/// <summary>
/// Creates a range proof that compares a UProve attribute to a target date.
/// Target attribute MUST NOT be hashed.
/// Value MUST be generated via RangeProofParameterFactory.EncodeYearAndDayAsUProveAttribute.
/// </summary>
/// <param name="prover">Token information.</param>
/// <param name="attributeIndexForProver">1-based index of target attribute.</param>
/// <param name="proofType">Range proof type</param>
/// <param name="targetDate">Compare token attribute to this date. (Time component is ignored).</param>
/// <param name="minYear">Minimum year for attribute and target date.</param>
/// <param name="maxYear">Maximum year for attribute and target date.</param>
public RangeProof(
ProverPresentationProtocolParameters prover1,
int attributeIndexForProver1,
VerifierRangeProofParameters.ProofType proofType,
ProverPresentationProtocolParameters prover2,
int attributeIndexForProver2,
int minValue,
int maxValue)
{
// make sure target attribute is not hashed
if ((prover1.IP.E[attributeIndexForProver1 - 1] == 0x01) || ((prover2.IP.E[attributeIndexForProver2 - 1]) == 0x01))
{
throw new ArgumentException("UProve attributes used in Range Proof must not be hashed.");
}
// generate Pedersen Commitments to token attributes
ProverPresentationProtocolParameters[] provers = new ProverPresentationProtocolParameters[] { prover1, prover2 };
int[] attributeIndices = new int[] { attributeIndexForProver1, attributeIndexForProver2 };
PedersenCommitment[] attributeCommitments = PedersenCommitment.PedersenCommmitmentsToAttributes(provers, attributeIndices);
// create range proof
ProverRangeProofParameters rangeProver = new ProverRangeProofParameters(
new CryptoParameters(prover1.IP),
attributeCommitments[0],
proofType,
attributeCommitments[1],
minValue,
maxValue);
ConstructorHelper(rangeProver);
// Add UProve Integration proof
this.UPIProof = new UProveIntegrationProof(provers, attributeIndices, attributeCommitments);
this.UPIProof.IsGroupSerializable = false;
}
/// <summary>
/// Returns array of DLRepOfGroupElement objects, where output[i] = openA[i] / openB[i].
/// Input arrays should be not null and of equal lengths.
/// </summary>
/// <param name="prover">Used to get bases G and H.</param>
/// <param name="openA">Each openA[i] should have RepresentationLength=2, with bases equal to prover.G and prover.H</param>
/// <param name="openB">Each openB[i] should have RepresentationLength=2, with bases equal to prover.G and prover.H</param>
/// <returns></returns>
public static DLRepOfGroupElement[] ComputeOpenAdivB(ProverRangeProofParameters prover, DLRepOfGroupElement [] openA, DLRepOfGroupElement [] openB)
{
DLRepOfGroupElement[] AdivB = new DLRepOfGroupElement[openA.Length];
for (int i = 0; i < AdivB.Length; ++i)
{
AdivB[i] = new PedersenCommitment(
prover.G,
prover.H,
openA[i].ExponentAtIndex(0) - openB[i].ExponentAtIndex(0),
openA[i].ExponentAtIndex(1) - openB[i].ExponentAtIndex(1),
prover.Group);
}
return(AdivB);
}
/// <summary>
/// Computes commitment to (a-b)^2.
/// Let openAdivB[i] be a commitment to (a[i]-b[i]). This method chooses
/// random u[i] and returns:
/// output[i] = (openAdivB[i].Value)^(a[i]-b[i]) * prover.H^u[i]
/// </summary>
/// <param name="prover">Range proof parameters</param>
/// <param name="openAdivB">Commitment to A/B</param>
/// <returns>Array of same length as openAdivB, first element is null.</returns>
public static DLRepOfGroupElement[] ComputeOpenX(ProverRangeProofParameters prover, DLRepOfGroupElement[] openAdivB)
{
FieldZqElement[] u = prover.FieldZq.GetRandomElements(openAdivB.Length, true);
DLRepOfGroupElement[] openX = new DLRepOfGroupElement[openAdivB.Length];
openX[0] = null;
for (int i = 1; i < openX.Length; ++i)
{
openX[i] = new PedersenCommitment(
openAdivB[i].Value,
prover.H,
openAdivB[i].ExponentAtIndex(0),
u[i],
prover.Group);
}
return(openX);
}
/// <summary>
/// Computes an array of commitments to d=Compute_d(prover,AdivB).
