The emergence of the Internet of Things (IoT) represents a significant trend, where integrating IP, data, and wireless technologies onto a single network yields substantial advantages that are both essential and appealing. However, the amalgamation of these entities introduces novel susceptibilities and opportunities for infiltrating IoT networks, thereby necessitating the perpetual advancement of integrated security methodologies. This study investigates the feasibility of utilizing the Rivest–Shamir–Adleman (RSA) method, based on the Miller-Rabin technique, as a stream key generator with five distinct hashing functions to attain robust digital signatures. The RSA encryption method underwent a comprehensive battery of tests to assess its validity, and its encryption efficacy was evaluated through mathematical analysis. This research examines the assessment of digital signatures by utilizing five distinct hash functions in conjunction with RSA keys. Each signature file was assessed based on four tests: entropy, floating frequency, autocorrelation, and histogram analysis. The tests were conducted on a document with a size of 256 bytes. In addition, nine hash algorithms were utilized, namely SHA224, SHA256, SHA384, SHA512, BLAKE2B, BLAKE2S, MD5, MD2, and RIPEMD160. Different algorithms were used for varying key sizes and word counts for hashing. The experiment was repeated 100 times to obtain precise measurements of the average time and entropy. The findings indicate that when implemented with an appropriate key length, RSA exhibits both efficiency and sufficient security to be deployed in IoT networks.