Optimal extension fields for XTR

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

Research output: Contribution to journalArticle

4 Citations (Scopus)


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
Pages (from-to)369-384
Number of pages16
JournalLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Publication statusPublished - 2003 Dec 1



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

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Cite this