Towards very fast modular exponentiations using ant colony

Abstract

The performance of public-key cryptosystems is primarily determined by the implementation efficiency of the modular multiplication and exponentiation. As the operands, i.e. the plain text of a message or the cipher (possibly a partially ciphered) text are usually large (1024 bits or more), and in order to improve time requirements of the encryption/decryption operations, it is essential to attempt to minimise the number of modular multiplications performed. In this paper, we exploit the ant colony's principles to engineer a minimal addition chain that allows one to compute modular exponentiations very efficiently. The obtained results are compared to existing heuristics as well as to genetically evolved addition chains, i.e. using genetic algorithms. © 2006 Springer.