New Algorithm for Public Key Cryptosystems Based on Lucas Sequences

Abstract

A novel algorithm for the computation of Lucas sequences is proposed to improve the efficiency of cryptosystems based on it. By the introduction of pre-computation, the original Characteristic polynomial algorithm is modified to reduce the number of multiplication operations. The influence of window size on efficiency of the algorithm is also analyzed, and a optimization scheme is presented. In circumstances that more than one values of Lucas sequence need to be calculated, the new algorithm is more efficient than the existing Yen-Laih algorithm.