An Algorithm for Generating Irreducible Cubic Trinomials over Prime Field

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Abstract

This paper proposes an algorithm for generating irreducible cubic trinomials in the form x(3) + ax + b, b ∈ F(p), where a is a certain fixed non-zero element in theprime field F(p). The proposed algorithm needs a certain irreducible cubic trinomial over F(p) to be previously given as a generator; however, the proposed algorithm can generate irreducible cubic polynomials one after another by changing a certain parameter in F(p). In this paper, we compare the calculation cost and the average computation time for generating an irreducible cubic polynomial, especially trinomial, among Hiramoto et al. irreducibility testing algorithm, Berlekamp-Massey minimal polynomial determining algorithm, and the proposed algorithm. Fromthe experimental results, it is shown that the proposed algorithm is the fastest among the three algorithms for generating irreducible cubic trinomials.

Journal

  • Memoirs of the Faculty of Engineering, Okayama University

    Memoirs of the Faculty of Engineering, Okayama University 41(1), 11-19, 2007-01

    Faculty of Engineering, Okayama University

Codes

  • NII Article ID (NAID)
    120002308381
  • NII NACSIS-CAT ID (NCID)
    AA10699856
  • Text Lang
    ENG
  • Article Type
    departmental bulletin paper
  • ISSN
    0475-0071
  • Data Source
    IR 
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