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arXiv:2306.12347 · Entropy

Improving the Performance of Quantum Cryptography by Using the Encryption of the Error Correction Data

Valeria A. Pastushenko, Dmitry Anatolevich Kronberg

Published Jun 20, 2023• 25 citations
arXivHTMLPDF

Abstract

Security of quantum key distribution (QKD) protocols rely solely on quantum physics laws, namely, on the impossibility to distinguish between non-orthogonal quantum states with absolute certainty. Due to this, a potential eavesdropper cannot extract full information from the states stored in their quantum memory after an attack despite knowing all the information disclosed during classical post-processing stages of QKD. Here, we introduce the idea of encrypting classical communication related to error-correction in order to decrease the amount of information available to the eavesdropper and hence improve the performance of quantum key distribution protocols. We analyze the applicability of the method in the context of additional assumptions concerning the eavesdropper's quantum memory coherence time and discuss the similarity of our proposition and the quantum data locking (QDL) technique.

DOI
10.3390/e25060956

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Security of quantum key distribution (QKD) protocols rely solely on quantum physics laws, namely, on the impossibility to distinguish between non-orthogonal quantum states with absolute certainty. Due to this, a potential eavesdropper cannot extract full information from the states stored in their quantum memory after an attack despite knowing all the information disclosed during classical post-processing stages of QKD. Here, we introduce the idea of encrypting classical communication related to error-correction in order to decrease the amount of information available to the eavesdropper and hence improve the performance of quantum key distribution protocols. We analyze the applicability of the method in the context of additional assumptions concerning the eavesdropper's quantum memory coherence time and discuss the similarity of our proposition and the quantum data locking (QDL) technique.
Quantum cryptography allows for unconditionally secure communication against an eavesdropper endowed with unlimited computational power and perfect technologies, who is only constrained by the laws of physics. We review recent results showing that, under the assumption that the eavesdropper can store quantum information only for a limited time, it is possible to enhance the performance of quantum key distribution in both a quantitative and qualitative fashion. We consider quantum data locking as a cryptographic primitive and discuss secure communication and key distribution protocols. For the case of a lossy optical channel, this yields the theoretical possibility of generating secret key at a constant rate of 1 bit per mode at arbitrarily long communication distances.
We present a technique for proving the security of quantum-key-distribution (QKD) protocols. It is based on direct information-theoretic arguments and thus also applies if no equivalent entanglement purification scheme can be found. Using this technique, we investigate a general class of QKD protocols with one-way classical post-processing. We show that, in order to analyze the full security of these protocols, it suffices to consider collective attacks. Indeed, we give new lower and upper bounds on the secret-key rate which only involve entropies of two-qubit density operators and which are thus easy to compute. As an illustration of our results, we analyze the Bennett-Brassard 1984, the six-state, and the Bennett 1992 protocols with one-way error correction and privacy amplification. Surprisingly, the performance of these protocols is increased if one of the parties adds noise to the measurement data before the error correction. In particular, this additional noise makes the protocols more robust against noise in the quantum channel.
[Shortened abstract:] This thesis investigates the importance of quantum memory in quantum cryptography, concentrating on quantum key distribution schemes. In the hands of an eavesdropper -- a quantum memory is a powerful tool, putting in question the security of quantum cryptography; Classical privacy amplification techniques, used to prove security against less powerful eavesdroppers, might not be effective when the eavesdropper can keep quantum states for a long time. In this work we suggest a possible direction for approaching this problem. We define strong attacks of this type, and show security against them, suggesting that quantum cryptography is secure. We start with a complete analysis regarding the information about a parity bit (since parity bits are used for privacy amplification). We use the results regarding the information on parity bits to prove security against very strong eavesdropping attacks, which uses quantum memories and all classical data (including error correction codes) to attack the final key directly. In the hands of the legitimate users, a quantum memory is also a useful tool. We suggest a new type of quantum key distribution scheme where quantum memories are used instead of quantum channels. This scheme is especially adequate for networks of many users. The use of quantum memory also allows reducing the error rate to improve large scale quantum cryptography, and to enable the legitimate users to work with reasonable error rate.
We introduce an explicit construction for a key distribution protocol in the Quantum Computational Timelock (QCT) security model, where one assumes that computationally secure encryption may only be broken after a time much longer than the coherence time of available quantum memories.Taking advantage of the QCT assumptions, we build a key distribution protocol called HM-QCT from the Hidden Matching problem for which there exists an exponential gap in one-way communication complexity between classical and quantum strategies.We establish that the security of HM-QCT against arbitrary i.i.d. attacks can be reduced to the difficulty of solving the underlying Hidden Matching problem with classical information. Legitimate users, on the other hand, can use quantum communication, which gives them the possibility of sending multiple copies of the same quantum state while retaining an information advantage. This leads to an everlasting secure key distribution scheme over n bosonic modes. Such a level of security is unattainable with purely classical techniques. Remarkably, the scheme remains secure with up to O ( n log ⁡ ( n ) ) input photons for each channel use, extending the functionalities and potentially outperforming QKD rates by several orders of magnitudes.