Finding minimal addition chains using ant colony

Abstract

Modular exponentiation is one of the most important operations in the almost all nowadays cryptosystems. It is performed using a series of modular multiplications. The latter operation is time consuming for large operands, which always the case in cryptography. Hence Accelerating public-key cryptography software or hardware needs either optimising the time consumed by a single modular multiplication and/or reducing the total number of modular multiplication required. This paper introduces a novel idea based on the principles of ant colony for finding a minimal addition chain that allows us to reduce the number of modular multiplication so that modular exponentiation can be implemented very efficently. © Springer-Verlag Berlin Heidelberg 2004.