Hybrid quantum–chaotic key expansion enhances QKD rates using the Lorenz system

Quantum key distribution (QKD) provides a foundation for information-theoretic security based on quantum mechanics, yet its practical deployment is often constrained by intrinsically low secure key generation rates, particularly in high-bandwidth or low-latency settings. This work introduces a hybrid cryptographic technique that integrates conventional QKD with deterministic chaos, modeled using the Lorenz attractor, to provide a software-based enhancement of the effective key expansion rate. From a short 20-bit QKD seed, the system generates long bitstreams within milliseconds; although these streams exhibit high empirical randomness, their fundamental entropy remains bounded by the seed, consistent with standard cryptographic principles. The method employs the exponential divergence of chaotic trajectories, such that even minute uncertainties in an adversary's estimate of the initial state lead to rapid desynchronization and, as established in Appendix A, an exponential decay of Eve's mutual information with respect to the expanded key. Simulation results confirm this theoretical behavior and demonstrate an effective rate amplification exceeding two orders of magnitude over the baseline QKD seed rate. The proposed chaotic expansion operates entirely in software and requires no modifications to existing QKD hardware, offering a practical pathway to enhance throughput for applications ranging from secure video communication to low-latency IoT and edge-computing environments.