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

Nam Su Chang, Eun Sook Kang, Seokhie Hong

Research output: Contribution to journalArticle

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
JournalDiscrete Applied Mathematics
DOIs
Publication statusAccepted/In press - 2015 Aug 28

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Keywords

  • Finite field
  • Irreducible polynomial
  • Multiplication
  • Polynomial basis

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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