The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
A survey of fast exponentiation methods
Journal of Algorithms
A Fast Algorithm for Multiplicative Inversion in GF(2m) Using Normal Basis
IEEE Transactions on Computers
Handbook of Applied Cryptography
Handbook of Applied Cryptography
Multi-objective hybrid PSO using µ-fuzzy dominance
Proceedings of the 9th annual conference on Genetic and evolutionary computation
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
Improving PSO-Based multi-objective optimization using crowding, mutation and ∈-dominance
EMO'05 Proceedings of the Third international conference on Evolutionary Multi-Criterion Optimization
An Artificial Immune System Heuristic for Generating Short Addition Chains
IEEE Transactions on Evolutionary Computation
Addition chain length minimization with evolutionary programming
Proceedings of the 13th annual conference companion on Genetic and evolutionary computation
Interactive visualization applets for modular exponentiation using addition chains
HAIS'10 Proceedings of the 5th international conference on Hybrid Artificial Intelligence Systems - Volume Part II
| Hi-index | 0.00 |
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.