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Fix/guardian proof (#432)
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* Add ParameterBaseHash constant and Election Variable

Add the ParameterBaseHash as a static member to the compiled code as well as to the CiphertextElectionContext as a serialized member since we must maintain compatibility with different elections using different parameters for this value.

* Add Parameter Hash and sequence ordering to Schnorr proofs

add parameter hash and sequence ordering to schnorr challenges and propagate the necessary dependencies down the stack

* reimplement schnorr response calculation

* Added comments to 2 methods to get rid of the linter issues since this file was touched in this PR

* add xml comments

* fixed spacing issue

* fixing spacing issue

* cleaned up linter warnings

* Add back original constructor and test for missing parameter hash

---------

Co-authored-by: SteveMaier-IRT <[email protected]>
Co-authored-by: Steve Maier <[email protected]>
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@AddressXception @SteveMaier-IRT
3 people authored Sep 25, 2023
1 parent 47c52ae commit 99ced18
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Showing 28 changed files with 749 additions and 263 deletions.
38 changes: 24 additions & 14 deletions bindings/netstandard/ElectionGuard/ElectionGuard.ElectionSetup.Tests/Extensions.cs
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Original file line number Diff line number Diff line change
Expand Up @@ -6,26 +6,27 @@ public static class CoefficientExtensions
/// Generate a Coefficient for testing purposes only.
/// In a production environment, nonce should be null and a random value will be generated.
/// </summary>
public static Coefficient GenerateCoefficient(ElementModQ nonce, int index)
public static Coefficient GenerateCoefficient(ulong offset, int index, ElementModQ parameterHash, ElementModQ seed)
{
Console.WriteLine("WARNING: GenerateCoefficient using a predetermined nonce for testing purposes only. This should not be used in production.");
var value = BigMath.AddModQ(nonce, (ulong)index);
return new(value);
var secret = BigMath.AddModQ(seed, (ulong)index);
return new(offset, index, parameterHash, secret);
}

/// <summary>
/// Generate a Coefficient for testing purposes only.
/// In a production environment, nonce should be null and a random value will be generated.
/// </summary>
/// <param name="nonce">A predetermined nonce parameter for testing purposes only.</param>
/// <param name="secret">A predetermined nonce parameter for testing purposes only.</param>
/// <param name="index">The index of the coefficient</param>
/// <param name="seed">A predetermined seed for testing purposes only.</param>
public static Coefficient GenerateCoefficient(ElementModQ nonce, ElementModQ seed, int index)
public static Coefficient GenerateCoefficient(
ulong offset, int index, ElementModQ parameterHash, ElementModQ nonce, ElementModQ seed)
{
Console.WriteLine("WARNING: GenerateCoefficient using a predetermined nonce for testing purposes only. This should not be used in production.");
var value = BigMath.AddModQ(nonce, (ulong)index);
Console.WriteLine($"value: {value}");
return new(value, seed);
var secret = BigMath.AddModQ(nonce, (ulong)index);
Console.WriteLine($"value: {secret}");
return new(offset, index, parameterHash, secret, seed);
}
}

