Most modern cryptographic protocols, which require a large number of processing steps, are based on modular evaluation. In fact modular arithmetic is the most dominant part of the computation which is performed in cryptographic applications especially for RSA encryption system. The operation is time-consuming for large operands. Therefore, a significant problem is how to reduce the time needed to perform modular arithmetic. These algorithms in the modular arithmetic are binary method, common multiplicand multiplication method, and signed-digit recoding method, addition chain method, and Montgomery algorithm. Most importantly, many relevant computer security papers and reports are issued in many journals to describe how to reduce the computational complexities in the cryptosystems.