Computational Complexity Analyses of Modular Arithmetic for RSA Cryptosystem

Modular arithmetic is fundamental to several public-key cryptography systems such as the RSA encryption system, as well as the most dominant part of the computation performed. The operation is time-consuming for large operands. Many relevant papers about computer security are issued in many reports and journals to describe how to reduce the computational complexities in the cryptosystems. In this paper, we describe the modular arithmetics and some improved algorithms. These algorithms by using binary method, common multiplicand multiplication method (CMM method), signed-digit recoding method, etc. will be depicted respectively. We will analyze and compare the complexity of various algorithms for computing large modular exponentiation.