/// <summary>
/// Create a verifiable encryption of a pseudonym. The output IECiphertext
/// object will contain the ciphertext and proof that it was formed correctly.
/// The pseudonym that is encrypted is (param.Ge)^(x_b), where x_b is an attribute
/// from the token.
/// </summary>
/// <param name="param"> Paramters of the ID escrow scheme.</param>
/// <param name="pk"> Public key of the Auditor (the authority who can decrypt the output ciphertex).</param>
/// <param name="tokenID"> The ID of the U-Prove token this ciphertext is assocaited with.</param>
/// <param name="Cxb"> The commitment value (commitment to x_b, with bases g, g1).</param>
/// <param name="x_b"> The attributed commited to by <c>Cxb</c></param>
/// <param name="o_b"> The randomizer value used to create <c>Cxb</c></param>
/// <param name="additionalInfo"> Arbitrary data that will be cryptographically bound to the ciphertext,
/// but <b>NOT</b> encrypted, and will be included with the output ciphertext.
/// The integrity of the <c>additionalInfo</c> is protected, i.e., modifying
/// the <c>additionalInfo</c> included in the ciphertext will cause verification/decryption to fail.
/// The <c>additionalInfo</c> field is sometimes referred to in the cryptographic literature
/// as a <i>label</i>. </param>
/// <param name="preGenRandom">Optional pre-generated random values to be used in the protocol.
/// Set to <c>null</c> if unused. The primary use of this field is for testing with test vectors.</param>
/// <returns>An <c>IECiphertext</c> object with the ciphertext and proof.</returns>
/// <remarks>
/// The additionalInfo field may be null to signify that there is no input, all other input
/// paramters must be non-null.
///
/// Input validation is limited to checking for non-null. We assume that all group & field elements are consistent
/// with the parameters specified by the IdEscrowParams.
/// </remarks>
public static IDEscrowCiphertext VerifiableEncrypt(IDEscrowParams param, IDEscrowPublicKey pk, byte[] tokenID, GroupElement Cxb,
FieldZqElement x_b, FieldZqElement o_b, byte[] additionalInfo, IDEscrowProofGenerationRandomData preGenRandom = null)
{
// Notation & numbering follows draft spec -- subject to change.
GroupElement g = param.ip.Gq.G; // first base for commitment Cxb
GroupElement g1 = param.ip.G[1]; // second base for Cxb
if (param == null || pk == null || tokenID == null || Cxb == null || g == null || g1 == null || x_b == null || o_b == null)
{
throw new ArgumentNullException("Null input to VerifiableEncrypt");
}
if (tokenID.Length == 0)
{
throw new ArgumentOutOfRangeException("tokenID has length 0");
}
Group G = param.G;
FieldZq F = param.Zq;
if (preGenRandom == null || preGenRandom.HasNullValue())
{
preGenRandom = IDEscrowProofGenerationRandomData.Generate(F);
}
// [1.] Encrypt
// Compute E1
FieldZqElement r = preGenRandom.R;
GroupElement E1 = param.Ge.Exponentiate(r); // E1 = (g_e)^r
// Compute E2 = (g_e)^x_b * H^r
GroupElement E2 = G.MultiExponentiate(new GroupElement[] { pk.H, param.Ge }, new FieldZqElement[] { r, x_b });
// [2.] Generate proof of correctness
// [2.a]
FieldZqElement xbPrime = preGenRandom.XbPrime;
FieldZqElement rPrime = preGenRandom.RPrime;
FieldZqElement obPrime = preGenRandom.ObPrime;
// [2.b]
GroupElement CxbPrime = G.MultiExponentiate(new GroupElement[] { g, g1 }, new FieldZqElement[] { xbPrime, obPrime }); // Cxb' = (g^xb')*(g1^ob')
GroupElement E1Prime = param.Ge.Exponentiate(rPrime); // E1' = (ge)^r'
GroupElement E2Prime = G.MultiExponentiate(new GroupElement[] { param.Ge, pk.H }, new FieldZqElement[] { xbPrime, rPrime }); // E2' = ((g_e)^xb')*(H^r')
// [2.c]
FieldZqElement c = ComputeChallenge(param.ip, tokenID, pk, Cxb, E1, E2, CxbPrime, E1Prime, E2Prime, additionalInfo);
// [2.d]
FieldZqElement rXb = ComputeResponse(xbPrime, c, x_b);
