CEC'09 Proceedings of the Eleventh conference on Congress on Evolutionary Computation
Finding Minimal Addition Chains with a Particle Swarm Optimization Algorithm
MICAI '09 Proceedings of the 8th Mexican International Conference on Artificial Intelligence
Dynamical immunological surveillance for network danger evaluation model
WiCOM'09 Proceedings of the 5th International Conference on Wireless communications, networking and mobile computing
Designing a code generator for pairing based cryptographic functions
Pairing'10 Proceedings of the 4th international conference on Pairing-based cryptography
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
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This paper deals with the optimal computation of finite field exponentiation, which is a well-studied problem with many important applications in the areas of error-correcting codes and cryptography. It has been shown that the optimal computation of finite field exponentiation is a problem which is closely related to finding a suitable addition chain with the shortest possible length. However, it is also known that obtaining the shortest addition chain for a given arbitrary exponent is an NP-hard problem. As a consequence, heuristics are an obvious choice to compute field exponentiation with a semi-optimal number of underlying arithmetic operations. In this paper, we propose the use of an artificial immune system to tackle this problem. Particularly, we study the problem of finding both the shortest addition chains for exponents e with moderate size (i.e., with a length of less than 20 bits), and for the huge exponents typically adopted in cryptographic applications, (i.e., in the range from 128 to 2048 bits).