public static PresentationProof Generate(IssuerParameters ip, int[] disclosed, int[] committed, int pseudonymAttribIndex, GroupElement gs, byte[] message, byte[] messageD, IDevicePresentationContext deviceContext, UProveKeyAndToken upkt, byte[][] attributes, ProofGenerationRandomData preGenW, out FieldZqElement[] tildeO)
{
CommitmentPrivateValues cpv;
PresentationProof proof = Generate(ip, disclosed, committed, pseudonymAttribIndex, gs, message, messageD, deviceContext, upkt, attributes, preGenW, out cpv);
tildeO = cpv.TildeO;
return(proof);
}
public PresentationProof presentation; // presentation for carry-over attribute commitments
// This is private because everyone should use CreateProof
private PreIssuanceProof(GroupElement h0, GroupElement CGamma, GroupElement Ch0, byte[] c,
Dictionary <String, FieldZqElement> responses, PresentationProof presentation)
{
this.h0 = h0;
this.CGamma = CGamma;
this.Ch0 = Ch0;
this.c = c;
this.responses = responses;
this.presentation = presentation;
}
/// <summary>
/// Generates a presentation proof including optionally presenting a pseudonym, creating attribute commitments, and passing pre-generated random values.
/// </summary>
/// <param name="ip">The issuer parameters corresponding to <code>upkt</code>.</param>
/// <param name="disclosed">An ordered array of disclosed attribute indices.</param>
/// <param name="committed">An ordered array of committed attribute indices.</param>
/// <param name="pseudonymAttribIndex">Index of the attribute used to create a scope-exclusive pseudonym, or 0 if no pseudonym is to be presented. The index must not be part of the disclosed attributes.</param>
/// <param name="gs">The pseudonym scope element, or null if no pseudonym is to be presented.</param>
/// <param name="message">The presentation message.</param>
/// <param name="messageD">The message for the Device, or null.</param>
/// <param name="deviceContext">The active device context, if token is device-protected, or null.</param>
/// <param name="upkt">The U-Proke key and token.</param>
/// <param name="attributes">The token attributes.</param>
/// <param name="preGenW">Optional pregenerated random data for the proof generation.</param>
/// <param name="cpv">Returned commitment private values if commitments are computed.</param>
/// <returns>A presentation proof.</returns>
internal static PresentationProof Generate(IssuerParameters ip, int[] disclosed, int[] committed, int pseudonymAttribIndex, GroupElement gs, byte[] message, byte[] messageD, IDevicePresentationContext deviceContext, UProveKeyAndToken upkt, byte[][] attributes, ProofGenerationRandomData preGenW, out CommitmentPrivateValues cpv)
{
if (upkt.Token.IsDeviceProtected && deviceContext == null)
{
throw new ArgumentNullException("Device context is not initialized");
}
bool generateCommitments = (committed != null && committed.Length > 0);
FieldZqElement[] tildeO = null;
// make sure disclosed and committed lists are sorted
if (disclosed == null)
{
// can't be null later, so make it an empty array
disclosed = new int[] { };
}
Array.Sort(disclosed);
if (generateCommitments)
{
Array.Sort(committed);
}
int n = 0;
if (ip.E != null)
n = ip.E.Length;
bool presentPseudonym = false;
if (gs != null)
{
if (pseudonymAttribIndex < 1 || (pseudonymAttribIndex > n && pseudonymAttribIndex != DeviceAttributeIndex))
{
throw new ArgumentException("pseudonymAttribIndex must be between 1 and " + n + " (inclusive)");
}
if (disclosed.Contains(pseudonymAttribIndex))
{
throw new ArgumentException("pseudonymAttribIndex cannot be in the disclosed attribute array");
}
presentPseudonym = true;
}
else if (pseudonymAttribIndex > 0)
{
throw new ArgumentNullException("gs is null");
}
