The alternative method to speed up RSA’s decryption process

Abstract

The aim of this paper is to propose the special methods to speed up RSA’ s decryption process. In fact, this method gives the option of selecting the best parameters to recover the plaintext. Assuming that the new integer has a lower Hamming Weight than the private key and is mathematically related to the private key, it will be used as the exponent in the decryption process instead of the private key. Furthermore, this method can be used in conjunction with the Chinese Remainder Theorem (CRT) to determine the best exponents. In addition, a method derived from the Square and Multiplication Algorithm is proposed to compute modular exponentiation in order to reduce computation time. However, this method can be performed when number 1 of the exponent’s binary value is not adjacent to each other. Assuming that the new integers for CRT have the lowest Hamming Weight, the experimental results show that if the proposed integers meet the condition, the proposed method is the best algorithm for completing the task. Furthermore, when 2048 bits of modulus is chosen and compared to CRT, the average time is reduced about 8%. Moreover, three-fourths of the cases require the proposed method with CRT in order to save the most computation costs on the decryption side. As a result, the proposed method is very likely to be chosen to complete the decrypting task.