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arXiv:1908.11423 · npj Quantum Information

Simple security proofs for continuous variable quantum key distribution with intensity fluctuating sources

Chenyang Li, Li Qian, Hoi‐Kwong Lo

Published Oct 14, 2021• 14 citations
arXivHTMLPDF

Abstract

Abstract Despite tremendous theoretical and experimental progress in continuous variable (CV) quantum key distribution (QKD), the security has not been rigorously established for most current continuous variable quantum key distribution systems that have imperfections. Among these imperfections, intensity fluctuation is one of the principal problems affecting security. In this paper, we provide simple security proofs for continuous variable quantum key distribution systems with intensity fluctuating sources. Specifically, depending on device assumptions in the source, the imperfect systems are divided into two general cases for security proofs. In the most conservative case, we prove the security based on the tagging idea, which is a main technique for the security proof of discrete variable quantum key distribution. Our proofs are simple to implement without any hardware adjustment for current continuous variable quantum key distribution systems. Also, we show that our proofs are able to provide secure secret keys in the finite-size scenario.

DOI
10.1038/s41534-021-00482-3

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Abstract Despite tremendous theoretical and experimental progress in continuous variable (CV) quantum key distribution (QKD), the security has not been rigorously established for most current continuous variable quantum key distribution systems that have imperfections. Among these imperfections, intensity fluctuation is one of the principal problems affecting security. In this paper, we provide simple security proofs for continuous variable quantum key distribution systems with intensity fluctuating sources. Specifically, depending on device assumptions in the source, the imperfect systems are divided into two general cases for security proofs. In the most conservative case, we prove the security based on the tagging idea, which is a main technique for the security proof of discrete variable quantum key distribution. Our proofs are simple to implement without any hardware adjustment for current continuous variable quantum key distribution systems. Also, we show that our proofs are able to provide secure secret keys in the finite-size scenario.
Despite tremendous theoretical and experimental progress in continuous variable (CV) quantum key distribution (QKD), its security has not been rigorously established for practical systems with multiple imperfections. The idea of tagging is widely used in security proofs of discrete variable quantum key distribution with imperfect devices. In this paper, we generalize the tagging idea from discrete variable to continuous variable. Based on untagged signals, we prove the security of the imperfect quantum key distribution system in the most conservative case. By introducing a generic imperfection model, we can evaluate and further incorporate multiple imperfections in the different stages such as modulation, channel and detection. Finally, with this generic model and tagging idea, we can prove the security of continuous variable key distribution system with multiple imperfections. Our case study shows our proofs are able to provide secure keys in the presence of both modulation and detection flaws.
Abstract Two-way continuous-variable quantum key distribution protocol, where the parties make a double use of the quantum channel, shows the general superadditivity in the security thresholds, which are proven to be higher than that of the classical one-way protocol. However, all existing security proofs for two-way protocols assume perfect source devices or a trusted source noise, which is hard to ensure in a practical system. In this paper, the effects of multiple source fluctuations on the security of the two-way protocol are proposed, where Eve may have access to the intensity fluctuation information with an arbitrary random distribution. This work is comprehensive of several practical scenarios, encompassing both ON and OFF configurations, with and without the assumption that trusted users can access the fluctuation information. The analysis shows that when the users have no fluctuation information, the intensity fluctuation effect in the ON configuration should be modeled as an additional thermal noise rather than being described by a beam splitter model as in the general one-way protocol. In addition, this untrusted noise is only related to the intensity fluctuation variance but has no relation to its distribution. Finally, the tagging idea is applied to the two-way protocol to obtain a conservative secure key.
Quantum key distribution (QKD) is a method that enables two parties separated by distance to share a secret data string. QKD is based on the principles of quantum mechanics and offers information-theoretical security, making it a strong contender for the next generation of cryptography. However, the use of imperfect devices can lead to vulnerabilities and potential quantum hacking schemes. It is crucial to address these imperfections and restore the security of QKD, especially for individuals who use realistic devices for secure communication. QKD can be categorized into two types based on key encoding methods: discrete-variable (DV) QKD and continuous-variable (CV) QKD. It can also be classified based on the transmission medium: fiber-based QKD, free-space-based QKD, and chip-based QKD. This thesis focuses on chip-based DVQKD and fiber-based CVQKD. In the first part, we study the chip-based DVQKD system in the presence of phase-and polarization-dependent loss. We develop innovative methods to restore the security and improve the key rate. The solution is practical, requiring no hardware modifications, and has been adopted by other groups. The second part focuses on fiber-based CVQKD systems that use intensity fluctuating sources. We establish the security by incorporating the concept from DVQKD. Our proposed techniques are practical and do not require any hardware adjustments for existing CVQKD systems. Lastly, we present a general framework for passive CVQKD. Our proposed passive protocol offers a one-time solution to eliminate all potential side channels or imperfections in the source. Interestingly, we discover that the passive source is an excellent choice for the discrete-modulated CVQKD protocol, since the passive protocol offers the same key rate as its active counterpart, while removing all modulator side channels that have plagued the active ones. To sum up, this thesis introduces novel techniques and practical solutions to address imperfections in source devices in different QKD systems. We also propose a passive protocol that can handle all loopholes in source devices in a one-time process. We anticipate that this thesis will facilitate significant advancements in chip-based and fiber-based QKD implementations in the future.
Abstract A quantum key distribution (QKD) system must fulfill the requirement of universal composability to ensure that any cryptographic application (using the QKD system) is also secure. Furthermore, the theoretical proof responsible for security analysis and key generation should cater to the number N of the distributed quantum states being finite in practice. Continuous-variable (CV) QKD based on coherent states, despite being a suitable candidate for integration in the telecom infrastructure, has so far been unable to demonstrate composability as existing proofs require a rather large N for successful key generation. Here we report a Gaussian-modulated coherent state CVQKD system that is able to overcome these challenges and can generate composable keys secure against collective attacks with N ≈ 2 × 10 8 coherent states. With this advance, possible due to improvements to the security proof and a fast, yet low-noise and highly stable system operation, CVQKD implementations take a significant step towards their discrete-variable counterparts in practicality, performance, and security.
As quantum key distribution becomes a mature technology, it appears clearly that some assumptions made in the security proofs cannot be justified in practical implementations. This might open the door to possible side-channel attacks. We examine several discrepancies between theoretical models and experimental setups in the case of continuous-variable quantum key distribution. We study in particular the impact of an imperfect modulation on the security of Gaussian protocols and show that approximating the theoretical Gaussian modulation with a discrete one is sufficient in practice. We also address the issue of properly calibrating the detection setup and in particular the value of the shot noise. Finally, we consider the influence of phase noise in the preparation stage of the protocol and argue that taking this noise into account can improve the secret key rate because this source of noise is not controlled by the eavesdropper.
In theory, quantum key distribution (QKD) offers information-theoretic security. In practice, however, it does not due to the discrepancies between the assumptions used in the security proofs and the behavior of the real apparatuses. Recent years have witnessed a tremendous effort to fill the gap, but the treatment of correlations among pulses has remained a major elusive problem. Here, we close this gap by introducing a simple yet general method to prove the security of QKD with arbitrarily long-range pulse correlations. Our method is compatible with those security proofs that accommodate all the other typical device imperfections, thus paving the way toward achieving implementation security in QKD with arbitrary flawed devices. Moreover, we introduce a new framework for security proofs, which we call the reference technique. This framework includes existing security proofs as special cases, and it can be widely applied to a number of QKD protocols.