Addition chains using continued fractions
Journal of Algorithms
Genetic algorithms + data structures = evolution programs (3rd ed.)
Genetic algorithms + data structures = evolution programs (3rd ed.)
Practical genetic algorithms
A method for obtaining digital signatures and public-key cryptosystems
Communications of the ACM
Elliptic Curve Public Key Cryptosystems
Elliptic Curve Public Key Cryptosystems
Using Genetic Algorithms to Solve NP-Complete Problems
Proceedings of the 3rd International Conference on Genetic Algorithms
An Analysis of the Interacting Roles of Population Size and Crossover in Genetic Algorithms
PPSN I Proceedings of the 1st Workshop on Parallel Problem Solving from Nature
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
A simulated annealing algorithm for the problem of minimal addition chains
EPIA'11 Proceedings of the 15th Portugese conference on Progress in artificial intelligence
Hardware for modular exponentiation suitable for smart cards
ICESS'04 Proceedings of the First international conference on Embedded Software and Systems
A mutation-selection algorithm for the problem of minimum brauer chains
MICAI'11 Proceedings of the 10th international conference on Artificial Intelligence: advances in Soft Computing - Volume Part II
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Modular exponentiation is a cornerstone operation to several public-key cryptosystems. It is performed using successive modular multiplications. This operation is time consuming for large operands, which is always the case in cryptography. For software or hardware fast cryptosystems, one needs thus reducing the total number of modular multiplication required. Existing methods attempt to reduce this number by partitioning the exponent in constant or variable size windows. However, these window methods require some pre-computations, which themselves consist of modular exponentiations. In this paper, we exploit genetic algorithms to evolving an optimal addition sequence that allows one to perform the pre-computations in window methods with a minimal number of modular multiplications. Hence we improve the efficiency of modular exponentiation. We compare the evolved addition sequences with those obtained using Brun's algorithm.