else
{
pseudonymAttribIndex = 0;
}
Group Gq = ip.Gq;
FieldZq Zq = ip.Zq;
FieldZqElement xt = ProtocolHelper.ComputeXt(ip, upkt.Token.TI, upkt.Token.IsDeviceProtected);
ProofGenerationRandomData random;
if (preGenW == null)
{
random = ProofGenerationRandomData.Generate(n - disclosed.Length, generateCommitments ? committed.Length : 0, Zq, upkt.Token.IsDeviceProtected);
}
else
{
random = preGenW;
}
FieldZqElement[] x = new FieldZqElement[n];
GroupElement temp = upkt.Token.H.Exponentiate(random.W0);
int uIndex = 0;
int dIndex = 0;
int cIndex = 0;
PresentationProof proof = new PresentationProof();
proof.DisclosedAttributes = new byte[disclosed.Length][];
int pseudonymRandomizerIndex = 0;
if (generateCommitments)
{
proof.Commitments = new CommitmentValues[committed.Length];
tildeO = new FieldZqElement[committed.Length];
}
HashFunction hash = ip.HashFunction;
for (int i = 0; i < n; i++)
{
x[i] = ProtocolHelper.ComputeXi(ip, i, attributes[i]);
if (!disclosed.Contains(i + 1))
{
temp = temp * ip.G[i + 1].Exponentiate(random.W[uIndex]);
if (presentPseudonym)
{
if (pseudonymAttribIndex == (i + 1))
{
pseudonymRandomizerIndex = uIndex;
}
}
if (generateCommitments && committed.Contains(i + 1))
{
GroupElement tildeC = ip.Gq.G.Exponentiate(x[i]) * ip.G[1].Exponentiate(random.TildeO[cIndex]);
tildeO[cIndex] = random.TildeO[cIndex];
GroupElement temp2 = ip.Gq.G.Exponentiate(random.W[uIndex]) * ip.G[1].Exponentiate(random.TildeW[cIndex]);
hash.Hash(temp2);
byte[] tildeA = hash.Digest;
proof.Commitments[cIndex] = new CommitmentValues(tildeC, tildeA, null);
cIndex++;
}
uIndex++;
}
else if (generateCommitments && committed.Contains(i + 1))
{
throw new ArgumentException("attribute " + (i + 1) + " cannot be both disclosed and committed");
}
else
{
proof.DisclosedAttributes[dIndex] = attributes[i];
dIndex++;
}
}
if (upkt.Token.IsDeviceProtected)
{
GroupElement ad;
// pseudonym computed by device
if (presentPseudonym && pseudonymAttribIndex == DeviceAttributeIndex)
{
GroupElement apPrime;
GroupElement Ps;
ad = deviceContext.GetInitialWitnessesAndPseudonym(gs, out apPrime, out Ps);
hash.Hash(apPrime * gs.Exponentiate(random.Wd));
proof.Ap = hash.Digest;
proof.Ps = Ps;
}
else
{
ad = deviceContext.GetInitialWitness();
}
temp = temp * ip.Gd.Exponentiate(random.Wd) * ad;
}
hash.Hash(temp);
proof.a = hash.Digest;
// pseudonym derived from one token attribute
if (presentPseudonym && pseudonymAttribIndex != DeviceAttributeIndex)
{
hash.Hash(gs.Exponentiate(random.W[pseudonymRandomizerIndex]));
proof.Ap = hash.Digest;
proof.Ps = gs.Exponentiate(x[pseudonymAttribIndex - 1]);
}
byte[] mdPrime;
FieldZqElement c = ProtocolHelper.GenerateChallenge(ip, upkt.Token, proof.a, pseudonymAttribIndex, proof.ap, proof.Ps, message, messageD, disclosed, GetDisclosedX(disclosed, x), committed, proof.Commitments, out mdPrime);
proof.r = new FieldZqElement[1 + n - disclosed.Length + (upkt.Token.IsDeviceProtected ? 1 : 0)]; // r_0, {r_i} for undisclosed i, r_d
proof.r[0] = c * upkt.PrivateKey + random.W0;
uIndex = 1;
for (int i = 1; i <= n; i++)
{
if (!disclosed.Contains(i))
{
proof.r[uIndex] = c.Negate() * x[i - 1] + random.W[uIndex - 1];
uIndex++;
}
}
if (upkt.Token.IsDeviceProtected)
{
proof.r[proof.r.Length - 1] = deviceContext.GetDeviceResponse(messageD, mdPrime, ip.HashFunctionOID) + random.Wd;
}
if (generateCommitments)
{
for (int i = 0; i < committed.Length; i++)
{
proof.Commitments[i].TildeR = c.Negate() * random.TildeO[i] + random.TildeW[i];
}
}
random.Clear();
cpv = new CommitmentPrivateValues(tildeO);
return proof;
}
/// <summary>
/// Generates a presentation proof including optionally presenting a pseudonym, creating attribute commitments, and passing pre-generated random values.
