Fast exponentiation in subgroups of finite fields

A new method for fast exponentiation is introduced by adapting the work of Gallant, Lambert and Vanstone (see Advances in Cryptology-Crypto 2001 LNCS 2139, p.190-200 Springer-Verlag, 2001) to finite fields: thus, it is applicable to the multiplicative subgroups of non-prime fields with efficient group homomorphisms such as pth powering maps. When applied to a quartic extension of a 256 bit prime field, the proposed method runs up to 60% faster than ordinary exponentiation in a 1024 bit prime field