Genetic algorithms + data structures = evolution programs (3rd ed.)
Genetic algorithms + data structures = evolution programs (3rd ed.)
A survey of fast exponentiation methods
Journal of Algorithms
Artificial Immune Systems: A New Computational Intelligence Paradigm
Artificial Immune Systems: A New Computational Intelligence Paradigm
Minimal Addition Chain for Efficient Modular Exponentiation Using Genetic Algorithms
IEA/AIE '02 Proceedings of the 15th international conference on Industrial and engineering applications of artificial intelligence and expert systems: developments in applied artificial intelligence
CRYPTO '89 Proceedings of the 9th Annual International Cryptology Conference on Advances in Cryptology
Efficient pre-processing for large window-based modular exponentiation using genetic algorithms
IEA/AIE'2003 Proceedings of the 16th international conference on Developments in applied artificial intelligence
Data-Flow Analysis for MPI Programs
ICPP '06 Proceedings of the 2006 International Conference on Parallel Processing
Parallel Programming in C with MPI and OpenMP
Parallel Programming in C with MPI and OpenMP
Strength Two Covering Arrays Construction Using a SAT Representation
MICAI '08 Proceedings of the 7th Mexican International Conference on Artificial Intelligence: Advances in Artificial Intelligence
Finding optimal addition chains using a genetic algorithm approach
CIS'05 Proceedings of the 2005 international conference on Computational Intelligence and Security - Volume Part I
Load balanced parallel simulated annealing on a cluster of SMP nodes
Euro-Par'06 Proceedings of the 12th international conference on Parallel Processing
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Cryptosystems require the computation of modular exponentiation, this operation is related to the problem of finding a minimal addition chain. However, obtaining the shortest addition chain of length n is an NP-Complete problem whose search space size is proportional to n!. This paper introduces a novel idea to compute the minimal addition chain problem, through an implementation of a Simulated Annealing (SA) algorithm. The representation used in our SA is based on Factorial Number System (FNS). We use a fine-tuning process to get the best performance of SA using a Covering Array (CA), Diophantine Equation solutions (DE) and Neighborhood Functions (NF). We present a parallel implementation to execute the fine-tuning process using a Message Passing Interface (MPI) and the Single Program Multiple Data (SPMD) model. These features, allowed us to calculate minimal addition chains for benchmarks considered difficult in very short time, the experimental results show that this approach is a viable alternative to solve the solution of the minimal addition chain problem.