/* constant time multiply by small integer of length bts - use ladder */
public ECP PinMul(int e, int bts)
{
if (CURVETYPE == MONTGOMERY)
{
return(Mul(new BIG(e)));
}
else
{
int i, b;
ECP P = new ECP();
ECP R0 = new ECP();
ECP R1 = new ECP();
R1.Copy(this);
for (i = bts - 1; i >= 0; i--)
{
b = (e >> i) & 1;
P.Copy(R1);
P.Add(R0);
R0.CSwap(R1, b);
R1.Copy(P);
R0.Dbl();
R0.CSwap(R1, b);
}
P.Copy(R0);
P.Affine();
return(P);
}
}
/**
* 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()));
}
/**
* Constructor creating a new credential
*
* @param key the issuer key pair
* @param m a credential request
* @param attrs an array of attribute values as BIG
*/
public IdemixCredential(IdemixIssuerKey key, IdemixCredRequest m, BIG[] attrs)
{
if (key == null || key.Ipk == null || m == null || attrs == null)
{
throw new ArgumentException("Cannot create idemix credential from null input");
}
if (attrs.Length != key.Ipk.AttributeNames.Length)
{
throw new ArgumentException("Amount of attribute values does not match amount of attributes in issuer public key");
}
RAND rng = IdemixUtils.GetRand();
// Place a BBS+ signature on the user key and the attribute values
// (For BBS+, see "Constant-Size Dynamic k-TAA" by Man Ho Au, Willy Susilo, Yi Mu)
E = rng.RandModOrder();
S = rng.RandModOrder();
B = new ECP();
B.Copy(IdemixUtils.GenG1);
B.Add(m.Nym);
B.Add(key.Ipk.HRand.Mul(S));
for (int i = 0; i < attrs.Length / 2; i++)
{
B.Add(key.Ipk.HAttrs[2 * i].Mul2(attrs[2 * i], key.Ipk.HAttrs[2 * i + 1], attrs[2 * i + 1]));
}
if (attrs.Length % 2 != 0)
{
B.Add(key.Ipk.HAttrs[attrs.Length - 1].Mul(attrs[attrs.Length - 1]));
}
BIG exp = new BIG(key.Isk).Plus(E);
exp.Mod(IdemixUtils.GROUP_ORDER);
exp.InvModp(IdemixUtils.GROUP_ORDER);
A = B.Mul(exp);
Attrs = new byte[attrs.Length][];
for (int i = 0; i < attrs.Length; i++)
{
byte[] b = new byte[IdemixUtils.FIELD_BYTES];
attrs[i].ToBytes(b);
Attrs[i] = b;
}
}
/**
* verify cryptographically verifies the credential
*
* @param sk the secret key of the user
* @param ipk the public key of the issuer
* @return true iff valid
*/
public bool Verify(BIG sk, IdemixIssuerPublicKey ipk)
{
if (ipk == null || Attrs.Length != ipk.AttributeNames.Length)
{
return(false);
}
foreach (byte[] attr in Attrs)
{
if (attr == null)
{
return(false);
}
}
ECP bPrime = new ECP();
bPrime.Copy(IdemixUtils.GenG1);
bPrime.Add(ipk.Hsk.Mul2(sk, ipk.HRand, S));
for (int i = 0; i < Attrs.Length / 2; i++)
{
bPrime.Add(ipk.HAttrs[2 * i].Mul2(BIG.FromBytes(Attrs[2 * i]), ipk.HAttrs[2 * i + 1], BIG.FromBytes(Attrs[2 * i + 1])));
}
if (Attrs.Length % 2 != 0)
{
bPrime.Add(ipk.HAttrs[Attrs.Length - 1].Mul(BIG.FromBytes(Attrs[Attrs.Length - 1])));
}
if (!B.Equals(bPrime))
{
return(false);
}
ECP2 a = IdemixUtils.GenG2.Mul(E);
a.Add(ipk.W);
a.Affine();
return(PAIR.FExp(PAIR.Ate(a, A)).Equals(PAIR.FExp(PAIR.Ate(IdemixUtils.GenG2, B))));
}
/* Return e.this+f.Q */
public ECP Mul2(BIG e, ECP Q, BIG f)
{
BIG te = new BIG();
BIG tf = new BIG();
BIG mt = new BIG();
ECP S = new ECP();
ECP T = new ECP();
ECP C = new ECP();
ECP[] W = new ECP[8];
sbyte[] w = new sbyte[1 + (BIG.NLEN * BIG.BASEBITS + 1) / 2];
int i, s, ns, nb;
sbyte a, b;
//affine();
//Q.affine();
te.Copy(e);
tf.Copy(f);
// precompute table
W[1] = new ECP();
W[1].Copy(this);
