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The Pairing Computation on Edwards Curves

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  • Hongfeng Wu
  • Liangze Li
  • Fan Zhang

Abstract

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.

Suggested Citation

  • Hongfeng Wu & Liangze Li & Fan Zhang, 2013. "The Pairing Computation on Edwards Curves," Mathematical Problems in Engineering, Hindawi, vol. 2013, pages 1-8, November.
    • Handle: RePEc:hin:jnlmpe:136767
    DOI: 10.1155/2013/136767
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