An improvement of Rabin's probabilistic algorithm for generating irreducible polynomials over GF(p)

This survey reviews several algorithms for the factorization of univariate polynomials over finite fields. We emphasize the main ideas of the methods and provide an up-to-date bibliography of the problem.

This talk reports on joint work with R. Loos (Univ. Karlsruhe) on algebraic algorithms for computing in large Galois Fields GF(q) with q = pⁿ where p is the characteristic of the field and may be arbitrarily large.

This work is materialized by a module of algorithms implemented in the ALDES/SAC2 computer algebra system, which will be available with the next release of this system.