An evolutionary algorithm for short addition chains

Abstract

The encryption efficiency of the Rivest-Shamir-Adleman cryptosystem is based on decreasing the number of multiplications in the modular exponentiation (ME) operation. An addition chain (AC) is one of the strategies used to reduce the time consumed by ME through generating a shortest/short chain. Due to the non-polynomial time required for generating a shortest AC, several algorithms have been proposed to find a short AC in a faster time. In this paper, we use the evolutionary algorithm (EA) to find a short AC for a natural number. We discuss and present the role of every component of the EA, including the population, mutation operator, and survivor selection. Then we study, practically, the effectiveness of the proposed method in terms of the length of chain it generates by comparing it with three kinds of algorithms: (1) exact, (2) non-exact deterministic, and (3) non-exact non-deterministic. The experiment is conducted on all natural numbers that have 10, 11, 12, 13, and 14 bits. The results demonstrate that the proposed algorithm has good performance compared to the other three types of algorithms.