A fast inversion algorithm and low-complexity architecture over GF(2 m)

Sosun Kim, Nam Su Chang, Chang Han Kim, Young Ho Park, Jong In Lim

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Citations (Scopus)

Abstract

The performance of public-key cryptosystems is mainly appointed by the underlying finite field arithmetic. Among the basic arithmetic operations over finite field, the multiplicative inversion is the most time consuming operation. In this paper, a fast inversion algorithm over GF(2m) with the polynomial basis representation is proposed, The proposed algorithm executes in about 27.5% or 45.6% less iterations than the extended binary gcd algorithm (EBGA) or the montgomery inverse algorithm (MIA) over GF(2163), respectively. In addition, we propose a new hardware architecture to apply for low-complexity systems. The proposed architecture takes approximately 48.3% or 24.0% less the number of reduction operations than [4] or [8] over GF(2 239), respectively. Furthermore, it executes in about 21.8% less the number of addition operations than [8] over GF(2163).

Original languageEnglish
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Pages1-8
Number of pages8
Volume3802 LNAI
Publication statusPublished - 2005 Dec 1
EventInternational Conference on Computational Intelligence and Security, CIS 2005 - Xi'an, China
Duration: 2005 Dec 152005 Dec 19

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume3802 LNAI
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

OtherInternational Conference on Computational Intelligence and Security, CIS 2005
CountryChina
CityXi'an
Period05/12/1505/12/19

Fingerprint

Algorithm Complexity
Low Complexity
Inversion
Finite Field Arithmetic
Polynomial Basis
Public-key Cryptosystem
Hardware Architecture
Cryptography
Galois field
Multiplicative
Polynomials
Binary
Hardware
Iteration
Architecture

ASJC Scopus subject areas

  • Computer Science(all)
  • Biochemistry, Genetics and Molecular Biology(all)
  • Theoretical Computer Science

Cite this

Kim, S., Chang, N. S., Kim, C. H., Park, Y. H., & Lim, J. I. (2005). A fast inversion algorithm and low-complexity architecture over GF(2 m). In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 3802 LNAI, pp. 1-8). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 3802 LNAI).

A fast inversion algorithm and low-complexity architecture over GF(2 m). / Kim, Sosun; Chang, Nam Su; Kim, Chang Han; Park, Young Ho; Lim, Jong In.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 3802 LNAI 2005. p. 1-8 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 3802 LNAI).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Kim, S, Chang, NS, Kim, CH, Park, YH & Lim, JI 2005, A fast inversion algorithm and low-complexity architecture over GF(2 m). in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). vol. 3802 LNAI, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 3802 LNAI, pp. 1-8, International Conference on Computational Intelligence and Security, CIS 2005, Xi'an, China, 05/12/15.
Kim S, Chang NS, Kim CH, Park YH, Lim JI. A fast inversion algorithm and low-complexity architecture over GF(2 m). In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 3802 LNAI. 2005. p. 1-8. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
Kim, Sosun ; Chang, Nam Su ; Kim, Chang Han ; Park, Young Ho ; Lim, Jong In. / A fast inversion algorithm and low-complexity architecture over GF(2 m). Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 3802 LNAI 2005. pp. 1-8 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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