public void TestGetLengthBigInteger(int valueInt, int expectedBitLength)
{
var value = new BigInteger(valueInt);
var result = NumberLength.GetLength(value).InBits;
Assert.AreEqual(expectedBitLength, result);
}
/// <summary>
/// Multiplies a group element with a scalar factor.
///
/// Scalar multiplication is understood as adding the group element to itself
/// as many times as dictated by the scalar factor.
///
/// The optional parameter factorBitLength allows to specify the bit length
/// of the scalar, which increases performance if it is significantly below
/// that of the order. However, this value should be held constant over
/// subsequent calls to this method to discourage timing and other side channel
/// attacks.
/// </summary>
/// <param name="e">A group element.</param>
/// <param name="k">A scalar.</param>
/// <param name="factorBitLength">Maximum bit length of a scalar.</param>
/// <returns>The given element multiplied with the given scalar.</returns>
public T MultiplyScalar(T e, BigInteger k, int factorBitLength)
{
if (k < BigInteger.Zero)
{
throw new ArgumentOutOfRangeException(nameof(k), "The given factor must be non-negative.");
}
if (NumberLength.GetLength(k).InBits > factorBitLength)
{
throw new ArgumentOutOfRangeException(nameof(k), "The given factor must not exceed the admittable factor bit length.");
}
return(MultiplyScalarUnchecked(e, k, factorBitLength));
}
/// <summary>
/// Returns a random <see cref="BigInteger"/> between (and including)
/// <paramref name="lower"/> and <paramref name="upper"/>.
/// </summary>
/// <returns>The <see cref="T:System.Numerics.BigInteger"/>.</returns>
/// <param name="randomNumberGenerator">Random number generator.</param>
/// <param name="lower">Inclusive lower bound.</param>
/// <param name="upper">Inclusive upper bound.</param>
public static BigInteger GetBigIntegerBetween(
this RandomNumberGenerator randomNumberGenerator, BigInteger lower, BigInteger upper
)
{
NumberLength length = NumberLength.GetLength(upper - lower);
BigInteger delta;
do
{
byte[] buffer = new byte[length.InBytes];
randomNumberGenerator.GetBytes(buffer);
delta = new BigInteger(buffer);
}while (delta >= upper - lower);
delta *= delta.Sign;
Debug.Assert(delta >= BigInteger.Zero);
return(lower + delta);
}
/// <inheritdoc/>
public bool IsSafeElement(T element)
{
if (!IsPotentialElement(element))
{
return(false);
}
// verifying that the point is not from a small subgroup of the whole curve (and thus outside
// of the safe subgroup over which operations are considered)
T check = MultiplyScalarUnchecked(element, Cofactor, NumberLength.GetLength(Cofactor).InBits);
if (check.Equals(NeutralElement))
{
return(false);
}
return(true);
}