Basis translation matrix between two isomorphic extension fields via optimal normal basis

Yasuyuki Nogami, Ryo Namba, Yoshitaka Morikawa

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

This paper proposes a method for generating a basis translation matrix between isomorphic extension fields. To generate a basis translation matrix, we need the equality correspondence of a basis between the isomorphic extension fields. Consider an extension field Fpm where p is characteristic. As a brute force method, when pm is small, we can check the equality correspondence by using the minimal polynomial of a basis element; however, when pm is large, it becomes too difficult The proposed methods are based on the fact that Type I and Type II optimal normal bases (ONBs) can be easily identified in each isomorphic extension field. The proposed methods efficiently use Type I and Type II ONBs and can generate a pair of basis translation matrices within 15 ms on Pentium 4 (3.6 GHz) when mlog2p = 160.

Original languageEnglish
Pages (from-to)326-334
Number of pages9
JournalETRI Journal
Volume30
Issue number2
DOIs
Publication statusPublished - Apr 2008

Keywords

  • Basic translation
  • Extension field
  • Optimal normal basis
  • Public key cryptography

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Computer Science(all)
  • Electrical and Electronic Engineering

Fingerprint Dive into the research topics of 'Basis translation matrix between two isomorphic extension fields via optimal normal basis'. Together they form a unique fingerprint.

Cite this