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Finding short and implementation-friendly addition chains with evolutionary algorithms

Author(s)
Coello, Carlos A C; Jakobovic, Domagoj; Mentens, Nele; Coello, Carlos A. Coello; Picek, Stjepan
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Abstract
Finding the shortest addition chain for a given exponent is a significant problem in cryptography. In this work, we present a genetic algorithm with a novel encoding of solutions and new crossover and mutation operators to minimize the length of the addition chains corresponding to a given exponent. We also develop a repair strategy that significantly enhances the performance of our approach. The results are compared with respect to those generated by other metaheuristics for exponents of moderate size, but we also investigate values up to 2²⁵⁵ - 21. For numbers of such size, we were unable to find any results produced by other metaheuristics which could be used for comparison purposes. Therefore, we decided to add three additional strategies to serve as benchmarks. Our results indicate that the proposed approach is a very promising alternative to deal with this problem. We also consider a more practical perspective by taking into account the implementation cost of the chains: we optimize the addition chains with regards to the type of operations as well as the number of instructions required for the implementation.
Date issued
2017-06
URI
http://hdl.handle.net/1721.1/115968
Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Journal
Journal of Heuristics
Publisher
Springer-Verlag
Citation
Picek, Stjepan et al. “Finding Short and Implementation-Friendly Addition Chains with Evolutionary Algorithms.” Journal of Heuristics 24, 3 (June 2017): 457–481 © 2017 Springer Science+Business Media, LLC
Version: Author's final manuscript
ISSN
1381-1231
1572-9397

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