Testing polynomial irreducibility without GCDs
نویسنده
چکیده
We determine classes of degrees where testing irreducibility for univariate polynomials over finite fields can be done without any GCD computation. This work was partly funded by the INRIA Associate Team “Algorithms, Numbers, Computers” (http://www.loria.fr/~zimmerma/anc.html). Key-words: finite fields, irreducible polynomial, GCD ∗ ANU, Canberra, [email protected] Test d’irréductibilité de polynôme sans PGCD Résumé : Nous identifions des familles pour lesquelles le test d’irréductibilité de polynômes univariés sur un corps fini peut être effectué sans aucun PGCD. Ce travail a été réalisé en partie dans le cadre de l’équipe associée INRIA “Algorithms, Numbers, Computers” (http://www.loria.fr/~zimmerma/anc.html). Mots-clés : corps fini, polynôme irréductible, PGCD Testing polynomial irreducibility without GCDs 3 Recall Rabin’s test for the irreducibility of a polynomial over GF(p) where p is prime [1, p.7]: A polynomial C ∈ GF(p)[x] of degree d is irreducible if and only if
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