public void TestAdd()
{
var algebra = new EllipticCurveAlgebra(EllipticCurveID.Prime256v1);
var generator = algebra.Generator;
var groupHandle = ECGroupHandle.CreateByCurveNID((int)EllipticCurveID.Prime256v1);
var ctx = BigNumberContextHandle.Create();
var kA = new BigInteger(27);
var kB = new BigInteger(13);
var pointA = new ECPoint(groupHandle);
ECPointHandle.Multiply(groupHandle, pointA.Handle, new BigNumber(kA).Handle, ECPointHandle.Null, BigNumberHandle.Null, ctx);
var pointB = new ECPoint(groupHandle);
ECPointHandle.Multiply(groupHandle, pointB.Handle, new BigNumber(kB).Handle, ECPointHandle.Null, BigNumberHandle.Null, ctx);
var expected = new ECPoint(groupHandle);
ECPointHandle.Multiply(groupHandle, expected.Handle, new BigNumber(kA + kB).Handle, ECPointHandle.Null, BigNumberHandle.Null, ctx);
var result = algebra.Add(pointA, pointB);
Assert.That(result.Equals(expected));
}
/// <summary>
/// Creates a new <see cref="EllipticCurveAlgebra" /> instance
/// for the curve identified by <paramref name="curveId"/>.
/// </summary>
/// <param name="curveId">Identifier of the elliptic curve.</param>
public EllipticCurveAlgebra(EllipticCurveID curveId)
{
Handle = ECGroupHandle.CreateByCurveNID((int)curveId);
using (var ctx = BigNumberContextHandle.Create())
{
ECGroupHandle.PrecomputeGeneratorMultiples(Handle, ctx);
}
}
/// <summary>
/// Decodes a <see cref="ECPoint" /> instance from a byte buffer.
/// </summary>
/// <param name="ecGroupHandle">Native handle for the group the point lies on.</param>
/// <param name="buffer">Byte array containing an encoding of the curve point.</param>
/// <returns><see cref="ECPoint" /> instance of the point encoded in the buffer.</returns>
internal static ECPoint CreateFromBytes(ECGroupHandle ecGroupHandle, byte[] buffer)
{
using (var ctx = BigNumberContextHandle.Create())
{
var point = new ECPoint(ecGroupHandle);
ECPointHandle.FromByteBuffer(point._ecGroup, point.Handle, buffer, ctx);
return(point);
}
}
/// <inheritdoc />
public override bool Equals(object?obj)
{
EllipticCurveAlgebra?other = obj as EllipticCurveAlgebra;
if (other == null)
{
return(false);
}
using (var ctx = BigNumberContextHandle.Create())
{
return(ECGroupHandle.Compare(this.Handle, other.Handle, ctx));
}
}
public void TestFromToBytes()
{
var algebra = new EllipticCurveAlgebra(EllipticCurveID.Prime256v1);
var generator = algebra.Generator;
var groupHandle = ECGroupHandle.CreateByCurveNID((int)EllipticCurveID.Prime256v1);
var ctx = BigNumberContextHandle.Create();
var index = new BigInteger(3);
var point = new ECPoint(groupHandle);
ECPointHandle.Multiply(groupHandle, point.Handle, new BigNumber(index).Handle, ECPointHandle.Null, BigNumberHandle.Null, ctx);
byte[] buffer = algebra.ToBytes(point);
var result = algebra.FromBytes(buffer);
Assert.That(result.Equals(point));
}
public void TestNegate()
{
var algebra = new EllipticCurveAlgebra(EllipticCurveID.Prime256v1);
var generator = algebra.Generator;
var groupHandle = ECGroupHandle.CreateByCurveNID((int)EllipticCurveID.Prime256v1);
var ctx = BigNumberContextHandle.Create();
var index = new BigInteger(3);
var point = new ECPoint(groupHandle);
ECPointHandle.Multiply(groupHandle, point.Handle, new BigNumber(index).Handle, ECPointHandle.Null, BigNumberHandle.Null, ctx);
var result = algebra.Negate(point);
var pointPlusNegated = algebra.Add(point, result);
Assert.That(pointPlusNegated.Equals(algebra.NeutralElement));
}
public void TestGenerateElement()
{
var algebra = new EllipticCurveAlgebra(EllipticCurveID.Prime256v1);
var generator = algebra.Generator;
var groupHandle = ECGroupHandle.CreateByCurveNID((int)EllipticCurveID.Prime256v1);
var ctx = BigNumberContextHandle.Create();
var index = SecureBigNumber.FromBigNumber(new BigNumber(
BigInteger.Parse("97752369786356789875745735", System.Globalization.NumberStyles.Integer)
));
var expected = new ECPoint(groupHandle);
ECPointHandle.Multiply(groupHandle, expected.Handle, index.Handle, ECPointHandle.Null, BigNumberHandle.Null, ctx);
var result = algebra.GenerateElement(index);
Assert.That(result.Equals(expected));
}
public void TestMultipy()
{
var algebra = new EllipticCurveAlgebra(EllipticCurveID.Prime256v1);
var generator = algebra.Generator;
var groupHandle = ECGroupHandle.CreateByCurveNID((int)EllipticCurveID.Prime256v1);
var ctx = BigNumberContextHandle.Create();
var factor = SecureBigNumber.FromBigNumber(new BigNumber(13));
var basePointFactor = new BigInteger(27);
var point = new ECPoint(groupHandle);
ECPointHandle.Multiply(groupHandle, point.Handle, new BigNumber(basePointFactor).Handle, ECPointHandle.Null, BigNumberHandle.Null, ctx);
var expected = new ECPoint(groupHandle);
ECPointHandle.Multiply(groupHandle, expected.Handle, BigNumberHandle.Null, point.Handle, factor.Handle, ctx);
var result = algebra.MultiplyScalar(point, factor);
Assert.That(result.Equals(expected));
}
public void SetUp()
{
groupHandle = ECGroupHandle.CreateByCurveNID((int)EllipticCurveID.Prime256v1);
rawPointHandle = ECGroupHandle.GetGenerator(groupHandle);
ctx = BigNumberContextHandle.Create();
}
/// <summary>
/// Creates a new <see cref="ECPoint" /> instance for a given
/// valid <see cref="ECPointHandle" />
/// on the curve defined by a valid <see cref="ECGroupHandle" />.
///
/// The structure pointed to by <paramref name="pointHandle"/> is copied into
/// this <see cref="ECPoint" /> instance.
/// </summary>
/// <param name="ecGroupHandle">Native handle for the group the point lies on.</param>
/// <param name="pointHandle">Native handle for the point on the curve.</param>
internal ECPoint(ECGroupHandle ecGroupHandle, ECPointHandle pointHandle) : this(ecGroupHandle)
{
Debug.Assert(!pointHandle.IsInvalid);
ECPointHandle.Copy(Handle, pointHandle);
}
/// <summary>
/// Creates a new default <see cref="ECPoint" />
/// on the curve defined by a valid <see cref="ECGroupHandle" />.
///
/// The coordinates of the point are unspecified.
/// </summary>
/// <param name="ecGroupHandle">Native handle for the group the point lies on.</param>
internal ECPoint(ECGroupHandle ecGroupHandle)
{
Debug.Assert(!ecGroupHandle.IsInvalid);
_ecGroup = ecGroupHandle;
Handle = ECPointHandle.Create(_ecGroup);
}
