Continuous-variable quantum secure direct communication with one-time pad

Physical implementations of quantum key distribution (QKD) protocols, like the Bennett-Brassard (BB84), are forced to use attenuated coherent quantum states, because the sources of single photon states are not functional yet for QKD applications. However, when using attenuated coherent states, the relatively high rate of multi-photonic pulses introduces vulnerabilities that can be exploited by the photon number splitting (PNS) attack to brake the quantum key. Some QKD protocols have been developed to be resistant to the PNS attack, like the decoy method, but those define a single photonic gain in the quantum channel. To overcome this limitation, we have developed a new QKD protocol, called ack-QKD, which is resistant to the PNS attack. Even more, it uses attenuated quantum states, but defines two interleaved photonic quantum flows to detect the eavesdropper activity by means of the quantum photonic error gain (QPEG) or the quantum bit error rate (QBER). The physical implementation of the ack-QKD is similar to the well-known BB84 protocol.

This paper presents theoretical analysis of Quantum Bit Error Rate (QBER) for Quantum Key Distribution (QKD) in mobile networks (5G/6G). The considered configuration of the underlying optical fiber network that is available for the establishment of the QKD in multi-site 5G networks assumes that the 5G sites are connected by a single optical fiber. Thus, multiplexing of both quantum and classical channels in a single optical fiber is thus necessary. This, in turn, results in a cross talk between classical and quantum channels, which increases QBER and imposes limitations on the maximum distance that can be reached. The approach followed in this paper provides an estimate of the maximum quantum link budget for the targeted QBER. The results of the analysis show that the QKD solution considered here can be potentially deployed using current Operators’ 5G infrastructures to replace currently used asymmetric key exchange algorithms if needed.

Chapter 6 - Quantum key distribution

Security of the quantum secure direct communication protocol (i.e., the C-S QSDC protocol) recently proposed by Cao and Song [Chin. Phys. Lett. 23 (2006) 290] is analyzed in the case of considerable quantum channel noise. The eavesdropping scheme is presented, which reveals that the C-S QSDC protocol is not secure if the quantum bit error rate (QBER) caused by quantum channel noise is higher than 4.17%. Our eavesdropping scheme induces about 4.17% QBER for those check qubits. However, such QBER can be hidden in the counterpart induced by the noisy quantum channel if the eavesdropper Eve replaces the original noisy channel by an ideal one. Furthermore, if the QBER induced by quantum channel noise is lower than 4.17%, then in the eavesdropping scheme Eve still can eavesdrop part of the secret messages by safely attacking a fraction of the transmitted qubits. Finally, an improvement on the C-S QSDC protocol is put forward.

We propose a multi-mode plug-and-play dual-phase-modulated continuous-variable (CV) quantum key distribution (QKD) protocol where Bob prepares independent and identically distributed dual-phase-modulated coherent states in multiple independent modes and Alice uses a conventional noisy, coherent detector to perform homodyne detection. Benefiting from the plug-and-play configuration, our protocol waives the necessity of propagation of a local oscillator (LO) between trusted parties and generates a real local LO for coherent detection. Therefore, the proposed protocol can effectively against the LO-aimed attacks. Moreover, we obtain enhancement in signal-to-noise ratio thanks to multi-mode coherent states. Simulation results show the performance of our protocol outperforms that of the single-mode plug-and-play dual-phase-modulated CV-QKD protocol. In addition, the performance of the proposed scheme is enhanced with the increased signal modes. Furthermore, we take the finite-size effect and composable security into consideration and thus obtain more practical results than those achieved in the asymptotic limit.

We report here a new side channel attack on a practical continuous-variable (CV) quantum key distribution (QKD) system. Inspired by blinding attack in discrete-variable QKD, we formalize an attack strategy by inserting an external light into a CV QKD system implemented Gaussian-modulated coherent state protocol and show that our attack can compromise its practical security. In this attack, we concern imperfections of a balanced homodyne detector used in CV QKD. According to our analysis, if one inserts an external light into Bob’s signal port, due to the imperfect subtraction from the homodyne detector, the leakage of the external light contributes a displacement on the homodyne signal which causes detector electronics saturation. In consequence, Bob’s quadrature measurement is not linear with the quadrature sent by Alice. By considering such vulnerability, a potential Eve can launch a full intercept-resend attack meanwhile she inserts an external light into Bob’s signal port. By selecting proper properties of the external light, Eve actively controls the induced displacement value from the inserted light which results saturation of homodyne detection. In consequence, Eve can bias the excess noise due to the intercept-resend attack and the external light, such that Alice and Bob believe their excess noise estimation is below the null key threshold and they can still share a secret key. Our attack shows that the detector loopholes also exist in CV QKD, and it seems influence all the CV QKD systems using homodyne detection, since all the practical detectors have finite detection range.