Expand All @@ -35,15 +36,19 @@ public static class PolynomialExtensions
/// Generate a Polynomial for testing purposes only.
/// In a production environment, nonce should be null and a random value will be generated.
/// </summary>
/// <param name="nonce">A predetermined nonce parameter for testing purposes only.</param>
/// <param name="secret">A predetermined nonce parameter for testing purposes only.</param>
/// <param name="quorum">The number of coefficients in the polynomial</param>
public static ElectionPolynomial GeneratePolynomial(ElementModQ nonce, int quorum)
public static ElectionPolynomial GeneratePolynomial(ulong sequenceOrder, int quorum, ElementModQ secret)
{
Console.WriteLine("WARNING: GeneratePolynomial using a predetermined nonce for testing purposes only. This should not be used in production.");
var coefficients = new List<Coefficient>();
for (var i = 0; i < quorum; i++)
{
coefficients.Add(CoefficientExtensions.GenerateCoefficient(nonce, i));
coefficients.Add(CoefficientExtensions.GenerateCoefficient(
sequenceOrder,
i,
CiphertextElectionContext.ParameterBaseHash,
secret));
}
return new(coefficients);
}
Expand All @@ -52,16 +57,21 @@ public static ElectionPolynomial GeneratePolynomial(ElementModQ nonce, int quoru
/// Generate a Polynomial for testing purposes only.
/// In a production environment, nonce should be null and a random value will be generated.
/// </summary>
/// <param name="nonce">A predetermined nonce parameter for testing purposes only.</param>
/// <param name="secret">A predetermined nonce parameter for testing purposes only.</param>
/// <param name="quorum">The number of coefficients in the polynomial</param>
/// <param name="seed">A predetermined seed for testing purposes only.</param>
public static ElectionPolynomial GeneratePolynomial(ElementModQ nonce, ElementModQ seed, int quorum)
public static ElectionPolynomial GeneratePolynomial(ulong sequenceOrder, int quorum, ElementModQ secret, ElementModQ seed)
{
Console.WriteLine("WARNING: GeneratePolynomial using a predetermined nonce for testing purposes only. This should not be used in production.");
var coefficients = new List<Coefficient>();
for (var i = 0; i < quorum; i++)
{
coefficients.Add(CoefficientExtensions.GenerateCoefficient(nonce, seed, i));
coefficients.Add(CoefficientExtensions.GenerateCoefficient(
sequenceOrder,
i,
CiphertextElectionContext.ParameterBaseHash,
secret,
seed));
}
return new(coefficients);
}
Expand Down
1 change: 1 addition & 0 deletions ...andard/ElectionGuard/ElectionGuard.ElectionSetup.Tests/Generators/KeyCeremonyGenerator.cs
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Original file line number Diff line number Diff line change
Expand Up @@ -60,6 +60,7 @@ public static List<Guardian> GenerateGuardians(
sequenceOrder,
keyCeremony.NumberOfGuardians,
keyCeremony.Quorum,
CiphertextElectionContext.ParameterBaseHash,
keyCeremony.Id,
random);
guardians.Add(guardian);
Expand Down
19 changes: 14 additions & 5 deletions ...ard/ElectionGuard/ElectionGuard.ElectionSetup.Tests/KeyCeremony/TestElectionPolynomial.cs
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Original file line number Diff line number Diff line change
Expand Up @@ -6,10 +6,12 @@ public class TestElectionPolynomial
public void Test_ElectionPolynomial_Constructs_WithDegrees()
{
// Arrange
var sequenceOrder = 2UL;
var degrees = 2;
var parameterHash = Constants.TWO_MOD_Q;

// Act
var result = new ElectionPolynomial(degrees);
var result = new ElectionPolynomial(sequenceOrder, degrees, parameterHash);

// Assert
Assert.That(result, Is.Not.Null);
Expand All @@ -20,11 +22,13 @@ public void Test_ElectionPolynomial_Constructs_WithDegrees()
public void Test_ElectionPolynomial_Constructs_WithSecretKey()
{
// Arrange
var sequenceOrder = 2UL;
var degrees = 2;
var parameterHash = Constants.TWO_MOD_Q;
var secretKey = Constants.TWO_MOD_Q;

// Act
var result = new ElectionPolynomial(degrees, secretKey);
var result = new ElectionPolynomial(sequenceOrder, degrees, parameterHash, secretKey);

// Assert
Assert.That(result, Is.Not.Null);
Expand All @@ -36,12 +40,14 @@ public void Test_ElectionPolynomial_Constructs_WithSecretKey()
public void Test_ElectionPolynomial_Constructs_WithKeyPair()
{
// Arrange
var sequenceOrder = 2UL;
var degrees = 3;
var parameterHash = Constants.TWO_MOD_Q;
using var secretKey = BigMath.RandQ();
using var keyPair = new ElGamalKeyPair(secretKey);

// Act
using var result = new ElectionPolynomial(degrees, keyPair);
using var result = new ElectionPolynomial(sequenceOrder, degrees, parameterHash, keyPair);

