论文信息 - Analysis of Rabin's Polynomial Irreducability Test

Analysis of Rabin's Polynomial Irreducability Test

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.

Alfredo Viola | Daniel Panario | D. Panario | Alfredo Viola

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