Optimal extension fields for XTR

Dong Guk Han, Ki Soon Yoon, Young Ho Park, Chang Han Kim, Jongin Lim

Research output: Chapter in Book/Report/Conference proceedingChapter

4 Citations (Scopus)

Abstract

Application of XTR in cryptographic protocols leads to substantial savings both in communication and computational overhead without compromising security [6]. XTR is a new method to represent elements of a subgroup of a multiplicative group of a finite field GF(p6) and it can be generalized to the field GF(p6m) [6,9]. This paper proposes optimal extension fields for XTR among Galois fields GF(p6m) which can be applied to XTR. In order to select such fields, we introduce a new notion of Generalized Optimal Extension Fields(GOEFs) and suggest a condition of prime p, a defining polynomial of GF(p2m) and a fast method of multiplication in GF(p2m) to achieve fast finite field arithmetic in GF(p2m). From our implementation results, GF(p36) → GF(p12) is the most efficient extension fields for XTR and computing Tr(gn) given Tr(g) in GF(p12) is on average more than twice faster than that of the XTR system[6,10] on Pentium III/700MHz which has 32-bit architecture.

Original languageEnglish
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
EditorsKaisa Nyberg, Howard Heys
PublisherSpringer Verlag
Pages369-384
Number of pages16
ISBN (Print)9783540006220
DOIs
Publication statusPublished - 2003

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume2595
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Keywords

  • Karatsuba's method
  • Pseudo-Mersenne prime
  • XTR public key system

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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