Abstract-Due to the ever-increasing computing capability of high performance computers today, in order to protect encrypted data from being cracked, the bit number used in RSA, a common and practicable public-key cryptosystem, is also getting longer, resulting in increasing operation time spent in executing the RSA algorithm. We also note that while the development of CPU has reached limits, the graphics processing unit (GPU), a highly parallel programmable processor, has become an integral part of today's mainstream computing systems. Therefore, it is a savvy choice to take advantage of GPU computing to accelerate computation of the RSA algorithm and enhance its applicability as well. After analyzing the RSA algorithm, we find that big number operations consume most parts of computing resources. As the benefit acquired from combining Montgomery with GPU-based parallel methods is not high enough, we further introduce the Fourier transform and Newton's method to design a new parallel algorithm to accelerate the computation of big numbers
