CEC'09 Proceedings of the Eleventh conference on Congress on Evolutionary Computation
Finding Minimal Addition Chains with a Particle Swarm Optimization Algorithm
MICAI '09 Proceedings of the 8th Mexican International Conference on Artificial Intelligence
An Artificial Immune System Heuristic for Generating Short Addition Chains
IEEE Transactions on Evolutionary Computation
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This paper presents the use of an evolutionary metaheuristic algorithm called evolutionary programming to minimize the length of addition chains, which is an NP-hard problem. Addition chains are used in modular exponentiation for data encryption and decryption public-key cryptosystems, such as RSA, DSA and others. The algorithm starts with a population of feasible addition chains. After that, the combination of a mutation operator, which allows each individual to generate a feasible offspring, and a replacement process based on stochastic encounters provides a simple approach which is tested on exponents with different features. The proposed algorithm is able to find competitive results with respect to other nature-inspired metaheuristic approaches but with a lower number of evaluations per run.