Quantum cryptographic dynamics: modeling cryptosystems via entropy operators Randy Kuang* [1]

https://www.academia.edu/3064-979X/2/3/10.20935/AcadQuant7841 This paper introduces Quantum Cryptographic Dynamics (QCD), a novel theoretical framework that models cryptographic processes through the lens of entropy injection and ejection. Drawing inspiration from classical mechanics, QCD establishes three fundamental laws: the Entropy Inertial Law (conservation of entropy in isolated systems), the Entropy Evolution Law (transformation of entropy via injection operators), and the Entropy Redistribution Law (reversibility through ejection operators). Applying these principles, we provide a unified, entropy-centric interpretation of classical and quantum cryptographic schemes, including symmetric-key systems, public-key protocols, and post-quantum cryptography (PQC) algorithms such as Learning With Errors (LWE), Kyber, and Homomorphic Polynomial Public Key (HPPK). By shifting the focus from computational hardness assumptions to the fundamental dynamics of entropy manipulation, QCD offers new insights into the security foundations of these cryptographic primitives. Furthermore, we reinterpret the Quantum Permutation Pad Random Number Generator (QPP-RNG) within the QCD framework. QPP-RNG is modeled as an entropy-driven process that harnesses system jitter to generate unpredictable random numbers, which in turn fuel PQC schemes like Kyber and HPPK for quantum-secure key establishment, forming a self-sustained quantum-secure eco-cryptosystem. This framework provides a rigorous approach to security analysis, unifying cryptographic security models across classical, quantum, and post-quantum domains. QCD establishes a robust foundation for designing quantum-resistant cryptographic primitives and assessing the fundamental security properties of cryptographic systems.