QKD Protocols Research Articles

Extended analysis of the Trojan-horse attack in quantum key distribution

The discrete-variable QKD protocols based on BB84 are known to be secure against an eavesdropper, Eve, intercepting the flying qubits and performing any quantum operation on them. However, these protocols may still be vulnerable to side-channel attacks. We investigate the Trojan-Horse side-channel attack where Eve sends her own state into Alice's apparatus and measures the reflected state to estimate the key. We prove that the separable coherent state is optimal for Eve amongst the class of multi-mode Gaussian attack states. We describe how Alice may defend against this by adding thermal noise to the system and give an analytic expression of the resulting secret key rate. We also provide a bound on the secret key rate in the case where Eve may use any separable state, and describe an active defense system based on optical modulators.

Continuous-variable measurement-device-independent quantum key distribution with virtual photon subtraction

The method of improving the performance of continuous-variable quantum key distribution protocols by post-selection has been recently proposed and verified. In continuous-variable measurement-device-independent quantum key distribution (CV-MDI QKD) protocols, the measurement results are obtained from untrusted third party Charlie. There is still not an effective method of improving CV-MDI QKD by the post-selection with untrusted measurement. We propose a method to improve the performance of coherent-state CV-MDI QKD protocol by non-Gaussian post-selection. The non-Gaussian post-selection of transmitted data is equivalent to an ideal photon subtraction on the two-mode squeezed vacuum state, which is favorable to enhance the performance of CV-MDI QKD. In CV-MDI QKD protocol with non-Gaussian post-selection, two users select their own data independently. We demonstrate that the optimal performance of the renovated CV-MDI QKD protocol is obtained with the transmitted data only selected by Alice. By setting appropriate parameters of the non-Gaussian post-selection, the secret key rate and tolerable excess noise are both improved at long transmission distance. The method provides an effective optimization scheme for the application of CV-MDI QKD protocols.

Layered quantum key distribution

We introduce a family of QKD protocols for distributing shared random keys within a network of $n$ users. The advantage of these protocols is that any possible key structure needed within the network, including broadcast keys shared among subsets of users, can be implemented by using a particular multi-partite high-dimensional quantum state. This approach is more efficient in the number of quantum channel uses than conventional quantum key distribution using bipartite links. Additionally, multi-partite high-dimensional quantum states are becoming readily available in quantum photonic labs, making the proposed protocols implementable using current technology.

Loss of information in quantum guessing game

Incompatibility of certain measurements—impossibility of obtaining deterministic outcomes simultaneously—is a well known property of quantum mechanics. This feature can be utilized in many contexts, ranging from Bell inequalities to device dependent QKD protocols. Typically, in these applications the measurements are chosen from a predetermined set based on a classical random variable. One can naturally ask, whether the non-determinism of the outcomes is due to intrinsic hiding property of quantum mechanics, or rather by the fact that classical, incoherent information entered the system via the choice of the measurement. Authors Rozpedek et al (2017 New J. Phys. 19 023038) examined this question for a specific case of two mutually unbiased measurements on systems of different dimensions. They have somewhat surprisingly shown that in case of qubits, if the measurements are chosen coherently with the use of a controlled unitary, outcomes of both measurements can be guessed deterministically. Here we extend their analysis and show that specifically for qubits, measurement result for any set of measurements with any a priori probability distribution can be faithfully guessed by a suitable state preparation and measurement. We also show that up to a small set of specific cases, this is not possible for higher dimensions. This result manifests a deep difference in properties of qubits and higher dimensional systems and suggests that these systems might offer higher security in specific cryptographic protocols. More fundamentally, the results show that the impossibility of predicting a result of a measurement is not caused solely by a loss of coherence between the choice of the measurement and the guessing procedure.