/// </summary>
/// <param name="prover">Used for bases G, H.</param>
/// <param name="AdivB">Used to compute committed values d.</param>
/// <returns>Array of same length as AdivB.</returns>
public static DLRepOfGroupElement[] ComputeOpenD(ProverRangeProofParameters prover, DLRepOfGroupElement [] AdivB)
{
FieldZqElement[] d = Compute_d(prover, AdivB);
DLRepOfGroupElement[] D = new DLRepOfGroupElement[d.Length];
FieldZqElement[] t = prover.FieldZq.GetRandomElements(d.Length, true);
D[0] = AdivB[0];
for (int i = 1; i < D.Length; ++i)
{
D[i] = new PedersenCommitment(
prover.G,
prover.H,
d[i],
t[i],
prover.Group);
}
return(D);
}
/// <summary>
/// Let a[i] be the committed bits in openAdivB,
///
/// Computes the arrray d as follows:
/// d[0] = a[0]
/// d[i] = d[i-1] - d[i-1]*a[i]^2 + a[i]
/// </summary>
/// <param name="prover">Prover parameters</param>
/// <returns>The array d</returns>
private static FieldZqElement[] Compute_d(ProverRangeProofParameters prover, DLRepOfGroupElement [] openAdivB)
{
FieldZqElement[] d = new FieldZqElement[openAdivB.Length];
for (int i = 0; i < d.Length; ++i)
{
FieldZqElement difference = openAdivB[i].ExponentAtIndex(0);
if (i == 0)
{
d[0] = difference;
}
else
{
d[i] = d[i - 1]
+ (d[i - 1].Negate() * difference * difference)
+ difference;
}
}
return(d);
}
/// <summary>
/// Creates a DL representation equation E[i].
/// Let d[i] be the committed value in D[i].
/// Let E[i].Value = D[i]/D[i-1] * AdivB[i]^{-1}.
/// Computes nu[i] so that the following relation holds
/// E[i].Value= (X[i]^{-1})^{d[i-1]} * prover.H^{nu[i]}.
/// </summary>
/// <param name="prover"></param>
/// <param name="D">Commitments to d</param>
/// <param name="X">Commitment to (a-b)^2</param>
/// <param name="AdivB">A/B</param>
/// <returns>Array of same length as D, first element is null.</returns>
public static DLRepOfGroupElement[] ComputeOpenE(ProverRangeProofParameters prover, DLRepOfGroupElement[] D, DLRepOfGroupElement [] X, DLRepOfGroupElement [] AdivB)
{
DLRepOfGroupElement[] E = new DLRepOfGroupElement[D.Length];
E[0] = null;
for (int i = 1; i < E.Length; ++i)
{
FieldZqElement nu =
D[i].ExponentAtIndex(1) // t[i]
- D[i - 1].ExponentAtIndex(1) // - t[i-1]
- AdivB[i].ExponentAtIndex(1) // - r[i]
+ (D[i - 1].ExponentAtIndex(0) // + (d[i-1] * r[i] * adivb[i])
* AdivB[i].ExponentAtIndex(1)
* AdivB[i].ExponentAtIndex(0))
+ (D[i - 1].ExponentAtIndex(0) // (d[i-1] * u[i])
* X[i].ExponentAtIndex(1));
E[i] = new PedersenCommitment(
prover.Group.Invert(X[i].Value),
prover.H,
D[i - 1].ExponentAtIndex(0),
nu,
prover.Group);
}
return(E);
}
/// <summary>
/// Creates a bit decomposition of prover.OpenIntegerA and prover.OpenIntegerB,
/// and proofs that they are valid. Sets member fields
/// A, B, ProofBitDecompositionOfA and ProofBitDecompositionOfB.
/// </summary>
/// <param name="prover">Prover range proof parameters</param>
/// <param name="bitProverA">outputs parameters for bit decomposition proof for A</param>
/// <param name="bitProverB">outputs parameters for bit decomposition proof for B</param>
/// <returns>Array AdivB with the bit decomposition of A divided by the bit decomposition of B.</returns>
private DLRepOfGroupElement [] CreateBitDecompositionProofs(ProverRangeProofParameters prover)
{
int decompositionLength = RangeProof.ComputeDecompositionLength(prover);
// create proof for A
ProverBitDecompositionParameters bitProverA = new ProverBitDecompositionParameters(prover.RangeNormalizedOpenIntegerA, decompositionLength, prover);
this.ProofBitDecompositionOfA = new BitDecompositionProof(bitProverA);
this.A = bitProverA.ClosedBitDecomposition();
// create proof for B if it is unknown.
