One of the general problems in modern digital society is undoubtedly the information security topic. It is critical to ensure the security of information transferred, processed, and stored throughout digital channels. Among this information, digital images draw attention in terms of frequency of use in digital channels. In this study, a new image encryption algorithm is proposed to address the security problems of digital images. The aspect that differentiates the proposed algorithm from thousands of image encryption algorithms in the literature is that it is designed within the framework of the provable security design principle. The provable security design approach has ensured that the proposed algorithm is theoretically secure with mathematical proof techniques. In addition to addressing the proposed architecture security concerns, the hybrid random number generator used as the key generator constitutes another unique aspect. This generator, which was designed using chaotic systems, physical unclonable functions, and optimization algorithms, stands out as the innovative aspect of the study. The statistical randomness properties of the proposed random number generator were tested using the NIST SP 800-22 Statistical Test Suite. Successful results were obtained for 15 tests in the test package. In addition, the success of these outputs was tested on a new image encryption algorithm. The security of the proposed algorithm was tested from different angles using various experimental analyzes and a 12-step provable security analysis roadmap. Successful analysis results and performance measurements indicate that the proposed cryptographic components can be used in many information security applications and many future designs.
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