AST Pre-Processing For The Sliding Window Method Using Genetic Algorithms

Modular exponentiation is a cornerstone operation to several public-key cryptography systems such as the RSA. It is performed using successive modular multiplications. The latter is time consuming for large operands. Accelerating public-key cryptography software or hardware needs reducing the total number of modular multiplication needed. This paper introduces a novel idea based on genetic algorithms for evolving an optimal addition chain that allows one to perform precomputations necessary in the window modular exponentiation methods. The obtained addition chain allows one to perform exponentiation with a minimal number of multiplication and hence implementing efficiently the exponentiation operation. We compare our results with those obtained using the algorithm of Brun.