Chaotic Real Number Generator with Quantum Wave Equation

Abstract

Randomness plays a crucial role in numerous applications, with cryptography being one of the most significant areas where its importance is evident. A major challenge in cryptographic applications is designing a reliable key generator that meets stringent security requirements. Existing methods often suffer from predictability and fail to provide robust randomness, necessitating novel mathematical approaches. In this study, we propose an innovative mathematical framework that integrates quantum wave functions with chaotic systems to enhance the unpredictability and security of random number generation. The proposed approach leverages the inherent uncertainty of quantum mechanics and the dynamic behavior of chaos to generate statistically strong random sequences. The analysis results confirm that the proposed generator successfully passes all standard statistical randomness tests, demonstrating its effectiveness in cryptographic applications. Additionally, we present a practical implementation of the proposed method as an image encryption algorithm, showcasing its potential for real-world information security solutions. The findings suggest that this approach can contribute significantly to secure communication systems, financial transactions, and other domains requiring high-level cryptographic security.