FieldZqElement rR = ComputeResponse(rPrime, c, r);
FieldZqElement rOb = ComputeResponse(obPrime, c, o_b);
IDEscrowProof proof = new IDEscrowProof(c, rXb, rR, rOb);
IDEscrowCiphertext ctext = new IDEscrowCiphertext(E1, E2, proof, additionalInfo);
return(ctext);
}
/// <summary>
/// Compare two <c>IDEscrowPublicKey</c> objects
/// </summary>
/// <param name="pk2">To be compared to this object</param>
/// <returns>True if equal, false otherwise.</returns>
public bool Equals(IDEscrowPublicKey pk2)
{
if (pk2 == null)
{
return(false);
}
if (!pk2.H.Equals(this.h))
{
return(false);
}
return(true);
}
// Compute c = H(IP, T, H, Cxb, E1, E2, Cxb', E1', E2', additionalInfo)
private static FieldZqElement ComputeChallenge(IssuerParameters ip, byte[] tokenID, IDEscrowPublicKey pk, GroupElement Cxb, GroupElement E1, GroupElement E2, GroupElement CxbPrime, GroupElement E1Prime, GroupElement E2Prime, byte[] additionalInfo)
{
HashFunction hasher = ip.HashFunction;
FieldZq F = ip.Zq;
hasher.Hash(ip.UidP);
hasher.Hash(tokenID);
hasher.Hash(pk.H);
hasher.Hash(Cxb);
hasher.Hash(E1);
hasher.Hash(E2);
hasher.Hash(CxbPrime);
hasher.Hash(E1Prime);
hasher.Hash(E2Prime);
hasher.Hash(additionalInfo); // additionalInfo may be null, and Hash() will handle this correctly.
return(F.GetElementFromDigest(hasher.Digest));
}
/// <summary>
/// Verifies that an <c>IECiphertext</c> was computed correctly.
/// </summary>
/// <param name="param">Paramters of the ID escrow scheme.</param>
/// <param name="ctext"> A ciphertext created with <c>param</c> and <c>pk</c>.</param>
/// <param name="tokenID">The ID of the U-Prove token this ciphertext is assocaited with.</param>
/// <param name="pk">Public key of the Auditor (the authority who can decrypt <c>ctext</c>).</param>
/// <param name="Cxb"> The commitment value (commitment to x_b, with bases g, g1).</param>
/// <returns><c>true</c> if the ciphertext is valid, and <c>false</c> otherwise.</returns>
/// <remarks>
/// The input <c>pk</c> is assumed to be valid, coming from a
/// trusted source (e.g., a certificate or a trusted store of parameters), and that they
/// are consistent with the group specified by <c>param</c>.
/// </remarks>
public static bool Verify(IDEscrowParams param, IDEscrowCiphertext ctext, byte[] tokenID, IDEscrowPublicKey pk, GroupElement Cxb)
{
GroupElement g = param.ip.Gq.G; // first base for commitment
GroupElement g1 = param.ip.G[1]; // second base for commitment
if (param == null || ctext == null || tokenID == null || pk == null || Cxb == null || g == null || g1 == null)
{
throw new ArgumentNullException("null input to Verify");
}
if (tokenID.Length == 0)
{
throw new ArgumentOutOfRangeException("tokenID has length 0");
}
Group G = param.ip.Gq;
FieldZq F = param.Zq;
IDEscrowProof proof = ctext.proof;
// [1.]Checks on inputs. These should be done during deserialization -- but we do
// them explicitly anyway, in case they were missed
if (!IsGroupElement(G, ctext.E1) || !IsGroupElement(G, ctext.E2) || !IsGroupElement(G, Cxb))
{
return(false);
}
if (!F.IsElement(proof.c) || !F.IsElement(proof.rOb) ||
!F.IsElement(proof.rR) || !F.IsElement(proof.rXb))
{
return(false);
}
// [2.] Recompute inputs to hash (using tilde{x} instead of x'' for this section.)
GroupElement tildeCxb = G.MultiExponentiate(
new GroupElement[] { g, g1, Cxb },
new FieldZqElement[] { proof.rXb, proof.rOb, proof.c }); // tildeCxb = (g^rXb)*(g1^rOb)*(Cxb^c)
GroupElement tildeE1 = G.MultiExponentiate(
new GroupElement[] { param.Ge, ctext.E1 },
new FieldZqElement[] { proof.rR, proof.c }); // tildeE1 = (E1^c)*(ge^rR)
GroupElement tildeE2 = G.MultiExponentiate(
new GroupElement[] { param.Ge, pk.H, ctext.E2 },
new FieldZqElement[] { proof.rXb, proof.rR, proof.c }); // tildeE2 = (ge^rXb)*(H^rR)*(E2^c)
// [3.]
