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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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
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