Efficient Pre-processing for Large Window-Based Modular Exponentiation Using Ant Colony

Abstract

Modular exponentiation is the main operation to RSA-based public-key cryptosystems. It is performed using successive modular multiplications. This operation is time consuming for large operands, which is always the case in cryptography. For software or hardware fast cryptosystems, one needs thus reducing the total number of modular multiplications required. Existing methods attempt to reduce this number by partitioning the exponent in constant or variable size windows. However, these window-based methods require some pre-computations, which themselves consist of modular exponentiations. It is clear that pre-processing needs to be performed efficiently also. In this paper, we exploit the ant colony strategy to finding an optimal addition sequence that allows one to perform the pre-computations in window-based methods with a minimal number of modular multiplications. Hence we improve the efficiency of modular exponentiation. We compare the yielded addition sequences with those obtained using Brun’s algorithm.