Cryptology ePrint Archive: Report 2012/551

Faster Pairing Computation on Jacobi quartic Curves with High-Degree Twists

Liangze Li and Hongfeng Wu and Fan Zhang

Abstract: In this paper, we propose an elaborate geometric approach to explain the group law on Jacobi quartic curves which are seen as the intersection of two quadratic surfaces in space. Using the geometry interpretation we construct the Miller function. Then we present explicit formulae for the addition and doubling steps in Miller's algorithm to compute Tate pairing on Jacobi quartic curves. Both the addition step and doubling step of our formulae for Tate pairing computation on Jacobi curves are faster than previously proposed ones. Finally, we present efficient formulas for Jacobi quartic curves with twists of degree 4 or 6. For twists of degree 4, both the addition steps and doubling steps in our formulas are faster than the fastest result on Weierstrass curves. For twists of degree 6, the addition steps of our formulae are faster than the fastest result on Weierstrass curves.

Category / Keywords: public-key cryptography / Elliptic curve,Jacobi quartic curve,Tate pairing,Miller function

Date: received 21 Sep 2012

Contact author: whfmath at gmail com

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Version: 20120924:055734 (All versions of this report)

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