Modular exponentiation is fundamental to several public-key cryptography systems such as the RSA encryption system. It is performed using successive modular multiplication. The latter operation is time consuming for large operands. Accelerating public-key cryptography software or hardware needs either optimising the time consumed by a single modular multiplication or reducing the total number of modular multiplication performed or both of them. This paper introduces a novel idea based on genetic algorithms for computing an optimal addition chain that allows us to minimise the number of modular multiplication and hence implementing efficiently the modular exponentiation.