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
Publication statusPublished - Apr 2008

Fingerprint

Polynomials

Keywords

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

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Computer Networks and Communications

Cite this

Basis translation matrix between two isomorphic extension fields via optimal normal basis. / Nogami, Yasuyuki; Namba, Ryo; Morikawa, Yoshitaka.

In: ETRI Journal, Vol. 30, No. 2, 04.2008, p. 326-334.

Research output: Contribution to journalArticle

Nogami, Yasuyuki ; Namba, Ryo ; Morikawa, Yoshitaka. / Basis translation matrix between two isomorphic extension fields via optimal normal basis. In: ETRI Journal. 2008 ; Vol. 30, No. 2. pp. 326-334.
@article{f915317e10d04ab08385dcf5bee646ec,
title = "Basis translation matrix between two isomorphic extension fields via optimal normal basis",
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.",
keywords = "Basic translation, Extension field, Optimal normal basis, Public key cryptography",
author = "Yasuyuki Nogami and Ryo Namba and Yoshitaka Morikawa",
year = "2008",
month = "4",
language = "English",
volume = "30",
pages = "326--334",
journal = "ETRI Journal",
issn = "1225-6463",
publisher = "ETRI",
number = "2",

}

TY - JOUR

T1 - Basis translation matrix between two isomorphic extension fields via optimal normal basis

AU - Nogami, Yasuyuki

AU - Namba, Ryo

AU - Morikawa, Yoshitaka

PY - 2008/4

Y1 - 2008/4

N2 - 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.

AB - 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.

KW - Basic translation

KW - Extension field

KW - Optimal normal basis

KW - Public key cryptography

UR - http://www.scopus.com/inward/record.url?scp=42149140576&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=42149140576&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:42149140576

VL - 30

SP - 326

EP - 334

JO - ETRI Journal

JF - ETRI Journal

SN - 1225-6463

IS - 2

ER -