Minimum Addition Chains Generation Using Evolutionary Strategies

Mauricio Olguin Carbajal, Juan Carlos Herrera-Lozada, Israel Rivera-Zárate, J. Felix Serrano-Talamantes, Rodrigo Cadena-Martínez, J. Irving Vásquez-Gómez


The calculus for a power of a number could be a time and computational cost-consuming task. A method for reducing this issue is welcome in all mayor computational areas as cryptography, numerical series and elliptic curves calculus,  just to mention a few. This paper details the development of a minimum length addition chains generator based on an Evolutionary Strategy, which makes fewer calls to the objective function with respect to other proposals that also use bio-inspirated algorithms as Particle Swarm Optimization or a Genetic Algorithm. By using fewer calls to the objective function, the number of calculations is lower and consequently decreases the generation time providing an improvement in computational cost but obtaining competitive results.


Minimum length, addition chains, evolutionary strategy, computational cost reduction

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