ProverBitDecompositionParameters bitProverB = new ProverBitDecompositionParameters(prover.RangeNormalizedOpenIntegerB, decompositionLength, prover);
if (prover.IntegerBIsKnown)
{
this.ProofBitDecompositionOfB = null;
this.B = null;
DLRepOfGroupElement[] defaultB = DefaultOpenDecompositionOfIntegerB(prover);
return(ComputeOpenAdivB(prover, bitProverA.OpenBitDecomposition(), defaultB));
}
this.ProofBitDecompositionOfB = new BitDecompositionProof(bitProverB);
this.B = bitProverB.ClosedBitDecomposition();
return(ComputeOpenAdivB(prover, bitProverA.OpenBitDecomposition(), bitProverB.OpenBitDecomposition()));
}
public void ConstructorHelper(ProverRangeProofParameters prover)
{
try
{
// verify prover parameters
if (!prover.Verify())
{
throw new ArgumentException("RangeProof: could not create RangeProof because prover parameters are invalid.");
}
// set group
this.Group = prover.Group;
this.IsGroupSerializable = true;
// set up the bit decomposition proof and compute helper values
DLRepOfGroupElement[] openAdivB = CreateBitDecompositionProofs(prover);
if (this.ProofBitDecompositionOfA != null)
{
this.ProofBitDecompositionOfA.IsGroupSerializable = false;
}
if (this.ProofBitDecompositionOfB != null)
{
this.ProofBitDecompositionOfB.IsGroupSerializable = false;
}
DLRepOfGroupElement[] openD = ComputeOpenD(prover, openAdivB);
DLRepOfGroupElement[] openX = ComputeOpenX(prover, openAdivB);
DLRepOfGroupElement[] openE = ComputeOpenE(prover, openD, openX, openAdivB);
// compute RangeProof
DLRepOfGroupElement[] allOpenDL = CombineAllOpenDLReps(openD, openAdivB, openX, openE);
EqualityMap map = ComputeEqualityMap(prover, A.Length);
ProverEqualityParameters peParams = new ProverEqualityParameters(
allOpenDL,
map,
prover);
this.FullRangeProof = new EqualityProof(peParams);
this.FullRangeProof.IsGroupSerializable = false;
// set X and D
this.SetX(openX);
this.SetD(openD);
// create additional proofs based on proof type
PedersenCommitment LastD = (PedersenCommitment)openD[openD.Length - 1];
switch (prover.RangeProofType)
{
case VerifierRangeProofParameters.ProofType.GREATER_THAN:
// Prove that D is a commitment to 1
case VerifierRangeProofParameters.ProofType.LESS_THAN:
// Prove that D is a commitment to -1
DLRepOfGroupElement equation = new DLRepOfGroupElement(
new GroupElement[1] {
prover.H
},
new FieldZqElement[1] {
LastD.ExponentAtIndex(1)
},
prover.Group);
ProverEqualityParameters strictProver = new ProverEqualityParameters(
equation,
prover);
this.StrictlyThanProof = new EqualityProof(strictProver);
this.StrictlyThanProof.IsGroupSerializable = false;
break;
case VerifierRangeProofParameters.ProofType.GREATER_THAN_OR_EQUAL_TO:
// Prove that D is a commitment to either 0 or 1
ProverSetMembershipParameters greaterEqualProver = new ProverSetMembershipParameters(
LastD,
new FieldZqElement[] { prover.FieldZq.Zero, prover.FieldZq.One },
prover);
this.OrEqualToProof = new SetMembershipProof(greaterEqualProver);
this.OrEqualToProof.IsGroupSerializable = false;
break;
case VerifierRangeProofParameters.ProofType.LESS_THAN_OR_EQUAL_TO:
// Prove that D is a commitment to either 0 or -1
ProverSetMembershipParameters lessEqualProver = new ProverSetMembershipParameters(
LastD,
new FieldZqElement[] { prover.FieldZq.Zero, prover.FieldZq.One.Negate() },
prover);
this.OrEqualToProof = new SetMembershipProof(lessEqualProver);
this.OrEqualToProof.IsGroupSerializable = false;
break;
}
}
catch (Exception e)
{
throw new Exception("RangeProof: Could not create range proof.", e);
}
}
/// <summary>
/// Creates a RangeProof given the parameters. Throws an ArgumentException on error.
/// </summary>
/// <param name="prover"></param>
public RangeProof(ProverRangeProofParameters prover)
{
ConstructorHelper(prover);
}
