Advertisement

Journal of Computer Science and Technology

, Volume 20, Issue 2, pp 264–269 | Cite as

Implementation of Cryptosystems Based on Tate Pairing

  • Lei HuEmail author
  • Jun-Wu Dong
  • Ding-Yi Pei
Article

Abstract

Tate pairings over elliptic curves are important in cryptography since they can be used to construct efficient identity-based cryptosystems, and their implementation dominantly determines the efficiencies of the cryptosystems. In this paper, the implementation of a cryptosystem is provided based on the Tate pairing over a supersingular elliptic curve of MOV degree 3. The implementation is primarily designed to re-use low-level codes developed in implementation of usual elliptic curve cryptosystems. The paper studies how to construct the underlying ground field and its extension to accelerate the finite field arithmetic, and presents a technique to speedup the time-consuming powering in the Tate pairing algorithm.

Keywords

identity-based cryptosystem elliptic curve Tate pairing implementation 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Shamir A. Identity based cryptosystems and signature schemes. In Advance in Cryptology-Crypto’84, Blakley GR, Chaum D (eds.), Berlin/Heidelberg: Springer-Verlag, 1985, pp.47–53.Google Scholar
  2. [2]
    Boneh D, Franklin M. Identity based encryption from the Weil pairing. In Advance in Cryptology-Crypto’2001, Kilian J (ed.), Berlin/Heidelberg: Springer-Verlag, 2001, pp.213–229.Google Scholar
  3. [3]
    Tao R, Chen S. An implementation of identity-based cryptosystems and signature schemes by finite automation public key cryptosystems. In Advance in Cryptology-Chinacrypt’92, Tao R, Li X, Pei D (eds.), Beijing: Science Press, 1992, pp.87–104. (in Chinese)Google Scholar
  4. [4]
    Sakai R, Ohgishi K, Kasahara M. Cryptosystems based on pairing. In Symposium on Cryptography and Information Security-SCIS’2000, Okinawa, Japan, Jan. 2000, pp.26–28.Google Scholar
  5. [5]
    Joux A. A one-round protocol for tripartite diffie-hellman. In Algorithm Number Theory Symposium-ANTS-IV, Bosma W (ed.), Berlin/Heidelberg: Springer-Verlag, 2000, pp.385–394.Google Scholar
  6. [6]
    Boneh D, Silverberg A. Applications of multilinear forms to cryptography. In Topics in Algebraic and Noncommutative Geometry–Proceedings in Memory of Ruth Michler, Melles G, Brasselet J, Kennedy G et al. (eds.), Contemporary Mathematics Series of American Mathematical Society, 2003, 324: 71–90.Google Scholar
  7. [7]
    Menezes A J, Okamoto T, Vanstone S A. Reducing elliptic curve logarithms to logarithms in a finite field. IEEE Trans. Information Theory, 1993, 39(5): 1639–1646.Google Scholar
  8. [8]
    Frey G, Ruck H G. A remark concerning m-divisibility and the discrete logarithm in the divisor class group of curves. Mathematics of Computation, 1994, 62(206): 865–874.Google Scholar
  9. [9]
    Miyaji A, Nakabayashi M, Takano S. New explicit conditions of elliptic curve traces for FR-reduction. IEICE Trans. Fundamentals, 2001, E84-A(5): 1234–1243.Google Scholar
  10. [10]
    Dupont R, Enge A, Morain F. Building curves with arbitrary small MOV degree over finite prime fields. Available at http://ePrint.iacr.org/2002/094 (Cryptology ePrint Archive, Report 2002/094).
  11. [11]
    Barreto P S L M, Lynn B, Scott M. Constructing elliptic curves with prescribed embedding degrees. In Third Workshop on Security in Communication Networks—SCN’2002, Yung M (ed.), Lecture Notes in Computer Science 2576, Springer-Verlag, 2003, pp.257–267.Google Scholar
  12. [12]
    Barreto P S L M, Kim H, Lynn B, Scott M. Efficient algorithms for pairing based cryptosystems. In Advance in Cryptology-Crypto’2002, Yung M (ed.), Berlin/Heidelberg: Springer-Verlag, 2002, pp.354–368.Google Scholar
  13. [13]
    Galbraith S D, Harrison K, Soldera D. Implementing the Tate pairing. In Algorithm Number Theory Symposium-ANTS-V, Kohel D R (ed.), Berlin/Heidelberg: Springer-Verlag, 2002, pp.324–337.Google Scholar
  14. [14]
    Harasawa R, Shikata J, Suzuki J, Imai H. Comparing the MOV and FR reductions in elliptic curve cryptography. In Advance in Cryptology-Eurocrypto’97, Fumy W (ed.), Berlin/Heidelberg, Springer-Verlag, 1997, pp.190–205.Google Scholar
  15. [15]
    Verheul E R. Evidence that XTR is more secure than supersingular elliptic curve cryptosystems. In Advance in Cryptology-Eurocrypt’2001, Pfitzmann B (ed.), Berlin/Heidelberg: Springer-Verlag, 2001, pp.195–210.Google Scholar
  16. [16]
    Joux A. The Weil and Tate pairings as building blocks for public key cryptosystems. In Algorithm Number Theory Symposium-ANTS-V, Kohel D R (ed.), Berlin/Heidelberg: Springer-Verlag, 2002, pp.20–32.Google Scholar
  17. [17]
    Miller V. Short programs for functions on curves. Unpublished manuscript, 1986. Available at http://crypto. stanford.edu.cn/miller/miller.pdf

Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  1. 1.State Key Laboratory of Information SecurityGraduate School of Chinese Academy of SciencesBeijingP.R. China
  2. 2.Institute of Information SecurityGuangzhou UniversityGuangzhouP.R. China

Personalised recommendations