FieldZqElement cPrime = ComputeChallenge(param.ip, tokenID, pk, Cxb, ctext.E1, ctext.E2, tildeCxb, tildeE1, tildeE2, ctext.additionalInfo);
// [4.]
if (cPrime.Equals(proof.c))
{
return(true);
}
return(false);
}
/// <summary>
/// Verifies that an <c>IECiphertext</c> was computed correctly.
/// This is a wrapper around <c>IEFunctions.Verify</c> for use with U-Prove.
/// </summary>
/// <param name="escrowParams">Parameters of the ID escrow scheme</param>
/// <param name="ctext">A ciphertext created with <c>param</c> and <c>pk</c>. </param>
/// <param name="proof">The associated U-Prove presentation proof.</param>
/// <param name="token">The associated U-Prove token.</param>
/// <param name="pk">The auditor's public key</param>
/// <returns> True if the ciphertext is valid, false if it is invalid.</returns>
/// <remarks>The identity <b>must be</b> the first committed attribute in the proof (as
/// in <c>UProveVerifiableEncrypt</c>).</remarks>
public static bool UProveVerify(IDEscrowParams escrowParams, IDEscrowCiphertext ctext, PresentationProof proof, UProveToken token, IDEscrowPublicKey pk)
{
if (escrowParams == null || ctext == null || proof == null || token == null || pk == null)
{
throw new ArgumentException("null input to UProveVerify");
}
if (proof.Commitments == null || proof.Commitments.Length < 1)
{
throw new InvalidUProveArtifactException("invalid inputs to UProveVerifiableEncrypt");
}
GroupElement Cx1 = proof.Commitments[0].TildeC;
byte[] tokenId = ProtocolHelper.ComputeTokenID(escrowParams.ip, token);
return(IDEscrowFunctions.Verify(escrowParams, ctext, tokenId, pk, Cx1));
}
/// <summary>
/// Create a verifiable encryption of a pseudonym based on a U-Prove presentation proof. This is a wrapper
/// of <c>VerifiableEncrypt</c>.
///
/// </summary>
/// <param name="escrowParams"> Parameters of the ID escrow scheme</param>
/// <param name="escrowPublicKey"> Public key of the Auditor (the authority who can decrypt the output ciphertex).</param>
/// <param name="token"> The U-Prove token corresponding to the <c>proof</c>. </param>
/// <param name="additionalInfo">See documentation of <c>VerifiableEncrypt</c></param>
/// <param name="proof">A U-Prove prsentation proof.</param>
/// <param name="cpv">Commitment opening information, output when generating <c>proof</c>.</param>
/// <param name="idAttributeIndex"> Index of the attribute to use for identity escrow (1-based indexing). This attribute <b>must be</b>
/// the first commited attribute (take care if using multiple extensions). </param>
/// <param name="attributes"> Attributes in <c>token</c>.</param>
/// <returns></returns>
public static IDEscrowCiphertext UProveVerifableEncrypt(IDEscrowParams escrowParams, IDEscrowPublicKey escrowPublicKey,
UProveToken token, byte[] additionalInfo, PresentationProof proof,
CommitmentPrivateValues cpv, int idAttributeIndex, byte[][] attributes)
{
if (token == null || escrowParams == null || proof == null || cpv == null)
{
throw new ArgumentNullException("null input to UProveVerifiableEncrypt");
}
if (proof.Commitments == null || proof.Commitments.Length < 1 ||
attributes.Length < idAttributeIndex || cpv.TildeO == null || cpv.TildeO.Length < 1)
{
throw new InvalidUProveArtifactException("invalid inputs to UProveVerifiableEncrypt");
}
byte[] tokenId = ProtocolHelper.ComputeTokenID(escrowParams.ip, token);
GroupElement Cx1 = proof.Commitments[0].TildeC; // x1 is the first committed attribute
FieldZqElement x1 = ProtocolHelper.ComputeXi(escrowParams.ip, idAttributeIndex - 1, attributes[idAttributeIndex - 1]); // arrays are 0-based
FieldZqElement tildeO1 = cpv.TildeO[0];
return(IDEscrowFunctions.VerifiableEncrypt(escrowParams, escrowPublicKey, tokenId, Cx1, x1, tildeO1, additionalInfo));
}
