International Workshop on Selected Areas in Cryptography

SAC 2001: Selected Areas in Cryptography pp 301-312

XTR Extended to GF(p6m)

  • Seongan Lim
  • Seungjoo Kim
  • Ikkwon Yie
  • Jaemoon Kim
  • Hongsub Lee
Conference paper

DOI: 10.1007/3-540-45537-X_23

Volume 2259 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Lim S., Kim S., Yie I., Kim J., Lee H. (2001) XTR Extended to GF(p6m). In: Vaudenay S., Youssef A.M. (eds) Selected Areas in Cryptography. SAC 2001. Lecture Notes in Computer Science, vol 2259. Springer, Berlin, Heidelberg

Abstract

A. K. Lenstra and E. R. Verheul in [2] proposed a very efficient way called XTR in which certain subgroup of the Galois field GF(p6) can be represented by elements in GF(p2). At the end of their paper [2], they briefly mentioned on a method of generalizing their idea to the field GF(p6m). In this paper, we give a systematic design of this generalization and discuss about optimal choices for p and m with respect to performances. If we choose m large enough, we can reduce the size of p as small as the word size of common processors. In such a case, this extended XTR is well suited for the processors with optimized arithmetic on integers of word size.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Seongan Lim
    • 1
  • Seungjoo Kim
    • 1
  • Ikkwon Yie
    • 2
  • Jaemoon Kim
    • 2
  • Hongsub Lee
    • 1
  1. 1.KISA (Korea Information Security Agency)SeoulKorea
  2. 2.Department of MathematicsInha UniversityIncheonKorea