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1993•Mathematics of ComputationOpen access

On bivariate polynomial factorization over finite fields

Igor E. Shparlinski

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Abstract

This paper shows that a recently proposed approach of D. Q. Wan to bivariate factorization over finite fields, the univariate factoring algorithm of V. Shoup, and the new bound of this paper for the average number of irreducible divisors of polynomials of a given degree over a finite field can be used to design a bivariate factoring algorithm that is polynomial for "almost all" bivariate polynomials.

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What this paper is about

This paper shows that a recently proposed approach of D. Q. Wan to bivariate factorization over finite fields, the univariate factoring algorithm of V. Shoup, and the new bound of this paper for the average number of irreducible divisors of polynomials of a given degree over a finite field can be used to design a bivariate factoring algorithm that is polynomial for "almost all" bivariate polynomials.

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Available abstract

This paper shows that a recently proposed approach of D. Q. Wan to bivariate factorization over finite fields, the univariate factoring algorithm of V. Shoup, and the new bound of this paper for the average number of irreducible divisors of polynomials of a given degree over a finite field can be used to design a bivariate factoring algorithm that is polynomial for "almost all" bivariate polynomials.

Key concepts: Bivariate analysis, Factorization of polynomials, Mathematics, Finite field, Factorization, Univariate, Factoring, Polynomial

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