/// </summary>
/// <param name="ip">The issuer parameters corresponding to <code>upkt</code>.</param>
/// <param name="disclosed">An ordered array of disclosed attribute indices.</param>
/// <param name="committed">An ordered array of committed attribute indices.</param>
/// <param name="pseudonymAttribIndex">Index of the attribute used to create a scope-exclusive pseudonym, or 0 if no pseudonym is to be presented. The index must not be part of the disclosed attributes.</param>
/// <param name="gs">The pseudonym scope element, or null if no pseudonym is to be presented.</param>
/// <param name="message">The presentation message.</param>
/// <param name="messageD">The message for the Device, or null.</param>
/// <param name="deviceContext">The active device context, if token is device-protected, or null.</param>
/// <param name="upkt">The U-Proke key and token.</param>
/// <param name="attributes">The token attributes.</param>
/// <param name="preGenW">Optional pregenerated random data for the proof generation.</param>
/// <param name="cpv">Returned commitment private values if commitments are computed.</param>
/// <returns>A presentation proof.</returns>
internal static PresentationProof Generate(IssuerParameters ip, int[] disclosed, int[] committed, int pseudonymAttribIndex, GroupElement gs, byte[] message, byte[] messageD, IDevicePresentationContext deviceContext, UProveKeyAndToken upkt, byte[][] attributes, ProofGenerationRandomData preGenW, out CommitmentPrivateValues cpv)
{
if (upkt.Token.IsDeviceProtected && deviceContext == null)
{
throw new ArgumentNullException("Device context is not initialized");
}
bool generateCommitments = (committed != null && committed.Length > 0);
FieldZqElement[] tildeO = null;
// make sure disclosed and committed lists are sorted
if (disclosed == null)
{
// can't be null later, so make it an empty array
disclosed = new int[] { };
}
Array.Sort(disclosed);
if (generateCommitments)
{
Array.Sort(committed);
}
int n = 0;
if (ip.E != null)
{
n = ip.E.Length;
if (n != attributes.Length)
{
throw new ArgumentException("number of attributes is inconsistent with issuer parameters");
}
}
bool presentPseudonym = false;
if (gs != null)
{
if (pseudonymAttribIndex < 1 || (pseudonymAttribIndex > n && pseudonymAttribIndex != DeviceAttributeIndex))
{
throw new ArgumentException("pseudonymAttribIndex must be between 1 and " + n + " (inclusive)");
}
if (disclosed.Contains(pseudonymAttribIndex))
{
throw new ArgumentException("pseudonymAttribIndex cannot be in the disclosed attribute array");
}
presentPseudonym = true;
}
else if (pseudonymAttribIndex > 0)
{
throw new ArgumentNullException("gs is null");
}
else
{
pseudonymAttribIndex = 0;
}
Group Gq = ip.Gq;
FieldZq Zq = ip.Zq;
FieldZqElement xt = ProtocolHelper.ComputeXt(ip, upkt.Token.TI, upkt.Token.IsDeviceProtected);
ProofGenerationRandomData random;
if (preGenW == null)
{
random = ProofGenerationRandomData.Generate(n - disclosed.Length, generateCommitments ? committed.Length : 0, Zq, upkt.Token.IsDeviceProtected);
}
else
{
random = preGenW;
}
// set up the multi-exponentiation arrays, with h^w0 as the first term
int multiExpArraySize = 1 + (n - disclosed.Length) + (upkt.Token.IsDeviceProtected ? 1 : 0);
GroupElement[] bases = new GroupElement[multiExpArraySize];
FieldZqElement[] exponents = new FieldZqElement[multiExpArraySize];
int multiExpIndex = 0;
bases[multiExpIndex] = upkt.Token.H;
exponents[multiExpIndex++] = random.W0;
FieldZqElement[] x = new FieldZqElement[n];
int uIndex = 0;
