This research is relevant in situations where there is the need to speed up the Rivest, Shamir, and Adleman (RSA) encryption process of audio data files that are transmitted or transferred through public channels, as well as when the security protocols involved in the transmission of such data is questionable or when data is being archived on suspicions storage devices locally. The research seeks to aid individuals, organisations or corporate bodies in implementing strategies to ensure a fast and secure way for audio data encryption. The following procedures or methods are used to implement the proposed algorithm. The audio data is obtained and pre-processed. The pre-processed information is then extracted and manipulated. The Residue Number System (RNS), specifically the Chinese Remainder Theorem (CRT)-based approach, is then applied to the RSA cryptographic process, and the reconstruction of data is done. The performance of the proposed scheme was evaluated using different audio files, which was much faster in terms of speed of execution and security than the traditional RSA.