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Explicit formulas for efficient multiplication in F_{3^{6m}}
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.Comment: 11 pages, to appear in the proceedings of SAC200