Speed up RSA’s Decryption Process with Large sub Exponents using Improved CRT

The aim of this paper is to present the improvement of Chinese Remainder Theorem (CRT) to speed up RSA’s decryption process by changing sub exponents and transforming ciphertext in another domain. Although applying CRT with RSA, called CRT-RSA, can be chosen to decrease time in decryption side, computing modular exponentiation still consumes enormous time whenever sub exponents are large. In addition, the proposed method suits to apply with high sub exponents of CRT-RSA because the new sub exponents are smaller. On the other hand, both of them become larger when CRT-RSA’s exponents are small. Therefore, the proposed method cannot be chosen to replace CRT-RSA but it is one of two choices for the implementation. If sub exponents are small, CRTRSA is a better choice to speed up RSA’s decryption. Nevertheless, the proposed method should be selected when sub exponents are large. The experimental results show that the proposed method can finish the process faster than CRT-RSA for both of key generation process and decryption process whenever sub exponents are large. Furthermore, in decryption side, the proposed method is faster than CRT-RSA about 20 – 40%.