RSA based Digital Signature algorithm is an electronic scheme to ensure the security, authenticity and integrity of an electronic document intended to be used on Internet. Due to the involvement of RSA in signing and signature verification which is based on the series of modular multiplications and modular reductions on very large integers, the RSA based digital signature algorithm become compute-intensive and takes lot of time and energy to execute. A potential solution to this problem is to use the massive parallel powers of the multiprocessors of GPU that can simplify its complex computational part via CUDA programming. This paper presents a faster GPU based pRDSA algorithm which serves the same purpose as the RSA Digital Signature Algorithm but with less computational complexity. Proposed algorithm is an energy efficient parallel version of Digital Signature Algorithm to achieve high performance in the area of network security. It is based on SIMD model of parallel programming and implements repeated square-and-multiply method to compute the digital signature. The conceptual model of pRDSA and its performance have been discussed in this paper.