public CurveGroupAlgebraTests()
{
curveEquationMock = new Mock <CurveEquation>(
BigPrime.CreateWithoutChecks(23),
BigInteger.Zero,
BigInteger.One
)
{
CallBase = true
};
curveParameters = new CurveParameters(
curveEquation: curveEquationMock.Object,
generator: TestCurveParameters.WeierstrassParameters.Generator,
order: TestCurveParameters.WeierstrassParameters.Order,
cofactor: TestCurveParameters.WeierstrassParameters.Cofactor
);
largeCurveEquationMock = new Mock <CurveEquation>(
BigPrime.CreateWithoutChecks(18392027),
BigInteger.Zero,
BigInteger.One
)
{
CallBase = true
}; // 25 bits prime
largeParameters = new CurveParameters(
curveEquation: largeCurveEquationMock.Object,
generator: new CurvePoint(),
order: BigPrime.CreateWithoutChecks(2),
cofactor: BigInteger.One
);
}
public void TestEqualsIsFalseForUnrelatedObject()
{
var order = BigPrime.CreateWithoutChecks(7);
var cofactor = new BigInteger(2);
var generator = CurvePoint.PointAtInfinity;
CurveParameters parameters = new CurveParameters(
equationMock.Object, generator, order, cofactor
);
Assert.AreNotEqual(parameters, new object());
}
/// <summary>
/// Initializes a new instance of <see cref="XOnlyMontgomeryCurveAlgebra"/>
/// with given curve parameters.
/// </summary>
/// <param name="parameters">The parameters of the elliptic curve.</param>
public XOnlyMontgomeryCurveAlgebra(CurveParameters parameters)
: base(
parameters.Generator.X,
parameters.Order,
parameters.Cofactor,
BigInteger.Zero,
NumberLength.GetLength(parameters.Equation.Field.Modulo).InBits
)
{
_parameters = parameters;
_aConstant = Field.Mod((_parameters.Equation.A + 2) * Field.InvertMult(4));
}
public XOnlyMontgomeryCurveAlgebraTests()
{
largeParameters = new CurveParameters(
curveEquation: new MontgomeryCurveEquation(
prime: BigPrime.CreateWithoutChecks(18392027), // 25 bits
a: 0, b: 0
),
generator: CurvePoint.PointAtInfinity,
order: BigPrime.CreateWithoutChecks(3),
cofactor: 1
);
}
public void TestInvalidElementRejectedAsGenerator()
{
var invalidGenerator = new CurvePoint(16, 1);
CurveParameters invalidParameters = new CurveParameters(
curveEquation: TestCurveParameters.WeierstrassParameters.Equation,
generator: invalidGenerator,
order: curveParameters.Order,
cofactor: curveParameters.Cofactor
);
Assert.Throws <ArgumentException>(
() => new CurveGroupAlgebra(invalidParameters)
);
}
public void TestIsElementForPointAtInfinityCofactorOne()
{
var parameters = new CurveParameters(
curveParameters.Equation,
curveParameters.Generator,
curveParameters.Order,
BigInteger.One
);
var curve = new CurveGroupAlgebra(parameters);
curveEquationMock.Setup(eq => eq.Add(It.IsAny <CurvePoint>(), It.IsAny <CurvePoint>())).Returns(CurvePoint.PointAtInfinity);
Assert.IsTrue(curve.IsPotentialElement(CurvePoint.PointAtInfinity), "IsPotentialElement not true for point at infinity!");
Assert.IsFalse(curve.IsSafeElement(CurvePoint.PointAtInfinity), "IsSafeElement not false for point at infinity!");
}
public void TestEqualsIsTrueForEqualObjects()
{
var order = BigPrime.CreateWithoutChecks(7);
var cofactor = new BigInteger(2);
var generator = CurvePoint.PointAtInfinity;
CurveParameters parameters = new CurveParameters(
equationMock.Object, generator, order, cofactor
);
CurveParameters otherParameters = new CurveParameters(
equationMock.Object, generator, order, cofactor
);
Assert.AreEqual(parameters, otherParameters);
}
/// <summary>
/// Initializes a new instance of the <see cref="CurveGroupAlgebra"/> class.
/// </summary>
/// <param name="parameters">The parameters of the elliptic curve.</param>
public CurveGroupAlgebra(CurveParameters parameters)
: base(
parameters.Generator,
parameters.Order,
parameters.Cofactor,
CurvePoint.PointAtInfinity,
2 * NumberLength.GetLength(parameters.Equation.Field.Modulo).InBits
)
{
_curveEquation = parameters.Equation;
if (!IsSafeElement(Generator))
{
throw new ArgumentException("The point given as generator is " +
"not a valid point on the curve.", nameof(parameters));
}
}
public void TestEqualsIsFalseForDifferentObjects()
{
var equation = equationMock.Object;
equationMock.Reset();
equationMock.Setup(eq => eq.Equals(It.IsAny <CurveEquation>())).Returns(false);
var order = BigPrime.CreateWithoutChecks(7);
var cofactor = new BigInteger(2);
var generator = CurvePoint.PointAtInfinity;
CurveParameters parameters = new CurveParameters(
equation, generator, order, cofactor
);
CurveParameters otherParameters = new CurveParameters(
equation, generator, order, cofactor
);
Assert.AreNotEqual(parameters, otherParameters);
equationMock.Reset();
equationMock.Setup(eq => eq.Equals(It.IsAny <CurveEquation>())).Returns(true);
otherParameters = new CurveParameters(
equation, new CurvePoint(1, 1), order, cofactor
);
Assert.AreNotEqual(parameters, otherParameters);
otherParameters = new CurveParameters(
equation, generator, BigPrime.CreateWithoutChecks(3), cofactor
);
Assert.AreNotEqual(parameters, otherParameters);
otherParameters = new CurveParameters(
equation, generator, order, BigInteger.One
);
Assert.AreNotEqual(parameters, otherParameters);
}
/// <summary>
/// Creates a <see cref="CryptoGroup{BigInteger, BigInteger}" /> instance using a <see cref="XOnlyMontgomeryCurveAlgebra" />
/// instance with the given <see cref="CurveParameters"/>.
/// </summary>
/// <param name="parameters">The parameters of the elliptic curve.</param>
public static CryptoGroup <BigInteger, BigInteger> CreateCryptoGroup(CurveParameters parameters)
{
return(new CryptoGroup <BigInteger, BigInteger>(
new XOnlyMontgomeryCurveAlgebra(parameters)
));
}
/// <summary>
/// Creates a <see cref="CryptoGroup{BigInteger, CurvePoint}" /> instance using a <see cref="CurveGroupAlgebra" />
/// instance with the given <see cref="CurveParameters"/>.
/// </summary>
/// <param name="parameters">The parameters of the elliptic curve.</param>
public static CryptoGroup <BigInteger, CurvePoint> CreateCryptoGroup(CurveParameters parameters)
{
return(new CryptoGroup <BigInteger, CurvePoint>(new CurveGroupAlgebra(parameters)));
}
