Explicit formulas for efficient multiplication in F_{3^{6m}}

Details Explicit formulas for efficient multiplication in F_{3^{6m}} Explicit formulas for efficient multiplication in F_{3^{6m}}

2007-08-22

arxiv.org/abs/0708.3014v1

Computer Science

Cryptography and Security

11 pages, to appear in the proceedings of SAC2007

Scientific paper

Efficient computation of the Tate pairing is an important part of pairing-based cryptography. Recently with the introduction of the Duursma-Lee method special attention has been given to the fields of characteristic 3. Especially multiplication in F_{3^{6m}}, where m is prime, is an important operation in the above method. In this paper we propose a new method to reduce the number of F_{3^m} multiplications for multiplication in F_{3^{6m}} from 18 in recent implementations to 15. The method is based on the fast Fourier tranmsform and explicit formulas are given. The execution times of our software implementations for F_{3^{6m}} show the efficiency of our results.

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