W[1].Sub(Q);
W[2] = new ECP();
W[2].Copy(this);
W[2].Add(Q);
S.Copy(Q);
S.Dbl();
W[0] = new ECP();
W[0].Copy(W[1]);
W[0].Sub(S);
W[3] = new ECP();
W[3].Copy(W[2]);
W[3].Add(S);
T.Copy(this);
T.Dbl();
W[5] = new ECP();
W[5].Copy(W[1]);
W[5].Add(T);
W[6] = new ECP();
W[6].Copy(W[2]);
W[6].Add(T);
W[4] = new ECP();
W[4].Copy(W[5]);
W[4].Sub(S);
W[7] = new ECP();
W[7].Copy(W[6]);
W[7].Add(S);
// if multiplier is odd, add 2, else add 1 to multiplier, and add 2P or P to correction
s = te.Parity();
te.Inc(1);
te.Norm();
ns = te.Parity();
mt.Copy(te);
mt.Inc(1);
mt.Norm();
te.CMove(mt, s);
T.CMove(this, ns);
C.Copy(T);
s = tf.Parity();
tf.Inc(1);
tf.Norm();
ns = tf.Parity();
mt.Copy(tf);
mt.Inc(1);
mt.Norm();
tf.CMove(mt, s);
S.CMove(Q, ns);
C.Add(S);
mt.Copy(te);
mt.Add(tf);
mt.Norm();
nb = 1 + (mt.NBits() + 1) / 2;
// convert exponent to signed 2-bit window
for (i = 0; i < nb; i++)
{
a = (sbyte)(te.LastBits(3) - 4);
te.Dec(a);
te.Norm();
te.FShr(2);
b = (sbyte)(tf.LastBits(3) - 4);
tf.Dec(b);
tf.Norm();
tf.FShr(2);
w[i] = (sbyte)(4 * a + b);
}
w[nb] = (sbyte)(4 * te.LastBits(3) + tf.LastBits(3));
S.Copy(W[(w[nb] - 1) / 2]);
for (i = nb - 1; i >= 0; i--)
{
T.Select(W, w[i]);
S.Dbl();
S.Dbl();
S.Add(T);
}
S.Sub(C); // apply correction
S.Affine();
return(S);
}
/* return e.this */
public ECP Mul(BIG e)
{
if (e.IsZilch() || IsInfinity())
{
return(new ECP());
}
ECP P = new ECP();
if (CURVETYPE == MONTGOMERY)
{
/* use Ladder */
int nb, i, b;
ECP D = new ECP();
ECP R0 = new ECP();
R0.Copy(this);
ECP R1 = new ECP();
R1.Copy(this);
R1.Dbl();
D.Copy(this);
D.Affine();
nb = e.NBits();
for (i = nb - 2; i >= 0; i--)
{
b = e.Bit(i);
P.Copy(R1);
P.DAdd(R0, D);
R0.CSwap(R1, b);
R1.Copy(P);
R0.Dbl();
R0.CSwap(R1, b);
}
P.Copy(R0);
}
else
{
// fixed size windows
int i, nb, s, ns;
BIG mt = new BIG();
BIG t = new BIG();
ECP Q = new ECP();
ECP C = new ECP();
ECP[] W = new ECP[8];
sbyte[] w = new sbyte[1 + (BIG.NLEN * BIG.BASEBITS + 3) / 4];
//affine();
// precompute table
Q.Copy(this);
Q.Dbl();
W[0] = new ECP();
W[0].Copy(this);
for (i = 1; i < 8; i++)
{
W[i] = new ECP();
W[i].Copy(W[i - 1]);
W[i].Add(Q);
}
// make exponent odd - add 2P if even, P if odd
t.Copy(e);
s = t.Parity();
t.Inc(1);
t.Norm();
ns = t.Parity();
mt.Copy(t);
mt.Inc(1);
mt.Norm();
t.CMove(mt, s);
Q.CMove(this, ns);
C.Copy(Q);
nb = 1 + (t.NBits() + 3) / 4;
// convert exponent to signed 4-bit window
for (i = 0; i < nb; i++)
{
w[i] = (sbyte)(t.LastBits(5) - 16);
t.Dec(w[i]);
t.Norm();
t.FShr(4);
}
w[nb] = (sbyte)t.LastBits(5);
P.Copy(W[(w[nb] - 1) / 2]);
for (i = nb - 1; i >= 0; i--)
{
Q.Select(W, w[i]);
P.Dbl();
P.Dbl();
P.Dbl();
P.Dbl();
P.Add(Q);
}
P.Sub(C); // apply correction
}
P.Affine();
return(P);
}
/**
* 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);
}
/**
* Verify this signature
*
* @param disclosure an array indicating which attributes it expects to be disclosed
* @param ipk the issuer public key
* @param msg the message that should be signed in this signature
* @param attributeValues BIG array where attributeValues[i] contains the desired attribute value for the i-th attribute if its disclosed
* @param rhIndex index of the attribute that represents the revocation-handle
* @param revPk the long term public key used to authenticate CRIs
