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Mathematical Problems in Engineering
Volume 2013, Article ID 136767, 8 pages
Research Article

The Pairing Computation on Edwards Curves

1College of Sciences, North China University of Technology, Beijing 100144, China
2School of Mathematical Sciences, Peking University, Beijing 100871, China
3Beijing International Center for Mathematical Research, Beijing 100871, China

Received 4 May 2013; Accepted 22 September 2013

Academic Editor: Jun Jiang

Copyright © 2013 Hongfeng Wu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We propose an elaborate geometry approach to explain the group law on twisted Edwards curves which are seen as the intersection of quadric surfaces in place. Using the geometric interpretation of the group law, we obtain the Miller function for Tate pairing computation on twisted Edwards curves. Then we present the explicit formulae for pairing computation on twisted Edwards curves. Our formulae for the doubling step are a little faster than that proposed by Arène et al. Finally, to improve the efficiency of pairing computation, we present twists of degrees 4 and 6 on twisted Edwards curves.