Minimal Addition-Subtraction Sequences for Efficient Pre-processing in Large Window-Based Modular Exponentiation Using Genetic Algorithms

Abstract

This paper introduces a novel application of genetic algorithms for evolving optimal addition-subtraction sequences that allow one to perform precomputations necessary in the window-based modular exponentiation methods. When the window size is large, the pre-processing step becomes very expensive. Evolved addition/addition-subtraction sequences are of minimal size so they allow one to perform exponentiation with a minimal number of multiplication and/or divisions and hence implementing efficiently the exponentiation operation. © Springer-Verlag 2003.