int dIndex = 0;
int cIndex = 0;
PresentationProof proof = new PresentationProof();
proof.DisclosedAttributes = new byte[disclosed.Length][];
int pseudonymRandomizerIndex = 0;
if (generateCommitments)
{
proof.Commitments = new CommitmentValues[committed.Length];
tildeO = new FieldZqElement[committed.Length];
}
HashFunction hash = ip.HashFunction;
GroupElement[] cBases = new GroupElement[2] {
Gq.G, ip.G[1]
};
for (int i = 0; i < n; i++)
{
x[i] = ProtocolHelper.ComputeXi(ip, i, attributes[i]);
if (!disclosed.Contains(i + 1))
{
bases[multiExpIndex] = ip.G[i + 1];
exponents[multiExpIndex++] = random.W[uIndex];
if (presentPseudonym)
{
if (pseudonymAttribIndex == (i + 1))
{
pseudonymRandomizerIndex = uIndex;
}
}
if (generateCommitments && committed.Contains(i + 1))
{
GroupElement tildeC = ip.Gq.MultiExponentiate(cBases, new FieldZqElement[2] {
x[i], random.TildeO[cIndex]
});
tildeO[cIndex] = random.TildeO[cIndex];
GroupElement temp2 = ip.Gq.MultiExponentiate(cBases, new FieldZqElement[2] {
random.W[uIndex], random.TildeW[cIndex]
});
hash.Hash(temp2);
byte[] tildeA = hash.Digest;
proof.Commitments[cIndex] = new CommitmentValues(tildeC, tildeA, null);
cIndex++;
}
uIndex++;
}
else if (generateCommitments && committed.Contains(i + 1))
{
throw new ArgumentException("attribute " + (i + 1) + " cannot be both disclosed and committed");
}
else
{
proof.DisclosedAttributes[dIndex] = attributes[i];
dIndex++;
}
}
GroupElement aPreImage;
if (upkt.Token.IsDeviceProtected)
{
GroupElement ad;
// pseudonym computed by device
if (presentPseudonym && pseudonymAttribIndex == DeviceAttributeIndex)
{
GroupElement apPrime;
GroupElement Ps;
ad = deviceContext.GetInitialWitnessesAndPseudonym(gs, out apPrime, out Ps);
hash.Hash(apPrime * gs.Exponentiate(random.Wd));
proof.Ap = hash.Digest;
proof.Ps = Ps;
}
else
{
ad = deviceContext.GetInitialWitness();
}
bases[multiExpIndex] = ip.Gd;
exponents[multiExpIndex++] = random.Wd;
aPreImage = Gq.MultiExponentiate(bases, exponents) * ad;
}
else
{
aPreImage = Gq.MultiExponentiate(bases, exponents);
}
hash.Hash(aPreImage);
proof.a = hash.Digest;
// pseudonym derived from one token attribute
if (presentPseudonym && pseudonymAttribIndex != DeviceAttributeIndex)
{
hash.Hash(gs.Exponentiate(random.W[pseudonymRandomizerIndex]));
proof.Ap = hash.Digest;
proof.Ps = gs.Exponentiate(x[pseudonymAttribIndex - 1]);
}
byte[] mdPrime;
FieldZqElement c = ProtocolHelper.GenerateChallenge(ip, upkt.Token, proof.a, pseudonymAttribIndex, proof.ap, proof.Ps, message, messageD, disclosed, GetDisclosedX(disclosed, x), committed, proof.Commitments, out mdPrime);
proof.r = new FieldZqElement[1 + n - disclosed.Length + (upkt.Token.IsDeviceProtected ? 1 : 0)]; // r_0, {r_i} for undisclosed i, r_d
proof.r[0] = c * upkt.PrivateKey + random.W0;
uIndex = 1;
for (int i = 1; i <= n; i++)
{
if (!disclosed.Contains(i))
{
proof.r[uIndex] = c.Negate() * x[i - 1] + random.W[uIndex - 1];
uIndex++;
}
}
if (upkt.Token.IsDeviceProtected)
{
proof.r[proof.r.Length - 1] = deviceContext.GetDeviceResponse(messageD, mdPrime, ip.HashFunctionOID) + random.Wd;
}
if (generateCommitments)
{
for (int i = 0; i < committed.Length; i++)
{
proof.Commitments[i].TildeR = c.Negate() * random.TildeO[i] + random.TildeW[i];
}
}
random.Clear();
cpv = new CommitmentPrivateValues(tildeO);
return(proof);
}
public static PresentationProofComposite convertPresentationProof(PresentationProof p, BigInteger[] commitmentValues, byte[] tokenId, byte[] proofSession)
{
PresentationProofComposite pc = new PresentationProofComposite();
