Título:
Analysis of Rabin's irreducibility test for polynomials over finite fields
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Autor:
Panario, Daniel
Pittel, Boris
Richmond, Bruce
Viola, Alfredo
Pittel, Boris
Richmond, Bruce
Viola, Alfredo
Tutor:
Tipo de documento:
Reporte técnico
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Palabras clave:
RANDOM POLYNOMIALS
FINITE FIELDS
ALGORITHMS
FINITE FIELDS
ALGORITHMS
Descriptores:
Año de publicación:
2001
Contenido:
Resumen:
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 study the expected value and the variance of the number of operations performed by the algorithm. We present a exact analysis when n=p1 and n=p1p2 for p1,p2 prime numbers, and as asymptotic analysis for the general case. Our method generalizes to other algorithms that deal with similar divisor conditions. In particular, we analyze the average-case number of operations for two variants of Rabin's algorithm, and determine the ordering of prime divisors of n that minimizes the leading factor.
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Editorial:
UR. FI – INCO.
EN:
Reportes Técnicos 01-16
Financiadores:
Citación:
PANARIO, D., PITTEL, B., RICHMOND, B., y otros. "Analysis of Rabin's irreducibility test for polynomials over finite fields". Reportes Técnicos 01-16. UR. FI – INCO, 2001.
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URI:
http://hdl.handle.net/20.500.12008/3455
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ISSN:
0797-6410
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Licencia Creative Commons Atribución – No Comercial – Sin Derivadas (CC BY-NC-ND 4.0)
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| Ficheros | Descripción | Tamaño | Formato | ||
|---|---|---|---|---|---|
| TR0116.pdf | — | 321.88 KB | Adobe PDF |