Explicit formulas for efficient multiplication in F_{3^{6m}}
Cryptography and Security
2007-08-23 v1 Computational Complexity
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
@article{arxiv.0708.3014,
title = {Explicit formulas for efficient multiplication in F_{3^{6m}}},
author = {Elisa Gorla and Christoph Puttmann and Jamshid Shokrollahi},
journal= {arXiv preprint arXiv:0708.3014},
year = {2007}
}
Comments
11 pages, to appear in the proceedings of SAC2007