Cryptography has traditionally depended on sophisticated mathematical structures to secure information, with newer advances employing computational approaches to deal with increasing data complexity. This study presents a new method for cryptographic encryption and decryption based on the Taylor series, which is improved by Message Passing Interface (MPI) and Compute Unified Device Architecture (CUDA) parallel computing frameworks. Although secure, traditional cryptographic techniques struggle with computational efficiency as data volumes increase, especially in real-time applications. Our method optimizes encryption procedures to attain greater speed and resource economy by parallelizing the Taylor series. While CUDA uses the computational capability of GPUs to greatly speed up calculations, MPI enables distributed processing over many CPUs. This study opens a new avenue in cryptography by combining state-of-the-art computational methods with mathematical approximation, not only by proving the viability of Taylor series-based encryption but also by demonstrating how parallelization might improve its practical applicability.