A genetic algorithm with a mutation mechanism based on a Gaussian and uniform distribution to minimize addition chains for small exponents

The purpose of this research is to minimize the length of an addition chain. Addition chains are employed to reduce the number of multiplications involved in modular exponentiation in public key cryptographic algorithms, such as RSA. Different heuristic methods have been used to optimize this length for a given exponent e. Among the main related works are: genetic algorithms (GA), evolutionary programming and particle swarm optimization. The related works based on GA have the common characteristic of using a uniform distribution to select the mutation point of a given individual in the population. The method proposed in this work includes a mutation mechanism based on a uniform and/or a Gaussian distribution within the mutation operator of the GA. For small exponents, we found experimentally that a scheme of this type generate results that are at least competitive with those produced by the state-of-the-art.