// Assert
Assert.That(result, Is.Not.Null);
Expand All @@ -55,11 +61,12 @@ public void Test_ElectionPolynomial_Constructs_WithKeyPair()
public void Test_ElectionPolynomial_ComputeCoordinate()
{
// Arrange
var offset = 0UL;
var coordinate = 1UL;
var degrees = 2;
var nonce = Constants.ONE_MOD_Q;
var seed = Constants.TWO_MOD_Q;
var polynomial = PolynomialExtensions.GeneratePolynomial(nonce, seed, degrees);
var polynomial = PolynomialExtensions.GeneratePolynomial(offset, degrees, nonce, seed);

// Act
var result = polynomial.ComputeCoordinate(coordinate);
Expand All @@ -73,9 +80,11 @@ public void Test_ElectionPolynomial_ComputeCoordinate()
public void Test_ElectionPolynomial_VerifyCoordinate()
{
// Arrange
var sequenceOrder = 2UL;
var coordinate = 1UL;
var degrees = 2UL;
var polynomial = new ElectionPolynomial((int)degrees);
var parameterHash = Constants.TWO_MOD_Q;
var polynomial = new ElectionPolynomial(sequenceOrder, (int)degrees, parameterHash);
var expected = polynomial.ComputeCoordinate(coordinate);

// Act
Expand Down
7 changes: 5 additions & 2 deletions ...etstandard/ElectionGuard/ElectionGuard.ElectionSetup.Tests/KeyCeremony/TestKeyCeremony.cs
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Original file line number Diff line number Diff line change
Expand Up @@ -24,8 +24,11 @@ public void Test_KeyCeremony()
var guardianId = sequenceOrder.ToString();
var random = new Random((int)sequenceOrder);
var guardian = new Guardian(
guardianId, sequenceOrder, numberOfGuardians,
quorum, keyCeremony.Id,
guardianId, sequenceOrder,
numberOfGuardians,
quorum,
CiphertextElectionContext.ParameterBaseHash,
keyCeremony.Id,
random);
guardians.Add(guardian);
}
Expand Down
77 changes: 50 additions & 27 deletions bindings/netstandard/ElectionGuard/ElectionGuard.ElectionSetup/Coefficient.cs
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Original file line number Diff line number Diff line change
Expand Up @@ -7,6 +7,16 @@ namespace ElectionGuard.ElectionSetup;
/// </summary>
public class Coefficient : DisposableBase
{
/// <summary>
/// The offset of the secret value in the polynomial (i in the spec)
/// </summary>
public ulong Offset { get; set; }

/// <summary>
/// The index of the proof corresponding to the coefficient (j in the spec)
/// </summary>
public int Index { get; set; }

/// <summary>
/// The key pair associated with the coefficient
/// </summary>
Expand All @@ -31,72 +41,85 @@ public class Coefficient : DisposableBase
public SchnorrProof Proof { get; private set; } = default!;

/// <summary>
/// Generate a coefficient with a predetermined value
/// Generate a coefficient with a predetermined secret
/// </summary>
public Coefficient(ElementModQ value)
public Coefficient(
ulong offset,
int index,
ElementModQ parameterHash,
ElementModQ secret)
{
var keyPair = ElGamalKeyPair.FromSecret(value);
Proof = new SchnorrProof(keyPair);
Offset = offset;
Index = index;
var keyPair = ElGamalKeyPair.FromSecret(secret);
Proof = new SchnorrProof(offset, index, parameterHash, keyPair);
KeyPair = new ElGamalKeyPair(keyPair);
}

/// <summary>
/// Generate a coefficient with a predetermined value and proof seed
/// Generate a coefficient with a predetermined secret and proof seed
/// </summary>
public Coefficient(ElementModQ value, ElementModQ seed)
public Coefficient(
ulong offset,
int index,
ElementModQ parameterHash,
ElementModQ secret, ElementModQ seed)
{
var keyPair = ElGamalKeyPair.FromSecret(value);
Proof = new SchnorrProof(keyPair, seed);
Offset = offset;
Index = index;
var keyPair = ElGamalKeyPair.FromSecret(secret);
Proof = new SchnorrProof(offset, index, parameterHash, keyPair, seed);
KeyPair = new ElGamalKeyPair(keyPair);
}

