
aPrime = PAIR.G1Mul(c.A, r1);
aBar = PAIR.G1Mul(c.B, r1);
aBar.Sub(PAIR.G1Mul(aPrime, c.E));
bPrime = PAIR.G1Mul(c.B, r1);
bPrime.Sub(PAIR.G1Mul(ipk.HRand, r2));
BIG sPrime = new BIG(c.S);
sPrime.Add(BIG.ModNeg(BIG.ModMul(r2, r3, IdemixUtils.GROUP_ORDER), IdemixUtils.GROUP_ORDER));
sPrime.Mod(IdemixUtils.GROUP_ORDER);
//Construct Zero Knowledge Proof
BIG rsk = rng.RandModOrder();
BIG re = rng.RandModOrder();
BIG rR2 = rng.RandModOrder();
BIG rR3 = rng.RandModOrder();
BIG rSPrime = rng.RandModOrder();
BIG rRNym = rng.RandModOrder();
BIG[] rAttrs = new BIG[hiddenIndices.Length];
for (int i = 0; i < hiddenIndices.Length; i++)
{
rAttrs[i] = rng.RandModOrder();
}
// Compute non-revoked proof
INonRevocationProver prover = NonRevocationProver.GetNonRevocationProver(revocationAlgorithm);
int hiddenRHIndex = Array.IndexOf(hiddenIndices, rhIndex);
if (hiddenRHIndex < 0)
{
// rhIndex is not present, set to last index position
hiddenRHIndex = hiddenIndices.Length;
}
byte[] nonRevokedProofHashData = prover.GetFSContribution(BIG.FromBytes(c.Attrs[rhIndex]), rAttrs[hiddenRHIndex], cri);
if (nonRevokedProofHashData == null)
{
throw new Exception("Failed to compute non-revoked proof");
}
ECP t1 = aPrime.Mul2(re, ipk.HRand, rR2);
ECP t2 = PAIR.G1Mul(ipk.HRand, rSPrime);
t2.Add(bPrime.Mul2(rR3, ipk.Hsk, rsk));
for (int i = 0; i < hiddenIndices.Length / 2; i++)
{
t2.Add(ipk.HAttrs[hiddenIndices[2 * i]].Mul2(rAttrs[2 * i], ipk.HAttrs[hiddenIndices[2 * i + 1]], rAttrs[2 * i + 1]));
}
if (hiddenIndices.Length % 2 != 0)
{
t2.Add(PAIR.G1Mul(ipk.HAttrs[hiddenIndices[hiddenIndices.Length - 1]], rAttrs[hiddenIndices.Length - 1]));
}
ECP t3 = ipk.Hsk.Mul2(rsk, ipk.HRand, rRNym);
// create proofData such that it can contain the sign label, 7 elements in G1 (each of size 2*FIELD_BYTES+1),
// the ipk hash, the disclosure array, and the message
byte[] proofData = new byte[0];
proofData = proofData.Append(SIGN_LABEL.ToBytes());
proofData = proofData.Append(t1.ToBytes());
proofData = proofData.Append(t2.ToBytes());
proofData = proofData.Append(t3.ToBytes());
proofData = proofData.Append(aPrime.ToBytes());
proofData = proofData.Append(aBar.ToBytes());
proofData = proofData.Append(bPrime.ToBytes());
proofData = proofData.Append(pseudonym.Nym.ToBytes());
proofData = proofData.Append(ipk.Hash);
proofData = proofData.Append(disclosure);
proofData = proofData.Append(msg);
BIG cvalue = proofData.HashModOrder();
byte[] finalProofData = new byte[0];
finalProofData = finalProofData.Append(cvalue.ToBytes());
finalProofData = finalProofData.Append(nonce.ToBytes());
proofC = finalProofData.HashModOrder();
proofSSk = rsk.ModAdd(BIG.ModMul(proofC, sk, IdemixUtils.GROUP_ORDER), IdemixUtils.GROUP_ORDER);
proofSE = re.ModSub(BIG.ModMul(proofC, c.E, IdemixUtils.GROUP_ORDER), IdemixUtils.GROUP_ORDER);
proofSR2 = rR2.ModAdd(BIG.ModMul(proofC, r2, IdemixUtils.GROUP_ORDER), IdemixUtils.GROUP_ORDER);
proofSR3 = rR3.ModSub(BIG.ModMul(proofC, r3, IdemixUtils.GROUP_ORDER), IdemixUtils.GROUP_ORDER);
proofSSPrime = rSPrime.ModAdd(BIG.ModMul(proofC, sPrime, IdemixUtils.GROUP_ORDER), IdemixUtils.GROUP_ORDER);
proofSRNym = rRNym.ModAdd(BIG.ModMul(proofC, pseudonym.RandNym, IdemixUtils.GROUP_ORDER), IdemixUtils.GROUP_ORDER);
nym = new ECP();
nym.Copy(pseudonym.Nym);
proofSAttrs = new BIG[hiddenIndices.Length];
for (int i = 0; i < hiddenIndices.Length; i++)
{
proofSAttrs[i] = new BIG(rAttrs[i]);
proofSAttrs[i].Add(BIG.ModMul(proofC, BIG.FromBytes(c.Attrs[hiddenIndices[i]]), IdemixUtils.GROUP_ORDER));
proofSAttrs[i].Mod(IdemixUtils.GROUP_ORDER);
}
// include non-revocation proof in signature
revocationPk = cri.EpochPk;
revocationPKSig = cri.EpochPkSig.ToByteArray();
epoch = cri.Epoch;
nonRevocationProof = prover.GetNonRevocationProof(proofC);
}
/**
* Modsub takes input BIGs a, b, m and returns a-b modulo m
*
* @param a the minuend of the modular subtraction
* @param b the subtrahend of the modular subtraction
* @param m the modulus
* @return returns a-b (mod m)
*/
public static BIG ModSub(this BIG a, BIG b, BIG m)
{
return(a.ModAdd(BIG.ModNeg(b, m), m));
}
