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

  • Nadia Nedjah
  • Luiza de Macedo Mourelle
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2690)


This paper introduces a novel application of genetic algorithms for evolving optimal addition-subtraction sequences that allow one to perform pre- computations 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.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Nadia Nedjah
    • 1
  • Luiza de Macedo Mourelle
    • 1
  1. 1.Department of Systems Engineering and Computation, Faculty of EngineeringState University of Rio de JaneiroBrazil

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