/// <summary>
/// Generate a coefficient with a predetermined value and proof
/// Generate a coefficient with a predetermined secret and proof
/// </summary>
public Coefficient(ElementModQ value, SchnorrProof proof)
public Coefficient(
ulong offset,
int index,
ElementModQ parameterHash,
ElementModQ secret, SchnorrProof proof)
{
if (!proof.IsValid())
if (!proof.IsValid(offset, index, parameterHash).Success)
{
throw new ArgumentException("Invalid proof");
}

var keyPair = ElGamalKeyPair.FromSecret(value);
var keyPair = ElGamalKeyPair.FromSecret(secret);
if (!proof.PublicKey.Equals(keyPair.PublicKey))
{
throw new ArgumentException("Proof does not match key pair");
}

Offset = offset;
Index = index;
KeyPair = new ElGamalKeyPair(keyPair);
Proof = new(proof);
}

[JsonConstructor]
public Coefficient(ElGamalKeyPair keyPair, SchnorrProof proof)
public Coefficient(
ulong offset,
int index,
ElGamalKeyPair keyPair, SchnorrProof proof)
{
if (!proof.IsValid())
{
throw new ArgumentException("Invalid proof");
}

// Dos not check the proof for validity when serializing from json
if (!proof.PublicKey.Equals(keyPair.PublicKey))
{
throw new ArgumentException("Proof does not match key pair");
}

Offset = offset;
Index = index;
KeyPair = new ElGamalKeyPair(keyPair);
Proof = new(proof);
}

public Coefficient(Coefficient that)

{
KeyPair = new ElGamalKeyPair(that.KeyPair);
Proof = new SchnorrProof(that.Proof);
}
public Coefficient(Coefficient other)

public bool IsValid()
{
return Proof.IsValid() && Proof.PublicKey.Equals(KeyPair.PublicKey);
KeyPair = new ElGamalKeyPair(other.KeyPair);
Proof = new SchnorrProof(other.Proof);
}

protected override void DisposeUnmanaged()
Expand Down
15 changes: 7 additions & 8 deletions bindings/netstandard/ElectionGuard/ElectionGuard.ElectionSetup/ElectionKeyPair.cs
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Original file line number Diff line number Diff line change
Expand Up @@ -44,13 +44,14 @@ public string OwnerId
public ElectionKeyPair(
string ownerId,
ulong sequenceOrder,
int quorum)
int quorum,
ElementModQ parameterHash)
{
GuardianId = ownerId;
SequenceOrder = sequenceOrder;
using var randQ = BigMath.RandQ();
KeyPair = new(randQ);
Polynomial = new ElectionPolynomial(quorum, KeyPair);
Polynomial = new ElectionPolynomial(sequenceOrder, quorum, parameterHash, KeyPair);
}

/// <summary>
Expand All @@ -62,25 +63,27 @@ public ElectionKeyPair(
string ownerId,
ulong sequenceOrder,
int quorum,
ElementModQ parameterHash,
ElGamalKeyPair keyPair)
{
GuardianId = ownerId;
SequenceOrder = sequenceOrder;
KeyPair = new(keyPair);
Polynomial = new(quorum, keyPair);
Polynomial = new(sequenceOrder, quorum, parameterHash, keyPair);
}

public ElectionKeyPair(
string ownerId,
ulong sequenceOrder,
int quorum,
ElementModQ parameterHash,
ElGamalKeyPair keyPair,
Random random)
{
GuardianId = ownerId;
SequenceOrder = sequenceOrder;
KeyPair = new(keyPair);
Polynomial = new(quorum, keyPair, random);
Polynomial = new(sequenceOrder, quorum, parameterHash, keyPair, random);
}

/// <summary>
Expand Down Expand Up @@ -118,8 +121,6 @@ public ElectionKeyPair(
SequenceOrder = sequenceOrder;
KeyPair = new(keyPair.SecretKey, keyPair.PublicKey);
Polynomial = new(polynomial);

// TODO: verify the polynomial is valid for the keypair
}

public ElectionKeyPair(ElectionKeyPair other)
Expand All @@ -128,8 +129,6 @@ public ElectionKeyPair(ElectionKeyPair other)
SequenceOrder = other.SequenceOrder;
KeyPair = new(other.KeyPair.SecretKey, other.KeyPair.PublicKey);
Polynomial = new(other.Polynomial);

// TODO: verify the polynomial is valid for the keypair
}

public ElectionPublicKey Share()
Expand Down
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