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Finding Optimal Addition Chains Using a Genetic Algorithm Approach

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Computational Intelligence and Security (CIS 2005)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3801))

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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.

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Author information

Authors and Affiliations

  1. Computer Science Section, Electrical Engineering Department, Centro de Investigación y de Estudios Avanzados del IPN, Av. Instituto Politécnico Nacional No. 2508, México D.F.

    Nareli Cruz-Cortés, Francisco Rodríguez-Henríquez, Raúl Juárez-Morales & Carlos A. Coello Coello

Authors
  1. Nareli Cruz-Cortés
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  2. Francisco Rodríguez-Henríquez
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  3. Raúl Juárez-Morales
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  4. Carlos A. Coello Coello
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Editor information

Editors and Affiliations

  1. Microelectronic Instiute, Xidian University, 710071, Xi’an, China

    Yue Hao

  2. Department of Computer Science, Hong Kong Baptist University, Kowloon Tong, Hong Kong

    Jiming Liu

  3. School of Computer Science and Technology, Xidian University, Xi’an, China

    Yuping Wang

  4. Department of Computer Science, Hong Kong Baptist University, Hong Kong,  

    Yiu-ming Cheung

  5. School of Electrical and Electronic Engineering, University of Manchester, UK

    Hujun Yin

  6. Life Science Research Center, School of Electronic Engineering, Xidian University, 710071, Xi’an, Shaanxi, China

    Licheng Jiao

  7. Key Laboratory of Computer Networks and Information Security (Ministry of Education), Xidian University, 710071, Xi’an, China

    Jianfeng Ma

  8. National Laboratory of Antennas and Microwave Technology, Xidian University, 710071, Xi’an, Shanxi, P.R. China

    Yong-Chang Jiao

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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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