* @param epoch monotonically increasing counter representing a time window
* @return true iff valid
*/
// ReSharper disable once ParameterHidesMember
public bool Verify(bool[] disclosure, IdemixIssuerPublicKey ipk, byte[] msg, BIG[] attributeValues, int rhIndex, KeyPair revPk, int epoch)
{
if (disclosure == null || ipk == null || msg == null || attributeValues == null || attributeValues.Length != ipk.AttributeNames.Length || disclosure.Length != ipk.AttributeNames.Length)
{
return(false);
}
for (int i = 0; i < ipk.AttributeNames.Length; i++)
{
if (disclosure[i] && attributeValues[i] == null)
{
return(false);
}
}
int[] hiddenIndices = HiddenIndices(disclosure);
if (proofSAttrs.Length != hiddenIndices.Length)
{
return(false);
}
if (aPrime.IsInfinity())
{
return(false);
}
if (nonRevocationProof.RevocationAlg >= Enum.GetValues(typeof(RevocationAlgorithm)).Length)
{
throw new ArgumentException("CRI specifies unknown revocation algorithm");
}
RevocationAlgorithm revocationAlgorithm = (RevocationAlgorithm)nonRevocationProof.RevocationAlg;
if (disclosure[rhIndex])
{
throw new ArgumentException("Attribute " + rhIndex + " is disclosed but also used a revocation handle attribute, which should remain hidden");
}
// Verify EpochPK
if (!RevocationAuthority.VerifyEpochPK(revPk, revocationPk, revocationPKSig, epoch, revocationAlgorithm))
{
// Signature is based on an invalid revocation epoch public key
return(false);
}
FP12 temp1 = PAIR.Ate(ipk.W, aPrime);
FP12 temp2 = PAIR.Ate(IdemixUtils.GenG2, aBar);
temp2.Inverse();
temp1.mul(temp2);
if (!PAIR.FExp(temp1).IsUnity())
{
return(false);
}
ECP t1 = aPrime.Mul2(proofSE, ipk.HRand, proofSR2);
ECP temp = new ECP();
temp.Copy(aBar);
temp.Sub(bPrime);
t1.Sub(PAIR.G1Mul(temp, proofC));
ECP t2 = PAIR.G1Mul(ipk.HRand, proofSSPrime);
t2.Add(bPrime.Mul2(proofSR3, ipk.Hsk, proofSSk));
for (int i = 0; i < hiddenIndices.Length / 2; i++)
{
t2.Add(ipk.HAttrs[hiddenIndices[2 * i]].Mul2(proofSAttrs[2 * i], ipk.HAttrs[hiddenIndices[2 * i + 1]], proofSAttrs[2 * i + 1]));
}
if (hiddenIndices.Length % 2 != 0)
{
t2.Add(PAIR.G1Mul(ipk.HAttrs[hiddenIndices[hiddenIndices.Length - 1]], proofSAttrs[hiddenIndices.Length - 1]));
}
temp = new ECP();
temp.Copy(IdemixUtils.GenG1);
for (int i = 0; i < disclosure.Length; i++)
{
if (disclosure[i])
{
temp.Add(PAIR.G1Mul(ipk.HAttrs[i], attributeValues[i]));
}
}
t2.Add(PAIR.G1Mul(temp, proofC));
ECP t3 = ipk.Hsk.Mul2(proofSSk, ipk.HRand, proofSRNym);
t3.Sub(nym.Mul(proofC));
// Check with non-revoked-verifier
INonRevocationVerifier nonRevokedVerifier = NonRevocationVerifier.GetNonRevocationVerifier(revocationAlgorithm);
int hiddenRHIndex = Array.IndexOf(hiddenIndices, rhIndex);
if (hiddenRHIndex < 0)
{
// rhIndex is not present, set to last index position
hiddenRHIndex = hiddenIndices.Length;
}
BIG proofSRh = proofSAttrs[hiddenRHIndex];
byte[] nonRevokedProofBytes = nonRevokedVerifier.RecomputeFSContribution(nonRevocationProof, proofC, revocationPk.ToECP2(), proofSRh);
if (nonRevokedProofBytes == null)
{
return(false);
}
// 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(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());
byte[] hashedProofData = finalProofData.HashModOrder().ToBytes();
return(Enumerable.SequenceEqual(proofC.ToBytes(), hashedProofData));
}
