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

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 F36m , 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 F3m -multiplications for multiplication in F36m from 18 in recent implementations to 15. The method is based on the fast Fourier transform and its explicit formulas are given. The execution times of our software implementations for F36m show the efficiency of our results.