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Finding Minimal Addition Chains with a Particle Swarm Optimization Algorithm

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MICAI 2009: Advances in Artificial Intelligence (MICAI 2009)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5845))

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Abstract

The addition chains with minimal length are the basic block to the optimal computation of finite field exponentiations. It has very important applications in the areas of error-correcting codes and cryptography. However, obtaining the shortest addition chains for a given exponent is a NP-hard problem. In this work we propose the adaptation of a Particle Swarm Optimization algorithm to deal with this problem. Our proposal is tested on several exponents whose addition chains are considered hard to find. We obtained very promising results.

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Author information

Authors and Affiliations

  1. Center for Computing Research, National Polytechnic Institute (CIC-IPN), Mexico

    Alejandro León-Javier, Nareli Cruz-Cortés, Marco A. Moreno-Armendáriz & Sandra Orantes-Jiménez

Authors
  1. Alejandro León-Javier
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  2. Nareli Cruz-Cortés
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  3. Marco A. Moreno-Armendáriz
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  4. Sandra Orantes-Jiménez
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Editor information

Editors and Affiliations

  1. Centro de Investigación en Matemáticas, AC. (CIMAT), Area de Computación, Calle Jalisco S/N, Mineral de Valenciana, Guanajuato, CP 36250, Guanajuato, México

    Arturo Hernández Aguirre

  2. Ciencias de la Computación, Tecnológico de Monterrey, Campus Estado de México, Carretera al lago de Guadalupe Km 3,5, Col. Margarita Maza de Juárez, Atizapán de Zaragoza,, CP 52926, Estado de México, México

    Raúl Monroy Borja

  3. Instituto Nacional de Astrofísica, Optica y Electrónica (INAOE), Ciencias Computacionales, Luis Enrique Erro No. 1, Santa María Tonantzintla, CP 72840, Puebla, México

    Carlos Alberto Reyes Garciá

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León-Javier, A., Cruz-Cortés, N., Moreno-Armendáriz, M.A., Orantes-Jiménez, S. (2009). Finding Minimal Addition Chains with a Particle Swarm Optimization Algorithm. In: Aguirre, A.H., Borja, R.M., Garciá, C.A.R. (eds) MICAI 2009: Advances in Artificial Intelligence. MICAI 2009. Lecture Notes in Computer Science(), vol 5845. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-05258-3_60

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  • DOI: https://doi.org/10.1007/978-3-642-05258-3_60

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-05257-6

  • Online ISBN: 978-3-642-05258-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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