pc.A = p.A;
pc.Ap = (p.Ap == null ? null : p.Ap);
pc.DisclosedAttributes = p.DisclosedAttributes;
pc.Ps = (p.Ps == null ? null : p.Ps.GetEncoded());
byte[][] byteArray = new byte[p.R.Length][];
for (int i = 0; i < byteArray.Length; i++)
{
byteArray[i] = p.R[i].ToByteArray();
}
pc.R = byteArray;
if (p.Commitments != null)
{
pc.TildeValues = new byte[3 * p.Commitments.Length][];
for (int i = 0; i < p.Commitments.Length; i++)
{
pc.TildeValues[(i * 3)] = p.Commitments[i].TildeC.GetEncoded();
pc.TildeValues[(i * 3) + 1] = p.Commitments[i].TildeA;
pc.TildeValues[(i * 3) + 2] = p.Commitments[i].TildeR.ToByteArray();
}
}
if (commitmentValues != null)
{
if (commitmentValues.Length != p.Commitments.Length)
{
throw new ArgumentException("inconsistent commitment values");
}
pc.TildeO = new byte[commitmentValues.Length][];
for (int i = 0; i < commitmentValues.Length; i++)
{
pc.TildeO[i] = commitmentValues[i].ToByteArray();
}
}
pc.TokenID = tokenId;
pc.MessageD = (proofSession == null ? null : proofSession);
return pc;
}
public static PresentationProof convertPresentationProofComposite(IssuerParameters ip, PresentationProofComposite pc, out byte[] tokenID, out byte[] proofSession)
{
PresentationProof p = new PresentationProof();
p.A = (pc.A == null ? null : pc.A);
p.Ap = (pc.Ap == null ? null : pc.Ap);
p.DisclosedAttributes = pc.DisclosedAttributes;
p.Ps = (pc.Ps == null ? null : ip.Gq.CreateGroupElement(pc.Ps));
BigInteger[] biArray = new BigInteger[pc.R.Length];
for (int i = 0; i < biArray.Length; i++)
{
biArray[i] = new BigInteger(1, pc.R[i]);
}
p.R = biArray;
if (pc.TildeValues != null)
{
int numCommitments = pc.TildeValues.Length / 3;
p.Commitments = new CommitmentValues[numCommitments];
for (int i = 0; i < numCommitments; i++)
{
p.Commitments[i] = new CommitmentValues(
ip.Gq.CreateGroupElement(pc.TildeValues[(i * 3)]), // tildeC
pc.TildeValues[(i * 3) + 1], // tildaA
new BigInteger(1, pc.TildeValues[(i * 3) + 2]) // tildeR
);
}
// we ignore the tildeO values. This method is called by the verifier, and
// the tildeO values should never be sent to the verifier.
}
tokenID = pc.TokenID;
proofSession = (pc.MessageD == null ? null : pc.MessageD);
return p;
}
/// <summary>
/// Create a new pre-issuance proof.
/// </summary>
/// <param name="pipp">The prover parameters.</param>
/// <param name="beta0">The random blinding value used to create the proof, output so that the prover can use it during the issuance protocol</param>
/// <param name="message">An optional message to sign while creating the proof.</param>
/// <returns></returns>
public static PreIssuanceProof CreateProof(ProverPreIssuanceParameters pipp, out FieldZqElement beta0, byte[] message)
{
// validate paramters first
pipp.Validate();
bool supportDevice = (pipp.DevicePublicKey == null) ? false : true;
IssuerParameters ip = pipp.IP;
FieldZq Zq = ip.Zq;
Group Gq = ip.Gq;
Dictionary <string, FieldZqElement> responses = new Dictionary <string, FieldZqElement>();
// these will be used if there is a carry-over attribute
CommitmentPrivateValues cpv = null;
PresentationProof presProof = null;
GroupElement[] C = null;
GroupElement[] tildeC = null;
FieldZqElement[] tildeR = null;
// extension by Fablei -> needs to calculate the ip.G.Length -> pipp.Attributes.Length + 2
int ipGLength = pipp.Attributes.Length + 2;
// Generate random values
beta0 = Zq.GetRandomElement(true);
FieldZqElement tildeBeta0 = Zq.GetRandomElement(true);
FieldZqElement rho = Zq.GetRandomElement(true);
FieldZqElement tildeRho = Zq.GetRandomElement(true);
