Low complexity bit-parallel multiplier for F2n defined by repeated polynomials

Nam Su Chang, Eun Sook Kang, Seokhie Hong

    Research output: Contribution to journalArticlepeer-review

    Abstract

    Wu recently proposed three types of irreducible polynomials for low-complexity bit-parallel multipliers over F2n . In this paper, we consider new classes of irreducible polynomials for low-complexity bit-parallel multipliers over F2n , namely, repeated polynomial (RP). The complexity of the proposed multipliers is lower than those based on irreducible pentanomials. A repeated polynomial can be classified by the complexity of bit-parallel multiplier based on RPs, namely, C1, C2 and C3. If we consider finite fields that have neither a ESP nor a trinomial as an irreducible polynomial when n≤1000, then, in Wu's result, only 11 finite fields exist for three types of irreducible polynomials when n≤1000. However, in our result, there are 181, 232(52.4%), and 443(100%) finite fields of class C1, C2 and C3, respectively.

    Original languageEnglish
    Pages (from-to)2-12
    Number of pages11
    JournalDiscrete Applied Mathematics
    Volume241
    DOIs
    Publication statusPublished - 2018 May 31

    Bibliographical note

    Publisher Copyright:
    © 2016 Elsevier B.V.

    Keywords

    • Finite field
    • Irreducible polynomial
    • Multiplication
    • Polynomial basis

    ASJC Scopus subject areas

    • Discrete Mathematics and Combinatorics
    • Applied Mathematics

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