Abstract
We give a precise average-case analysis of Rabin's algorithm for testing the irreducibility of polynomials over finite fields. The main technical contribution of the paper is the study of the probability that a random polynomial of degree n contains an irreducible factor of degree dividing several maximal divisors of the degree n. We provide upper and lower bounds for this probability. Our method generalizes to other algorithms that deal with similar divisor conditions. In particular, we analyze the average-case behavior of Rabin's variants presented by von zur Gathen & Shoup and by Gao & Panario.
Cite
CITATION STYLE
Panario, D., & Viola, A. (1998). Analysis of rabin’s polynomial irreducibility test. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 1380, pp. 1–10). Springer Verlag. https://doi.org/10.1007/bfb0054305
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