Improving and extending the Lim/Lee exponentiation algorithm

Abstract

In [5] Lim and Lee present an algorithm for fast exponentia- tion in a given group which is optimized for a limited amount of storage. The algorithm uses one precomputation for several computations in or- der to minimize the average time needed for one exponentiation. This paper generalizes the previous work proposing several improvements and a method for fast precomputation. The basic Lim/Lee algorithm is im- proved by determining the optimal segmentation of the exponent. Fi- nally, it is shown that the improved Lim/Lee algorithm is faster than the previous one in average case.