Plug-and-play round-robin differential phase-shift quantum key distribution

The round-robin differential-phase-shift quantum key distribution (RRDPS-QKD) protocol could provide an effective way to estimate the leakage information without monitoring the signal disturbance. Moreover, the self-compensating property of plug-and-play (P&P) setup can eliminate the variations of phase or polarization in QKD procedure. In the paper, we introduce the P&P concept into RRDPS-QKD, and propose a QKD protocol, named P&P RRDPS-QKD protocol, to make the RRDPS-QKD scheme more practical. We analyze the security, and discuss the key generation rate with infinite-intensity decoy state method. The results show that the proposed protocol is a good solution to RRDPS-QKD protocol with untrusted sources. It has a high security and its key generation rate could be as good as the protocol with trusted sources when the average input photon number N is greater than 106. In addition, the proposed protocol has a high noise tolerance in comparison with P&P BB84-QKD protocol.

Finite-size analysis of continuous-variable measurement-device-independent quantum key distribution

We study the impact of the finite-size effect on the continuous-variable measurement-device-independent quantum key distribution (CV-MDI QKD) protocol, mainly considering the finite-size effect on the parameter estimation procedure. The central-limit theorem and maximum likelihood estimation theorem are used to estimate the parameters. We also analyze the relationship between the number of exchanged signals and the optimal modulation variance in the protocol. It is proved that when Charlie's position is close to Bob, the CV-MDI QKD protocol has the farthest transmission distance in the finite-size scenario. Finally, we discuss the impact of finite-size effects related to the practical detection in the CV-MDI QKD protocol. The overall results indicate that the finite-size effect has a great influence on the secret key rate of the CV-MDI QKD protocol and should not be ignored.

Game-theoretic perspective of Ping-Pong protocol

We analyse Ping-Pong protocol from the point of view of a game. The analysis helps us in understanding the different strategies of a sender and an eavesdropper to gain the maximum payoff in the game. The study presented here characterizes strategies that lead to different Nash equilibriums. We further demonstrate the condition for Pareto optimality depending on the parameters used in the game. Moreover, we also analysed LM05 protocol and compared it with PP protocol from the point of view of a generic two-way QKD game with or without entanglement. Our results provide a deeper understanding of general two-way QKD protocols in terms of the security and payoffs of different stakeholders in the protocol.

Design a new protocol for quantum key distribution

Quantum key distribution is the latest advancement in quantum cryptography. There are several QKD protocols like BB84, B92, Ekert91, COW, SARG04, etc. out of which B92 is the Second protocol developed in 1992 based on Heisenberg’s Uncertainty Principle. In this paper we are discussing first about the working of B92 protocol and then proposing a new protocol which is a variation over B92 protocol, second the design of simulation setup is discussed. Object oriented approach is used in the simulation designing of new protocol and B92 protocol.

Practical issues in decoy-state quantum key distribution based on the central limit theorem

Decoy-state quantum key distribution is a standard tool for long-distance quantum communications. An important issue in this field is processing the decoy-state statistics taking into account statistical fluctuations (or "finite-key effects"). In this work, we propose and analyze an option for decoy statistics processing, which is based on the central limit theorem. We discuss such practical issues as an inclusion of the failure probability of the decoy-states statistical estimates in the total failure probability of a QKD protocol and also taking into account the deviations of the binomially distributed random variables used in the estimations from the Gaussian distribution. The results of numerical simulations show that the obtained estimations are quite tight. The proposed technique can be used as a part of post-processing procedures for industrial quantum key distribution systems.

Efficient and Secure Authenticated Quantum Dialogue with Single Photons

A new quantum dialogue (QD) protocol with single photons is proposed. In the proposed protocol, two participants perform different operations according to their own secret information. A key previously shared by the two communicants through a secure QKD protocol is used to control not only the encoding operation of the dialogue initiator but also security detection. The analysis on efficiency demonstrates the proposed protocol is more efficient.

Robustness of reference-frame-independent quantum key distribution against the relative motion of the reference frames

Reference-Frame-Independent quantum key distribution (RFI-QKD) is known to be robust against slowly varying reference frames. However, other QKD protocols such as BB84 can also provide secrete keys if the speed of the relative motion of the reference frames is slow enough. While there has been a few studies to quantify the speed of the relative motion of the reference frames in RFI-QKD, it is not yet clear if RFI-QKD provides better performance than other QKD protocols under this condition. Here, we analyze and compare the security of RFI-QKD and BB84 protocol in the presence of the relative motion of the reference frames. In order to compare their security in real world implementation, we also consider the QKD protocols with decoy state method. Our analysis shows that RFI-QKD provides more robustness than BB84 protocol against the relative motion of the reference frames.

