Algebraic operations on the finite field GF(2^m).

This public domain software was written by Stuart D. Gathman,
based on C software written by Paulo S.L.M. Barreto
based on original C++ software written by
George Barwood

THIS SOFTWARE IS PROVIDED BY THE AUTHORS ''AS IS'' AND ANY EXPRESS
OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHORS OR CONTRIBUTORS BE
LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR
BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY,
WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE
OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE,
EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

References
==========

1. Erik De Win et alii:
"A Fast Software Implementation for Arithmetic Operations in GF(2^n)",
presented at Asiacrypt96 (preprint).

Change log
==========

1997.09.15:
-- Fixed a bug in gfTrace() which would give wrong values (and
possibly also addressing error once in a while) for every field
where where GF_TM0 != 1. Thanks to Dave Dahm
for pointing out this bug and providing debugging data.

Allocate a new polynomial. */

/*
public boolean equals(Object obj) {
if (!(obj instanceof ECField)) return false;
ECField q = (ECField)obj;
int n = p[0] + 1;
for (int i = 0; i <= n; ++i)
if (p[i] != q.p[i]) return false;
return true;
}

Set p := q + r */

set r := p * q mod (x^GF_K + x^GF_T + 1) */

set r := p^2 mod (x^GF_K + x^GF_T + 1). */

sets p := (b^(-1))*p mod (x^GF_K + x^GF_T + 1) */

sets b := a^(-1) mod (x^GF_K + x^GF_T + 1)
warning: a and b must not overlap!
return  true on failure

sets p := sqrt(b) = b^(2^(GF_M-1)) */

Quickly evaluates to the trace of p. */

set p to a solution of p^2 + p = beta.
return  true if there is no solution

Evaluates to the rightmost (least significant) bit of p */

Packs a field point into a BigInteger. */

Unpacks a BigInteger into a field point. */

Formats the contents of p. */

sets p := */