/* 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);
}
/* GLV method */
public static BIG[] Glv(BIG e)
{
BIG[] u = new BIG[2];
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[2];
for (i = 0; i < 2; i++)
{
t.Copy(new BIG(ROM.CURVE_W[i])); // why not just t=new BIG(ROM.CURVE_W[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 < 2; i++)
{
for (j = 0; j < 2; j++)
{
t.Copy(new BIG(ROM.CURVE_SB[j][i]));
t.Copy(BIG.ModMul(v[j], t, q));
u[i].Add(q);
u[i].Sub(t);
u[i].Mod(q);
}
}
}
else
{
// -(x^2).P = (Beta.x,y)
BIG q = new BIG(ROM.CURVE_Order);
BIG x = new BIG(ROM.CURVE_Bnx);
BIG x2 = BIG.SMul(x, x);
u[0] = new BIG(e);
u[0].Mod(x2);
u[1] = new BIG(e);
u[1].Div(x2);
u[1].RSub(q);
}
return(u);
}
/**
* Constructor
*
* @param sk the secret key of the user
* @param issuerNonce a nonce
* @param ipk the issuer public key
*/
public IdemixCredRequest(BIG sk, BIG issuerNonce, IdemixIssuerPublicKey ipk)
{
if (sk == null)
{
throw new ArgumentException("Cannot create idemix credrequest from null Secret Key input");
}
if (issuerNonce == null)
{
throw new ArgumentException("Cannot create idemix credrequest from null issuer nonce input");
}
if (ipk == null)
{
throw new ArgumentException("Cannot create idemix credrequest from null Issuer Public Key input");
}
RAND rng = IdemixUtils.GetRand();
Nym = ipk.Hsk.Mul(sk);
this.issuerNonce = new BIG(issuerNonce);
// Create Zero Knowledge Proof
BIG rsk = rng.RandModOrder();
ECP t = ipk.Hsk.Mul(rsk);
// Make proofData: total 3 elements of G1, each 2*FIELD_BYTES+1 (ECP),
// plus length of String array,
// plus one BIG
byte[] proofData = new byte[0];
proofData = proofData.Append(CREDREQUEST_LABEL.ToBytes());
proofData = proofData.Append(t.ToBytes());
proofData = proofData.Append(ipk.Hsk.ToBytes());
proofData = proofData.Append(Nym.ToBytes());
proofData = proofData.Append(issuerNonce.ToBytes());
proofData = proofData.Append(ipk.Hash);
proofC = proofData.HashModOrder();
// Compute proofS = ...
proofS = BIG.ModMul(proofC, sk, IdemixUtils.GROUP_ORDER).Plus(rsk);
proofS.Mod(IdemixUtils.GROUP_ORDER);
}
/**
* Constructor
*
* @param sk the secret key
* @param pseudonym the pseudonym with respect to which this signature can be verified
* @param ipk the issuer public key
* @param msg the message to be signed
*/
public IdemixPseudonymSignature(BIG sk, IdemixPseudonym pseudonym, IdemixIssuerPublicKey ipk, byte[] msg)
{
if (sk == null || pseudonym == null || pseudonym.Nym == null || pseudonym.RandNym == null || ipk == null || msg == null)
{
throw new ArgumentException("Cannot create IdemixPseudonymSignature from null input");
}
RAND rng = IdemixUtils.GetRand();
nonce = rng.RandModOrder();
//Construct Zero Knowledge Proof
BIG rsk = rng.RandModOrder();
BIG rRNym = rng.RandModOrder();
ECP t = ipk.Hsk.Mul2(rsk, ipk.HRand, rRNym);
// create array for proof data that will contain the sign label, 2 ECPs (each of length 2* FIELD_BYTES + 1), the ipk hash and the message
byte[] proofData = new byte[0];
proofData = proofData.Append(NYM_SIGN_LABEL.ToBytes());
proofData = proofData.Append(t.ToBytes());
proofData = proofData.Append(pseudonym.Nym.ToBytes());
proofData = proofData.Append(ipk.Hash);
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 = new BIG(rsk);
proofSSk.Add(BIG.ModMul(proofC, sk, IdemixUtils.GROUP_ORDER));
proofSSk.Mod(IdemixUtils.GROUP_ORDER);
proofSRNym = new BIG(rRNym);
proofSRNym.Add(BIG.ModMul(proofC, pseudonym.RandNym, IdemixUtils.GROUP_ORDER));
proofSRNym.Mod(IdemixUtils.GROUP_ORDER);
}
/**
* 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);
}
/**
* Constructor
*
* @param attributeNames the names of attributes as String array (must not contain duplicates)
* @param isk the issuer secret key
*/
public IdemixIssuerPublicKey(string[] attributeNames, BIG isk)
{
// check null input
if (attributeNames == null || isk == null)
{
throw new ArgumentException("Cannot create IdemixIssuerPublicKey from null input");
}
// Checking if attribute names are unique
HashSet <string> map = new HashSet <string>();
foreach (string item in attributeNames)
{
if (map.Contains(item))
{
throw new ArgumentException("Attribute " + item + " appears multiple times in attributeNames");
}
map.Add(item);
}
RAND rng = IdemixUtils.GetRand();
// Attaching Attribute Names array correctly
AttributeNames = attributeNames;
// Computing W value
W = IdemixUtils.GenG2.Mul(isk);
// Filling up HAttributes correctly in Issuer Public Key, length
// preserving
HAttrs = new ECP[attributeNames.Length];
for (int i = 0; i < attributeNames.Length; i++)
{
HAttrs[i] = IdemixUtils.GenG1.Mul(rng.RandModOrder());
}
// Generating Hsk value
Hsk = IdemixUtils.GenG1.Mul(rng.RandModOrder());
// Generating HRand value
HRand = IdemixUtils.GenG1.Mul(rng.RandModOrder());
// Generating BarG1 value
BarG1 = IdemixUtils.GenG1.Mul(rng.RandModOrder());
// Generating BarG2 value
BarG2 = BarG1.Mul(isk);
// Zero Knowledge Proofs
// Computing t1 and t2 values with random local variable r for later use
BIG r = rng.RandModOrder();
ECP2 t1 = IdemixUtils.GenG2.Mul(r);
ECP t2 = BarG1.Mul(r);
// 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());
// Hashing proofData to proofC
ProofC = proofData.HashModOrder();
// Computing ProofS = (ProofC*isk) + r mod GROUP_ORDER
ProofS = BIG.ModMul(ProofC, isk, IdemixUtils.GROUP_ORDER).Plus(r);
ProofS.Mod(IdemixUtils.GROUP_ORDER);
// Compute Hash of IdemixIssuerPublicKey
byte[] serializedIpk = ToProto().ToByteArray();
Hash = serializedIpk.HashModOrder().ToBytes();
}
