A multiplication algorithm in Fpm such that p > m with a special class of Gauss period normal bases

Hidehiro Kato, Yasuyuki Nogami, Tomoki Yoshida, Yoshitaka Morikawa

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)


In this paper, a multiplication algorithm in extension field F pm is proposed. Different from the previous works, the proposed algorithm can be applied for an arbitrary pair of characteristic p and extension degree m only except for the case when 4p divides m(p-1) and m is an even number. As written in the title, when p > m, 4p does not divide m(p - 1). The proposed algorithm is derived by modifying cyclic vector multiplication algorithm (CVMA). We adopt a special class of Gauss period normal bases. At first in this paper, it is formulated as an algorithm and the calculation cost of the modified algorithm is evaluated. Then, compared to those of the previous works, some experimental results are shown. Finally, it is shown that the proposed algorithm is sufficient practical when extension degree m is small.

Original languageEnglish
Pages (from-to)173-181
Number of pages9
JournalIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Issue number1
Publication statusPublished - Jan 2009


  • Extension field
  • Fast implementation
  • Gauss period normal bases
  • Optimal normal basis
  • Public-key cryptography

ASJC Scopus subject areas

  • Signal Processing
  • Computer Graphics and Computer-Aided Design
  • Electrical and Electronic Engineering
  • Applied Mathematics


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