It is well known, the security of RSA cryptography heavily relies on the inability to effectively factor large integers. Two different approaches are often used to reduce the execution time of the modular exponentiation operation. The motivation of studying high-speed and space-efficient algorithms for modular exponentiation comes from the applications in cryptography such as RSA and Diffie-Hellman key exchange scheme. Fast computation of the modular exponentiations and its designs are very crucial and useful for cryptography. Fast modular exponentiation algorithms are often considered of practical significance in RSA cryptosystem. Since the “signed-digit recoding algorithm” has less occurrence probability of the nonzero digit than binary number representation. Taking this advantage, we can effectively decrease the amount of modular multiplications. By using the technique of recording the common parts in the folded substrings, signed-digit recoding arithmetic technique with minimal Hamming weight can improve the efficiency of the binary algorithm, thus can further decrease the computational complexity of modular exponentiation.