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Finite-key security analysis of quantum cryptographic protocols

Weilong Wang

Published Jan 1, 2019• 0 citations
OpenAlex

Abstract

We will analyse the security of practical Quantum Key Distribution (QKD) protocols based on Weak Coherent Pulses (WCP) or entangled states in the finite-key regime. Such analysis will take into account the typical imperfections that are presented both in the transmitter and receiver of the experimental realisations. The goal is to achieve tight finite-key security bounds for both the secret key rate and distance that can be achieved with practical QKD systems.

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We will analyse the security of practical Quantum Key Distribution (QKD) protocols based on Weak Coherent Pulses (WCP) or entangled states in the finite-key regime. Such analysis will take into account the typical imperfections that are presented both in the transmitter and receiver of the experimental realisations. The goal is to achieve tight finite-key security bounds for both the secret key rate and distance that can be achieved with practical QKD systems.

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We will analyse the security of practical Quantum Key Distribution (QKD) protocols based on Weak Coherent Pulses (WCP) or entangled states in the finite-key regime. Such analysis will take into account the typical imperfections that are presented both in the transmitter and receiver of the experimental realisations. The goal is to achieve tight finite-key security bounds for both the secret key rate and distance that can be achieved with practical QKD systems.
Quantum key distribution (QKD) allows two distant parties to share a secret key and realizes a communication with information-theoretic security by combining it with one-time-pad encryption.Since the Bennett-Brassard 1984 (BB84) protocol was proposed, a large number of researches on QKD have been conducted from both aspects of theory and implementations.For implementations of QKD, weak coherent pulses (WCP) are heavily used as optical signals because they are easily generated by typical lasers and attenuators.The security for QKD with WCP has been also studied along the development of the implementations.In this thesis, the security analysis of the QKD with WCP is considered and further developed from two aspects.First, the security of the differential-quadrature-phase-shift (DQPS) protocol is proved.The DQPS protocol has essentially the same set up as the phase-encoding BB84 (PE-BB84) protocol, which is one of the most frequently demonstrated protocols.Since the known proof techniques for the BB84 protocol is not directly applicable, a modified approach is developed which is suitable for the DQPS protocol.As a result, the advantage of the DQPS protocol in the key generation rate over the PE-BB84 protocol is shown in the asymptotic limit where the size of communication data is assumed to be infinite.Second, a new method for security analysis with finite-key size is proposed as a suitable method for QKD protocols using WCP.Differently from the current method based on simple random sampling, the proposed method relies on Bernoulli sampling, which is associated with binomial distribution.The security of the BB84 protocol is proved by using the Bernoulli-sampling method, enabling a simpler analysis with a smaller number of parameters to be estimated compared to the method with simple random sampling.The required number of detected signals to generate a secret key is shown to be smaller than 10 4 , which is drastic improvement from the number ∼ 10 7 obtained in the previous result.The proposed method is also applied to the DQPS protocol, and its advantage over the PE-BB84 protocol is certified even in the finite-key regime.i
In recent years, the gap between theory and practice in quantum key distribution (QKD) has been significantly narrowed, particularly for QKD systems with arbitrarily flawed optical receivers. The status for QKD systems with imperfect light sources is however less satisfactory, in the sense that the resulting secure key rates are often overly dependent on the quality of state preparation. This is especially the case when the channel loss is high. Very recently, to overcome this limitation, Tamaki et al proposed a QKD protocol based on the so-called 'rejected data analysis', and showed that its security—in the limit of infinitely long keys—is almost independent of any encoding flaw in the qubit space, being this protocol compatible with the decoy state method. Here, as a step towards practical QKD, we show that a similar conclusion is reached in the finite-key regime, even when the intensity of the light source is unstable. More concretely, we derive security bounds for a wide class of realistic light sources and show that the bounds are also efficient in the presence of high channel loss. Our results strongly suggest the feasibility of long distance provably secure communication with imperfect light sources.
Decoy-state quantum key distribution (QKD) is the most widely adopted approach for overcoming the limitations of imperfect single-photon sources. However, existing security proofs typically either neglect important device imperfections or rely on assumptions that are difficult to justify in realistic high-speed implementations, such as the independent and identically distributed nature of the emitted signals. In this work, we combine and extend several recent theoretical advances to provide a comprehensive analytical finite-key security proof for decoy-state QKD that simultaneously incorporates multiple practically relevant transmitter and receiver imperfections, including state-preparation flaws, bit and basis side-channel leakage and correlations, setting-independent intensity fluctuations, and detection-efficiency mismatches.
The main goal of this research project is to analyse the security of practical implementations of discrete-variable QKD systems. While it is true that in theory QKD can offer unconditional security based on the laws of physics, in practice, however, at the moment it does not, because typical security proofs of QKD include assumptions that are not actually met by current implementations, as they usually ignore many experimental device imperfections. This means that these proofs cannot be applied to practical realisations because real devices behave differently from the theoretical models that are assumed in the proofs. This project aims to fill in this big gap between the theory and the practice of QKD by developing efficient security proof methods for the finite sample-size setting scenario that can include typical devices’ flaws to be applied to QKD experiments, particularly to decoy-state-based QKD platforms.
Quantum key distribution (QKD) promises information-theoretic security based on quantum mechanics and idealized device models. Practical implementations, however, deviate from these models due to unavoidable device imperfections, and existing security proofs fall short of capturing the complexity of real-world systems. Here we introduce a versatile numerical finite-key security framework valid against general coherent attacks and applicable to a broad class of practical QKD setups. It accommodates most relevant imperfections at both transmitter and receiver, including non-independent-and-identically-distributed (non-IID) signals arising in high-speed QKD systems due to the limited bandwidth of optical modulators, while requiring only partial characterization of the apparatuses. We demonstrate the power of our framework by proving the security of a realistic decoy-state QKD implementation with laser sources, providing a practical route towards rigorous security certification of real-world QKD setups.