Abstract
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.
Cite
CITATION STYLE
Gorla, E., Puttmann, C., & Shokrollahi, J. (2007). Explicit Formulas for Efficient Multiplication in $\mathbb{F}_{3^{6m}}$. In Selected Areas in Cryptography (pp. 173–183). Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-540-77360-3_12
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