Cryptology ePrint Archive: Report 2012/247

On Efficient Pairings on Elliptic Curves over Extension Fields

Xusheng Zhang and Kunpeng Wang and Dongdai Lin

Abstract: In implementation of elliptic curve cryptography, three kinds of finite fields have been widely studied, i.e. prime field, binary field and optimal extension field. In pairing-based cryptography, however, pairing-friendly curves are usually chosen among ordinary curves over prime fields and supersingular curves over extension fields with small characteristics. In this paper, we study pairings on elliptic curves over extension fields from the point of view of accelerating the Miller's algorithm to present further advantage of pairing-friendly curves over extension fields, not relying on the much faster field arithmetic. We propose new pairings on elliptic curves over extension fields can make better use of the multi-pairing technique for the efficient implementation. By using some implementation skills, our new pairings could be implemented much more efficiently than the optimal ate pairing and the optimal twisted ate pairing on elliptic curves over extension fields. At last, we use the similar method to give more efficient pairings on Estibals's supersingular curves over composite extension fields in parallel implementation.

Category / Keywords: implementation / pairing, elliptic curve over extension field, multi-pairing technique

Publication Info: The 5th International Conference on Pairing-Based Cryptography (Pairing 2012)

Date: received 2 May 2012

Contact author: xszhang is at gmail com

Available format(s): PDF | BibTeX Citation

Version: 20120503:095450 (All versions of this report)

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