Cryptology ePrint Archive: Report 2010/475

Pairing Computation on Elliptic Curves of Jacobi Quartic Form

Hong Wang and Kunpeng Wang and Lijun Zhang and Bao Li

Abstract: This paper proposes explicit formulae for the addition step and doubling step in Miller's algorithm to compute Tate pairing on Jacobi quartic curves.

We present a geometric interpretation of the group law on Jacobi quartic curves, %and our formulae for Miller's %algorithm come from this interpretation. which leads to formulae for Miller's algorithm. The doubling step formula is competitive with that for Weierstrass curves and Edwards curves. Moreover, by carefully choosing the coefficients, there exist quartic twists of Jacobi quartic curves from which pairing computation can benefit a lot. Finally, we provide some examples of supersingular and ordinary pairing friendly Jacobi quartic curves.

Category / Keywords: public-key cryptography / elliptic curve, pairing, geometric interpretation

Publication Info: unpublished

Date: received 6 Sep 2010, last revised 25 Oct 2010

Contact author: hwang at is ac cn

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Version: 20101025:075258 (All versions of this report)

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