Quantum key distribution with mismatched measurements over arbitrary channels

In this paper, we derive key-rate expressions for different quantum key distribution protocols. Our key-rate equations utilize multiple channel statistics, including those gathered from mismatched measurement bases - i.e., when Alice and Bob choose incompatible bases. In particular, we will consider an Extended B92 and a two-way semi-quantum protocol. For both these protocols, we demonstrate that their tolerance to noise is higher than previously thought - in fact, we will show the semi-quantum protocol can actually tolerate the same noise level as the fully quantum BB84 protocol. Along the way, we will also consider an optimal QKD protocol for various quantum channels. Finally, all the key-rate expressions which we derive in this paper are applicable to any arbitrary, not necessarily symmetric, quantum channel.

Round-robin differential-phase-shift quantum key distribution with a passive decoy state method

Recently, a new type of protocol named Round-robin differential-phase-shift quantum key distribution (RRDPS QKD) was proposed, where the security can be guaranteed without monitoring conventional signal disturbances. The active decoy state method can be used in this protocol to overcome the imperfections of the source. But, it may lead to side channel attacks and break the security of QKD systems. In this paper, we apply the passive decoy state method to the RRDPS QKD protocol. Not only can the more environment disturbance be tolerated, but in addition it can overcome side channel attacks on the sources. Importantly, we derive a new key generation rate formula for our RRDPS protocol using passive decoy states and enhance the key generation rate. We also compare the performance of our RRDPS QKD to that using the active decoy state method and the original RRDPS QKD without any decoy states. From numerical simulations, the performance improvement of the RRDPS QKD by our new method can be seen.

Proof of Security of a Semi-Device-Independent Quantum Key Distribution Protocol**Supported by the National Basic Research Program of China under Grant No 2013CB338002, and the National Natural Science Foundation of China under Grant Nos 11304397 and 61505261.

Semi-device-independent quantum key distribution (SDI-QKD) has been proposed by applying the quantum dimension correlation, and the security relies on the violation of quantum dimension witness inequalities. We prove the security of the SDI-QKD protocol under the depolarization channel by considering the quantum dimension witness inequalities and minimum entropy and the specific process of the QKD protocol, combining with a four-quantum-state preparation and three measurement bases. We also provide the relationship between the dimension witness value, the error rate and the security key rate by the numerical simulation.

Floodlight quantum key distribution: Demonstrating a framework for high-rate secure communication

Floodlight quantum key distribution (FL-QKD) is a radically different QKD paradigm that can achieve Gbit/s secret-key rates over metropolitan area distances without multiplexing [Phys. Rev. A 94, 012322 (2016)]. It is a two-way protocol that transmits many photons per bit duration and employs a high-gain optical amplifier, neither of which can be utilized by existing QKD protocols to mitigate channel loss. FL-QKD uses an optical bandwidth that is substantially larger than the modulation rate and performs decoding with a unique broadband homodyne receiver. Essential to FL-QKD is Alice's injection of photons from a photon-pair source--in addition to the light used for key generation--into the light she sends to Bob. This injection enables Alice and Bob to quantify Eve's intrusion and thus secure FL-QKD against collective attacks. Our proof-of-concept experiment included 10 dB propagation loss--equivalent to 50 km of low-loss fiber--and achieved a 55 Mbit/s secret-key rate (SKR) for a 100 Mbit/s modulation rate, as compared to the state-of-the-art system's 1 Mbit/s SKR for a 1 Gbit/s modulation rate [Opt. Express 21, 24550-24565 (2013)], representing ~500-fold and ~50-fold improvements in secret-key efficiency (SKE) (bits per channel use) and SKR (bits per second), respectively.