Quantum key distribution (QKD) is a cornerstone of secure communication in the quantum era, yet most existing protocols are designed for point-to-point transmission, limiting their scalability in networked environments. In this work, we introduce Loop-Back QKD, a novel QKD protocol that supports both two-party linear configurations and scalable multiuser ring topologies. By leveraging a structured turn-based mechanism and bidirectional pulse propagation, the protocol enables efficient key distribution while reducing the quantum bit error rate (QBER) through a multi-pulse approach. Unlike trusted-node QKD networks, Loop-Back QKD eliminates intermediate-node vulnerabilities, as secret keys are never processed by intermediate nodes. Furthermore, unlike Measurement-Device-Independent (MDI-QKD) and Twin-Field QKD (TF-QKD), which require complex entanglement-based setups, Loop-Back QKD relies solely on direct polarization transformations, reducing vulnerability to side-channel attacks and practical implementation challenges. Additionally, our analysis indicates that multi-pulse Loop-Back QKD can tolerate higher QBER thresholds. However, this increased robustness comes at the cost of a lower key rate efficiency compared to standard QKD schemes. This design choice enhances its robustness against real-world adversarial threats, making it a strong candidate for secure multiuser communication in local and metropolitan-scale quantum networks.

To establish a secure and high-bandwidth communication link between the gateway node and the central node in the internet of underwater things (IoUwT), it is meaningful to introduce quantum key distribution (QKD) protocols into underwater wireless optical communication (UWOC) systems. However, the line-of-sight (LOS) requirement for photon transmission will pose an inevitable challenge to the QKD-based UWOC system. In this work, an optical intelligent reflecting surface (OIRS) array mounted on an autonomous underwater vehicle (AUV) is utilized for the first time to alleviate the LOS blockage and enable more reliable underwater wireless optical quantum link for both discrete-variable quantum key distribution (DV-QKD) and continuous-variable quantum key distribution (CV-QKD). To begin with, a novel statistical model of the aggregated channel transmissivity experienced by the OIRS-based quantum states in underwater link is derived by combing the effects of oceanic absorption, scattering, turbulence and OIRS misalignment, where the oceanic turbulence-induced irradiance fluctuation is modeled by exponential and generalized gamma (EGG) distribution, and the jitter angle associated with AUV-carried OIRS misalignment is characterized by a Rayleigh distribution. Then, on the basis of this statistical model and the Gauss-Chebyshev quadrature, the quantum bit error rate and the lower bound secret key rate (SKR) for the AUV-carried OIRS-assisted DV-QKD link are obtained with weak coherent optical source and decoy state idea by utilizing Gottesman-Lo-Lütkenhaus-Preskill. In terms of univariate Fox-H function, the average Pirandola-Laurenza-Ottaviani-Banchi (PLOB) bound over the bosonic pure-loss channel, as well as the thermal upper and lower bounds over the thermal-loss channel are both derived for the AUV-carried OIRS-assisted CV-QKD link. Additionally, the achievable SKR for a practical GG02 CV-QKD protocol in underwater channels is also presented through the worst-case analysis. Furthermore, the impacts of the number of OIRS elements, OIRS positioning, jitter variances, the probability of erroneous detection and link distance on the security performance of the proposed links are studied with different water types, thereby offering valuable insights for the QKD-based UWOC system in IoUwT.

This paper presents the development, comparison, and analysis of several implementations of the B92 Quantum Key Distribution (QKD) protocol. To achieve this goal three prototypes which consists of traditional simulators (non-quantum) were created, one for the B92 protocol, one for the B92 protocol with an eavesdropper, and one for the B92 protocol with the Quantum Bit Travel Time (QBTT) eavesdropper detection method. The principles of quantum mechanics were studied, as a foundation of quantum cryptography, for the implementation of the simulation programs that were written in C++, focusing mainly on the B92 protocol and QBTT eavesdropper detection method. We compared the Quantum Bit Error Rate (QBER) for the implementation of the B92 protocol without an eavesdropper, the B92 protocol with an eavesdropper and the B92 protocol with the QBTT eavesdropper detection method and found that the latest one significantly reduces the QBER from the final key.

