Entropy-Driven Privacy Amplification with Adaptive Chaotic Statistical Conditioning for Quantum Key Distribution

Privacy amplification is the final and most critical stage of quantum key distribution (QKD), where any residual correlation between the reconciled key and an eavesdropper must be eliminated. In practical systems, however, the corrected key may deviate from ideal uniformity due to channel asymmetries and finite-size effects, limiting the effectiveness of conventional hash-based methods. This work presents an entropy-driven privacy amplification framework that combines deterministic matrix-based entropy equalization with adaptive chaotic statistical conditioning. The reconciled key is first transformed into a structured decimal matrix, where controlled numerical diversification enables entropy evaluation across row- and column-wise representations. The entropy-dominant component is then mapped to an intermediate binary key. A subsequent stage applies coupled Logistic and Chebyshev maps whose parameters are adaptively tuned by the measured entropy of the intermediate sequence, allowing residual statistical imbalance to be suppressed without fixed parameter selection. The chaotic stage acts as a statistical conditioner and does not replace formal randomness extractors. The simulation results for key lengths ranging from 128 to 1024 bits show that Shannon entropy is greater than 0.999, min-entropy is greater than 0.97, with bit uniformity approaching 0.5. All of the sequences pass standard NIST randomness tests. In comparison with commonly used privacy amplification techniques, the proposed approach exhibits improved entropy stability under biased input conditions while maintaining linear computational complexity, making it suitable for practical QKD post-processing.