Algorithms for finding almost irreducible and almost primitive trinomials
Identifieur interne : 007581 ( Main/Curation ); précédent : 007580; suivant : 007582Algorithms for finding almost irreducible and almost primitive trinomials
Auteurs : Richard Brent ; Paul ZimmermannSource :
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Abstract
Consider polynomials over \GF(2). We describe efficient algorithms for finding trinomials with large irreducible (and possibly primitive) factors, and give examples of trinomials having a primitive factor of degree~r for all Mersenne exponents r = \pm 3 \mmod 8 in the range 5 < r < 10^7, although there is no irreducible trinomial of degree~r. We also give trinomials with a primitive factor of degree r = 2^k for 3 \le k \le 12. These trinomials enable efficient representations of the finite field \GF(2^r). We show how trinomials with large primitive factors can be used efficiently in applications where primitive trinomials would normally be used.
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