Finite Field classes

1. FFp: This class represents an implementation of a finite field over prime p (i.e. integer modulo $$p$$: $$\mathbb{Z}_p$$).
2. FFq:
3. FFpoly:
4. Polynomial: Auxiliary polynomial template class. Implements all basic operations with polynomials.

All classes are written for use with Eigen3 library for linear algebra, so GenericNumTraits is defined for all of them.

Tests

Unit tests are written using catch2 testing framework, which is included in this project.

Use

To define a new field over prime p use:

const int p = 5;
FFp<p> x; //x = 0
FFp<p> y(4); // y = 4
FFp<p> z;

z = x + y;
z = x - y;
z = x * y;
z = x / y;

To do:

1. In the case of FFp class, the table of multiplicative inverses is generated using an exhaustive search (with complexity $$\mathcal{O}(p^2)$$). Instead of an exhaustive search an extended Euclid algorithm can be used to generate all multiplicative inverses. As this library is intended for use with relatively small $$p$$ values, this is not a big priority.

2. Assertion isPrime<p>() (for the FFp class) is done only in debug mode.