We know modular arithmetic is the most dominant part of the computation which is performed in modern encryption systems and key-exchange scheme. Modular exponentiation is the most important operation in modern public-key cryptosystems. Computational complexity theory is a branch of the mathematical theory of computation in theoretical computer science. The modular exponentiation is composed of repetition of modular multiplications. It is performed by adopting successive modular multiplications. Modular exponentiation is to compute M^E for a positive integer E and modular exponentiation is to compute M^E mod N for positive integers E and N. When the lengths of the operators are at least 512 to 1024 binary representations. In fact, modular exponentiation can be time-consuming and is often the dominant part of the computation in many computer systems. Computation infeasible for restricted time implies to secure the information, therefore, the study of this domain bring a lot attention for modern security experts. In this paper, I will describe some methods, which use some software. Most importantly, I will also detailed analyze the computational complexities for these methods respectively.