A secure family of composite finite fields suitable for fast implementation of elliptic curve cryptography

Mathieu Ciet, Jean Jacques Quisquater, Francesco Sica

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

13 Citations (Scopus)

Abstract

In 1999 Silverman [21] introduced a family of binary finite fields which are composite extensions of F2 and on which arithmetic operations can be performed more quickly than on prime extensions of F2 of the same size. We present here a fast approach to elliptic curve cryptography using a distinguished subset of the set of Silverman fields F2N = Fhn. This approach leads to a theoretical computation speedup over fields of the same size, using a standard point of view (cf. [7]). We also analyse their security against prime extension fields F2p, where p is prime, following the method of Menezes and Qu [12]. We conclude that our fields do not present any significant weakness towards the solution of the elliptic curve discrete logarithm problem and that often the Weil descent of Galbraith-Gaudry-Hess-Smart (GGHS) does not offer a better attack on elliptic curves defined over F2N than on those defined over F2p, with a prime p of the same size as N. A noteworthy example is provided by F2226: a generic elliptic curve Y2 + XY = X3 + αX2 + β defined over F2226 is as prone to the GGHS Weil descent attack as a generic curve defined on the NIST field F2233.

Original languageEnglish
Title of host publicationProgress in Cryptology - INDOCRYPT 2001 - 2nd International Conference on Cryptology in India, Proceedings
EditorsC. Pandu Rangan, Cunsheng Ding
PublisherSpringer Verlag
Pages108-116
Number of pages9
ISBN (Print)9783540453116
DOIs
Publication statusPublished - 2001
Event2nd International Conference on Cryptology in India, INDOCRYPT 2001 - Chennai, India
Duration: Dec 16 2001Dec 20 2001

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume2247
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other2nd International Conference on Cryptology in India, INDOCRYPT 2001
CountryIndia
CityChennai
Period12/16/0112/20/01

Keywords

  • Elliptic curve cryptography
  • Fast performance
  • Finite fields
  • Weil descent

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Fingerprint Dive into the research topics of 'A secure family of composite finite fields suitable for fast implementation of elliptic curve cryptography'. Together they form a unique fingerprint.

  • Cite this

    Ciet, M., Quisquater, J. J., & Sica, F. (2001). A secure family of composite finite fields suitable for fast implementation of elliptic curve cryptography. In C. P. Rangan, & C. Ding (Eds.), Progress in Cryptology - INDOCRYPT 2001 - 2nd International Conference on Cryptology in India, Proceedings (pp. 108-116). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2247). Springer Verlag. https://doi.org/10.1007/3-540-45311-3_11