/**
* 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.
*
* <p>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).
*
* @param m with 2^{@code m} being the number of elements.
* @param rp the BigInteger whose i-th bit corresponds to the i-th coefficient of the reduction
* polynomial.
* @exception NullPointerException if {@code rp} is null.
* @exception IllegalArgumentException if {@code m} is not positive, or {@code rp} does not
* represent a valid reduction polynomial.
*/
public ECFieldF2m(int m, 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
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.getLowestSetBit();
this.ks[i] = index;
temp = temp.clearBit(index);
}
}
