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Finding Optimal Addition Chains Using a Genetic Algorithm Approach

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Computational Intelligence and Security (CIS 2005)

Abstract

Since most public key cryptosystem primitives require the computation of modular exponentiation as their main building block, the problem of performing modular exponentiation efficiently has received considerable attention over the years. It is known that optimal (shortest) addition chains are the key mathematical concept for accomplishing modular exponentiations optimally. However, finding an optimal addition chain of length r is an NP-hard problem whose search space size is comparable to r !. In this contribution we explore the usage of a Genetic Algorithm (GA) approach for the problem of finding optimal (shortest) addition chains. We explain our GA strategy in detail reporting several promising experimental results that suggest that evolutionary algorithms may be a viable alternative to solve this illustrious problem in a quasi optimal fashion.

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© 2005 Springer-Verlag Berlin Heidelberg

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Cruz-Cortés, N., Rodríguez-Henríquez, F., Juárez-Morales, R., Coello Coello, C.A. (2005). Finding Optimal Addition Chains Using a Genetic Algorithm Approach. In: Hao, Y., et al. Computational Intelligence and Security. CIS 2005. Lecture Notes in Computer Science(), vol 3801. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11596448_30

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  • DOI: https://doi.org/10.1007/11596448_30

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-30818-8

  • Online ISBN: 978-3-540-31599-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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