Cryptology ePrint Archive: Report 2012/532

Pairing computation on Edwards curves with high-degree twists

Liangze Li and Hongfeng Wu and Fan Zhang

Abstract: In this paper, 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 littler faster than that proposed by Arene Finally, to improve the efficiency of pairing computation we present twists of degree 4 and 6 on twisted Edwards curves.

Category / Keywords: public-key cryptography / Edwards curves, Tate pairing, Miller functions, Cryptography

Date: received 9 Sep 2012, last revised 27 Sep 2012

Contact author: whfmath at gmail com

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Version: 20120927:093516 (All versions of this report)

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