The Software gf2x

gf2x is a C/C++ software package containing routines for fast arithmetic in GF(2)[x] (multiplication, squaring, GCD) and searching for irreducible/primitive trinomials. The most up-to-date source of information on gf2x is the gforge page https://gforge.inria.fr/projects/gf2x/.

References

Richard P. Brent and Paul Zimmermann,
A multi-level blocking distinct degree factorization algorithm, presented at the Eighth International Conference on Finite Fields and Applications (Fq8), Melbourne, 9-13 July 2007. Published in Contemporary Mathematics, Vol. 461, 2008, 47-58. Also appeared as INRIA Tech Report RR-6331, October 2007, 16 pp. See also arXiv:0710.4410.

Richard P. Brent, Pierrick Gaudry, Emmanuel Thomé and Paul Zimmermann,
Faster multiplication in GF(2)[x], Proc. ANTS-VIII (Banff, May 2008), Lecture Notes in Computer Science, Vol. 5011, Springer-Verlag, 2008, 153-166. Also INRIA Tech. Report RR-6359, Nov. 2007, 19 pp.

Richard P. Brent and Paul Zimmermann,
Ten new primitive binary trinomials, Mathematics of Computation 78 (2009), 1197-1199.

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