Memoirs of the Faculty of Engineering, Okayama University
Published by Faculty of Enginerring, Okayama University

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Memoirs of the School of Engineering, Okayama University

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An Algorithm for Generating Irreducible Cubic Trinomials over Prime Field

Nogami, Yasuyuki The Graduate School of Natural Science and Technology Okayama University
Morikawa, Yoshitaka The Graduate School of Natural Science and Technology Okayama University
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 the prime 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. From the experimental results, it is shown that the proposed algorithm is the fastest among the three algorithms for generating irreducible cubic trinomials.
irreducible cubic polynomial
minimal polynomial