/// <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 ks} whose content
/// contains the order of the middle term(s) of the
/// reduction polynomial.
/// 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), so {@code ks} should
/// have length 1 or 3. </summary>
/// <param name="m"> with 2^{@code m} being the number of elements. </param>
/// <param name="ks"> the order of the middle term(s) of the
/// reduction polynomial. Contents of this array are copied
/// to protect against subsequent modification. </param>
/// <exception cref="NullPointerException"> if {@code ks} is null. </exception>
/// <exception cref="IllegalArgumentException"> if{@code m}
/// is not positive, or the length of {@code ks}
/// is neither 1 nor 3, or values in {@code ks}
/// are not between {@code m}-1 and 1 (inclusive)
/// and in descending order. </exception>
public ECFieldF2m(int m, int[] ks)
{
// check m and ks
this.m = m;
this.Ks = ks.clone();
if (m <= 0)
{
throw new IllegalArgumentException("m is not positive");
}
if ((this.Ks.Length != 1) && (this.Ks.Length != 3))
{
throw new IllegalArgumentException("length of ks is neither 1 nor 3");
}
for (int i = 0; i < this.Ks.Length; i++)
{
if ((this.Ks[i] < 1) || (this.Ks[i] > m - 1))
{
throw new IllegalArgumentException("ks[" + i + "] is out of range");
}
if ((i != 0) && (this.Ks[i] >= this.Ks[i - 1]))
{
throw new IllegalArgumentException("values in ks are not in descending order");
}
}
// convert ks into rp
this.Rp = System.Numerics.BigInteger.ONE;
this.Rp = Rp.setBit(m);
for (int j = 0; j < this.Ks.Length; j++)
{
Rp = Rp.setBit(this.Ks[j]);
}
}
