/// <summary>
/// Creates an elliptic curve characteristic 2 finite
/// field which has 2^{@code m} elements with
/// polynomial basis.
/// The reduction polynomial for this field is based
/// on {@code rp} whose i-th bit corresponds to
/// the i-th coefficient of the reduction polynomial.<para>
/// Note: A valid reduction polynomial is either a
/// trinomial (X^{@code m} + X^{@code k} + 1
/// with {@code m} > {@code k} >= 1) or a
/// pentanomial (X^{@code m} + X^{@code k3}
/// + X^{@code k2} + X^{@code k1} + 1 with
/// {@code m} > {@code k3} > {@code k2}
/// > {@code k1} >= 1).
/// </para>
/// </summary>
/// <param name="m"> with 2^{@code m} being the number of elements. </param>
/// <param name="rp"> the BigInteger whose i-th bit corresponds to
/// the i-th coefficient of the reduction polynomial. </param>
/// <exception cref="NullPointerException"> if {@code rp} is null. </exception>
/// <exception cref="IllegalArgumentException"> if {@code m}
/// is not positive, or {@code rp} does not represent
/// a valid reduction polynomial. </exception>
public ECFieldF2m(int m, System.Numerics.BigInteger rp)
{
// check m and rp
this.m = m;
this.Rp = rp;
if (m <= 0)
{
throw new IllegalArgumentException("m is not positive");
}
int bitCount = this.Rp.bitCount();
if (!this.Rp.testBit(0) || !this.Rp.testBit(m) || ((bitCount != 3) && (bitCount != 5)))
{
throw new IllegalArgumentException("rp does not represent a valid reduction polynomial");
}
// convert rp into ks
System.Numerics.BigInteger temp = this.Rp.clearBit(0).clearBit(m);
this.Ks = new int[bitCount - 2];
for (int i = this.Ks.Length - 1; i >= 0; i--)
{
int index = temp.LowestSetBit;
this.Ks[i] = index;
temp = temp.clearBit(index);
}
}