Software Implementation of Arithmetic in Open image in new window

  • Omran Ahmadi
  • Darrel Hankerson
  • Alfred Menezes
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4547)


Fast arithmetic for characteristic three finite fields Open image in new window is desirable in pairing-based cryptography because there is a suitable family of elliptic curves over Open image in new window having embedding degree 6. In this paper we present some structure results for Gaussian normal bases of Open image in new window , and use the results to devise faster multiplication algorithms. We carefully compare multiplication in Open image in new window using polynomial bases and Gaussian normal bases. Finally, we compare the speed of encryption and decryption for the Boneh-Franklin and Sakai-Kasahara identity-based encryption schemes at the 128-bit security level, in the case where supersingular elliptic curves with embedding degrees 2, 4 and 6 are employed.


Elliptic Curf Normal Basis Cube Root Nonzero Term Cryptology ePrint Archive 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Omran Ahmadi
    • 1
  • Darrel Hankerson
    • 2
  • Alfred Menezes
    • 3
  1. 1.Dept. of Electrical and Computer Engineering, University of Toronto 
  2. 2.Dept. of Mathematics and Statistics, Auburn University 
  3. 3.Dept. of Combinatorics & Optimization, University of Waterloo 

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