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2011•KTH Publication Database DiVA (KTH Royal Institute of Technology)Open access

Factorization Algorithms for Polynomials over Finite Fields

Sajid Hanif, Muhammad Imran

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Abstract

Integer factorization is a dicult task. Some cryptosystem such asRSA (which stands for Rivest, Shamir and Adleman ) are in fact designedaround the diculty of integer factorization.For factorization of polynomials in a given nite eld Fp we can useBerlekamp's and Zassenhaus algorithms. In this project we will see howBerlekamp's and Zassenhaus algorithms work for factorization of polyno-mials in a nite eld Fp. This project is aimed toward those with interestsin computational algebra, nite elds, and linear algebra.

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What this paper is about

Integer factorization is a dicult task. Some cryptosystem such asRSA (which stands for Rivest, Shamir and Adleman ) are in fact designedaround the diculty of integer factorization.For factorization of polynomials in a given nite eld Fp we can useBerlekamp's and Zassenhaus algorithms. In this project we will see howBerlekamp's and Zassenhaus algorithms work for factorization of polyno-mials in a nite eld Fp. This project is aimed toward those with interestsin computational algebra, nite elds, and linear algebra.

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Available abstract

Integer factorization is a dicult task. Some cryptosystem such asRSA (which stands for Rivest, Shamir and Adleman ) are in fact designedaround the diculty of integer factorization.For factorization of polynomials in a given nite eld Fp we can useBerlekamp's and Zassenhaus algorithms. In this project we will see howBerlekamp's and Zassenhaus algorithms work for factorization of polyno-mials in a nite eld Fp. This project is aimed toward those with interestsin computational algebra, nite elds, and linear algebra.

Key concepts: Factorization, Integer factorization, Integer (computer science), Mathematics, Factorization of polynomials, Algebra over a field, Dixon's factorization method, Finite field

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