FieldZqElement tilde_d = Zq.GetRandomElement(true);
FieldZqElement[] tildeX = new FieldZqElement[ipGLength - 1];
for (int i = 1; i < ipGLength - 1; i++)
{
if (!pipp.K.Contains(i))
{
tildeX[i] = Zq.GetRandomElement(true);
}
}
// Compute the U-Prove presentation proof, if there are carry-over attributes
if (pipp.HasCarryOverAttributes)
{
// generate the presentation proof
int[] disclosed = new int[] { };
ProverPresentationProtocolParameters pppp = new ProverPresentationProtocolParameters(pipp.SourceIP, disclosed, message, pipp.KeyAndToken, pipp.SourceAttributes);
pppp.Committed = pipp.Corig;
// TODO: What if the source token is device protected? need to handle this as well. (a pointer to the device should be included in pipp
//if (device != null)
//{
// pppp.SetDeviceData(deviceMessage, device.GetPresentationContext());
//}-
// For now just fail:
if (pipp.KeyAndToken.Token.IsDeviceProtected)
{
throw new NotImplementedException("Device protected tokens may not be used for carry-over attributes");
}
presProof = PresentationProof.Generate(pppp, out cpv);
//set C
C = new GroupElement[pipp.C.Length];
// Generate random values for the commitment randomizers
tildeR = Zq.GetRandomElements(pipp.C.Length, true);
tildeC = new GroupElement[C.Length];
for (int i = 0; i < C.Length; i++)
{
C[i] = presProof.Commitments[i].TildeC;
tildeC[i] = Gq.MultiExponentiate(Gq.G, ip.G[1], tildeX[pipp.C[i]], tildeR[i]);
}
} // end if cary-over attributes
// Compute gamma
GroupElement gamma = ProtocolHelper.ComputeIssuanceInput(ip, pipp.Attributes, pipp.TI, pipp.DevicePublicKey);
// Compute h0, Cgamma, Ch0, tildeD, tildeT:
GroupElement h0 = gamma.Exponentiate(beta0);
GroupElement Cgamma = gamma.Multiply(Gq.G.Exponentiate(rho)); // Cgamma = gamma*(g^rho)
GroupElement Ch0 = Cgamma.Exponentiate(beta0);
GroupElement tildeD = Gq.G.Exponentiate(tilde_d);
GroupElement tildeT = Cgamma.Exponentiate(tildeBeta0);
// Compute tildeCgamma:
List <GroupElement> bases = new List <GroupElement>();
List <FieldZqElement> exponents = new List <FieldZqElement>();
bases.Add(Gq.G);
exponents.Add(tildeRho);
for (int i = 1; i < ipGLength - 1; i++)
{
if (!pipp.K.Contains(i)) // i \not\in K
{
bases.Add(ip.G[i]);
exponents.Add(tildeX[i]);
}
}
GroupElement tildeCgamma = Gq.MultiExponentiate(bases.ToArray(), exponents.ToArray());
// TODO: if device protected, then multiply tildeCgamma by the public key
// Note: We leave TI out, (i.e., (g_t)^(x_t) because t \in K implicitly.
// Compute the challenge
byte[] c = ComputeChallenge(ip, h0, Cgamma, Ch0, C, tildeD, tildeCgamma, tildeT, tildeC, message);
FieldZqElement negc = Zq.GetElementFromDigest(c).Negate();
// Compute the responses
responses.Add("sBeta0", tildeBeta0.Add(beta0.Multiply(negc))); // sBeta0 = tildeBeta0 - beta0*c
responses.Add("sD", tilde_d.Add(beta0.Multiply(rho).Multiply(negc))); // sD = tilde_d - beta0*rho*c
responses.Add("sRho", tildeRho.Add(rho.Multiply(negc))); // sRho = tildeRho - rho*c
for (int i = 1; i < ipGLength - 1; i++)
{
if (!pipp.K.Contains(i)) // in \not\in K
{
FieldZqElement xi = ProtocolHelper.ComputeXi(ip, i - 1, pipp.Attributes[i - 1]);
responses.Add("sx" + i, tildeX[i].Add(xi.Multiply(negc))); // sxi = tildeX[i] - xi*c
}
}
if (pipp.HasCarryOverAttributes)
{
for (int i = 0; i < C.Length; i++)
{
responses.Add("sR" + i, tildeR[i].Add(cpv.TildeO[i].Multiply(negc))); // sRi = tildeR[i] - tildeO[i]*c
}
}
return(new PreIssuanceProof(h0, Cgamma, Ch0, c, responses,
pipp.HasCarryOverAttributes ? presProof : null, pipp.Attributes.Length));
}