Abstract 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.
Abstract 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.
Quantum Key Distribution (QKD) protocols typically involve two separate steps of error-verification and privacy amplification. Both steps involve the application of a hash function sampled from a suitable hash family to classical data. A potentially simpler alternative is to implement a single-step hashing procedure, announce and compare a fixed number of bits of its output for error-verification, and retain the remaining bits as the final output key. This reduces the complexity of classical postprocessing, the amount of classical communication, and the amount of randomness needed in the protocol. While this construction has appeared in the literature, a suitable mathematical justification is lacking. In this work, we show that the security of such protocols, under certain simple conditions, follows from a slightly modified notion of secrecy of the protocol without the final error-verification step. In particular, we show that for most entropy-based proofs, the combined protocol can be implemented with no change to the key rate, and a minor change to the security parameter.
From the past few years, the rapid growth in quantum computing and large-scale data systems has created an important need for advanced encryption techniques that withstand quantum-level attacks. However, traditional cryptographic systems are becoming increasingly vulnerable, particularly in big-data environments. To overcome this limitation, this research proposes a secure framework for big data encryption namely Quantum-Chaotic Key-Based Encryption System (QC-KES), which combines quantum randomness and chaos theory to make highly secure encryption keys. Therefore, the methodology begins by producing a quantum random seed utilizing Quantum Random Number Generation (QRNG). It is then enhanced through a chaotic logistic map to generate unpredictable key sequences that are securely shared using Quantum Key Distribution (QKD). Subsequently, quantum optical elements are tuned based on the key sequence to encrypt data at the hardware level. Moreover, Quantum Error Correction (QEC) confirms the signal integrity, while the data are encrypted, transmitted, and later decrypted by the shared key. This system improves key security, accuracy, and resistance to quantum-based threats. Finally, the proposed QC-KES obtained better results in entropy (8.000%) and avalanche effect (52.5 bits) when compared the existing Advanced Encryption Standard (AES) model.
In a quantum key distribution (QKD) system, privacy amplification (PA) is an essential procedure that can effectively eliminate the leaked information to an eavesdropper and distill a secret key. The processing speed of the PA algorithm inevitably affects the final key rate of the QKD system. We propose a high-speed PA algorithm based on field-programmable gate array (FPGA), where the matrix multiplications are divided into a number of rhomboid-block operations. The implementation of the PA reduces significantly the required number of FPGA Block RAMs. Meanwhile, it automatically adapts to different lengths of input and output blocks. Finally, we verified the correctness and high-speed of the algorithm when implemented in a Xilinx Virtex-7 FPGA.
We introduce list privacy amplification (LPA), a relaxation of the final step of quantum key distribution (QKD) in which Alice and Bob extract a list of L candidate keys from a raw string correlated with an eavesdropper Eve, with the guarantee that at least one key is perfectly secret while Eve cannot identify which. This parallels list decoding in error-correcting codes: relaxing unique decoding to list decoding increases the decoding radius; analogously, list extraction increases achievable key length beyond the standard quantum leftover hash lemma (QLHL). Within the abstract cryptography framework, we formalise LPA and prove the \emph{Quantum List Leftover Hash Lemma} (QLLHL): an L-list of ℓ-bit keys can be extracted from an n-bit source with smooth min-entropy k iff ℓ≤k+logL−2log(1/ε)−3, yielding a tight additive logL gain over QLHL. This gain arises because the index of the secure key is chosen after hashing and hidden from Eve, effectively contributing logL bits of entropy. Applying QLLHL to BB84-type QKD, a list size L=2αn′ increases the tolerable phase-error threshold from h−1(1−h(eb)) to h−1(1−h(eb)+α), exceeding the standard ≈11% bound for any α>0. We prove tightness via a matching intercept-resend attack, establish composability with Wegman--Carter authentication, and present two constructions: a polynomial inner-product hash over F2m and a Toeplitz-based variant, running in O(nL) and O(nLlogn) time.
Quantum Key Distribution (QKD) utilizes the principles of quantum mechanics for secure communication. Despite its theoretical robustness, practical implementations of QKD systems contain imperfections enabling loopholes. This paper presents a practical validation of the security of a commercially available entanglement-based QKD system. We conduct an attack where we imitate Detector Efficiency Mismatch (DEM) behavior. By investigating the bitstreams over all intermediate key generation steps, we find that Privacy Amplification (PA) restores statistical randomness in the final key, even when intermediate material shows significant bias. However, statistical uniformity does not necessarily imply full information-theoretic security as residual correlations may persist beyond the scope of statistical testing. Our findings indicate that while the manufacturer's anti-tampering mechanisms effectively prevent observable bias, further analysis is required to assess hidden leakage channels.
Abstract Quantum computing threatens classical security protocols such as RSA and ECC, motivating Quantum Key Distribution (QKD) schemes such as BB84 and E91. Over 100\,km optical links, however, channel-noise and selective-measurement attacks can mimic normal degradation, making single-metric monitoring (e.g., QBER alone) unreliable. We propose a hybrid framework that combines an SVM-RBF classifier -- driven by a trilateral feature vector of Quantum Bit Error Rate (QBER), Bell-CHSH S-parameter, and Temporal Shannon Entropy -- with a quantum-perturbed Logistic Map for post-verification session-key expansion. On a 50,000-sample digital-twin dataset (12,500 SAFE / 37,500 BREACHED) under extreme 100\,km channel perturbation, the classifier attains 87.82\% accuracy and an F1-score of 0.9187, outperforming nine baselines including a Compact CNN, under both batched and realistic single-query latency. All three features are individually significant (ANOVA, p<0.001). The expanded session key was evaluated with the NIST SP~800-22 suite at a 105-bit stream length (nine tests, including Binary Matrix Rank): the raw Logistic-Map output passes only 3 of 9 tests, confirming that chaotic expansion alone preserves the residual bias of the quantum seed, whereas applying SHA-256-based cryptographic whitening (per NIST SP~800-90B) to the same material raises the pass rate to 9 of 9, showing that the whitened key meets NIST-grade randomness and is directly deployable for symmetric encryption.