Finding optimal addition chains using a genetic algorithm approach

Authors:
Nareli Cruz-Cortés;Francisco Rodríguez-Henríquez;Raúl Juárez-Morales;Carlos A. Coello Coello
Affiliations:
Computer Science Section, Electrical Engineering Department, Centro de Investigación y de Estudios Avanzados del IPN, México D.F.;Computer Science Section, Electrical Engineering Department, Centro de Investigación y de Estudios Avanzados del IPN, México D.F.;Computer Science Section, Electrical Engineering Department, Centro de Investigación y de Estudios Avanzados del IPN, México D.F.;Computer Science Section, Electrical Engineering Department, Centro de Investigación y de Estudios Avanzados del IPN, México D.F.
Venue:
CIS'05 Proceedings of the 2005 international conference on Computational Intelligence and Security - Volume Part I
Year:
2005

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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.