Valid conditions of the reference-frame-independent quantum key distribution

Reference-frame-independent quantum key distribution (RFI QKD) has been experimental demonstrated to be robust for slowly varying reference frames. However, the protocol fails when reference frame varies rapidly. Furthermore, the rigorous definition of ``slowly varying'' is still not clear. Here we analyze the relationship of the related parameters and show how to adjust these parameters to make RFI QKD to be valid. This work provides a clear valid condition for the RFI QKD protocol and opens a way for researchers and users to handle the RFI QKD process practically.

Finite-key security analysis for multilevel quantum key distribution

We present a detailed security analysis of a d-dimensional quantum key distribution protocol based on two and three mutually unbiased bases (MUBs) both in an asymptotic and finite-key-length scenario. The finite secret key rates (in bits per detected photon) are calculated as a function of the length of the sifted key by (i) generalizing the uncertainly relation-based insight from BB84 to any d-level 2-MUB QKD protocol and (ii) by adopting recent advances in the second-order asymptotics for finite block length quantum coding (for both d-level 2- and 3-MUB QKD protocols). Since the finite and asymptotic secret key rates increase with d and the number of MUBs (together with the tolerable threshold) such QKD schemes could in principle offer an important advantage over BB84. We discuss the possibility of an experimental realization of the 3-MUB QKD protocol with the orbital angular momentum degrees of freedom of photons.

Trojan Horse Attack Free Fault-Tolerant Quantum Key Distribution Protocols Using GHZ States

Recently, Yang and Hwang (Quantum Inf. Process. 13(3): 781–794, 19) proposed two fault-tolerant QKD protocols based on their proposed coding functions for resisting the collective noise, and their QKD protocols are free from Trojan horse attack without employing any specific detecting devices (e.g., photon number splitter (PNS) and wavelength filter). By using four-particle Greenberger-Horne-Zeilinger (GHZ) state and four-particle GHZ-like state in their proposed coding functions, Yang and Hwang’s QKD protocols can resist each kind of the collective noise–collective-dephasing noise, collective-rotation noise. However, their proposed coding function can be improved by the utilization of three-particle GHZ state (three-particle GHZ-like state) instead of four-particle GHZ state (four-particle GHZ-like state) that will eventually reduce the consumption of the qubits. As a result, this study proposed the improved version of Yang and Hwang’s coding functions to enhance the qubit efficiency of their schemes from 20 % to 22 %.

Non-Gaussian postselection and virtual photon subtraction in continuous-variable quantum key distribution

Photon subtraction can enhance the performance of continuous-variable quantum key distribution (CV QKD). However, the enhancement effect will be reduced by the imperfections of practical devices, especially the limited efficiency of a single-photon detector. In this paper, we propose a non-Gaussian postselection method to emulate the photon substraction used in coherent-state CV QKD protocols. The virtual photon subtraction not only can avoid the complexity and imperfections of a practical photon-subtraction operation, which extends the secure transmission distance as the ideal case does, but also can be adjusted flexibly according to the channel parameters to optimize the performance. Furthermore, our preliminary tests on the information reconciliation suggest that in the low signal-to-noise ratio regime, the performance of reconciliating the postselected non-Gaussian data is better than that of the Gaussian data, which implies the feasibility of implementing this method practically.

E91 QKD protocol for authentication in online banking systems

Online banking is a new industry which allows people to interact with their banking accounts via the internet from virtually anywhere in the world. In this system, a strong security system is used but sometimes it is not so much effective. Security of the overall online banking system is reduced to that of the classical approach used for authentication, which could be merely computationally secure rather than unconditionally secure. Thus, for the authentication purpose the concept of quantum cryptography comes into the picture. When quantum cryptography enters widespread public use it will only protect data in transit across public networks. But we are using this quantum cryptography for enhancing the authentication process for user authentication in online banking system. The use of E91 protocol in the authentication does give unconditional security that is what we are going to discuss in this paper. The ultimate goal is to make online banking systems more reliable, integrate it with E91 protocol for the user authentication.