Currently, quantum key distribution (QKD) using continuous variable (CV) technology has only been demonstrated over short-range terrestrial links. Here we attempt to answer whether CV-QKD over the much longer satellite-to-Earth channel is feasible. To this end, we first review the concepts and technologies that will enable CV-QKD over the satellite-to-Earth channels. We then consider, in the infinite key limit, the simplest-to-deploy QKD protocols, the coherent state (CS) QKD protocol with homodyne detection and the CS-QKD protocol with heterodyne detection. We then focus on the CS-QKD protocol with heterodyne detection in the pragmatic setting of finite keys, where complete security against general attacks is known. We pay particular attention to the relevant noise terms in the satellite-to-Earth channel and their impact on the secret key rates. In system set-ups where diffraction dominates losses, we find that the main components of the total excess noise are the intensity fluctuations due to scintillation, and the time-of-arrival fluctuations between signal and local oscillator. We conclude that for a wide range of pragmatic system models, CS-QKD with information-theoretic security in the satellite-to-Earth channel is feasible.

In the BB84 quantum key distribution (QKD) protocol, the communicating parties do a quantum bit error rate (QBER) test to determine whether there is an eavesdropper trying to gain information about the secret key. However, the QBER is not only influenced by the eavesdropper’s strategies, but also by the imperfections of the physical devices and the channel through which the quantum states propagate. We developed a simple channel model with error parameters describing the channel and the potential polarization switching in the transmitter, to see how those effects influence the QBER in a polarization-qubit BB84 implementation. Certain well-defined probabilistic channel models are compared to see which is responsible for the highest error probability.

A new method to quantify the eavesdropper's accessible information on continuous variable quantum key distribution for protocols implementing homodyne and heterodyne detections is introduced. We have derived upper bounds for the eavesdropping collective attacks on general continuous variable quantum key distribution protocols. Our focus is especially on deriving bounds which are Gaussian optimal for Eve collective attacks that involve non maximally entanglement (i.e. Alice and Bob use non maximally entangled states or non-Gaussian modulation for their quantum key distribution protocols). The new bounds derived are tight for all continuous variable quantum key distribution protocols. We show that the eavesdropper's accessible information is independent of the initial correlation between Alice and Bob modes in reverse reconciliation scheme, while in direct reconciliation scheme, Eve information is given as a function of Alice and Bob initial correlation.

With the increasing information being shared online, the vast potential for cybercrime is a serious issue for individuals and businesses. Quantum key distribution (QKD) provides a way for distribution of secure key between two communicating parties. However, the current Quantum Key Distribution method, BB84 protocol, is prone to several weaknesses. These are Photon-Number-Splitting (PNS) attack, high Quantum Bit Error Rate (QBER), and low raw key efficiency. Thus, the objectives of this paper are to investigate the impacts of BB84 protocol towards QBER and raw key efficiencies in single quantum channel. Experiments were set up using a QKD simulator that was developed in Java NetBeans. The simulation study has reaffirmed the results of QBER and raw key efficiencies for the single quantum channel BB84 protocol.

The full time-jitter response of a single-photon detector can make a significant contribution to the quantum bit error rate (QBER) of high repetition rate quantum key distribution (QKD) implementations. Although there have been studies into understanding the contribution for single-mode optical fiber coupled single-photon detectors, the contribution of larger, multimode core diameters to the QBER have not been explored in detail. With the growing importance of free-space QKD, which typically use multimode fibers to reduce coupling loss, it is vitally important to understand how the multimode fiber coupling will impact the total QBER. This work studies the impact of the time-jitter contribution to QBER when coupling a commercial off-the-shelf silicon single-photon avalanche diode with various multimode fibers while simulating operating at 1 GHz with empirical measurements taken at 1 MHz repetition rate. It was found that step-index multimode fibers can significantly increase the QBER, while graded-index fibers can provide an QBER contribution similar to a single-mode fiber. The results highlight that there is a significant benefit in using graded index multimode fibers for a free-space QKD receiver, particularly for high repetition rate applications.

Quantum cryptography, and especially quantum key distribution (QKD), is steadily progressing to become a viable tool for cryptographic services. In recent years we have witnessed a dramatic increase in the secure bit rate of QKD, as well as its extension to ever longer fibre- and air-based links and the emergence of metro-scale trusted networks. In the foreseeable future even global-scale communications may be possible using quantum repeaters or Earth–satellite links. A handful of start-ups and some bigger companies are already active in the field. The launch of an initiative to form industrial standards for QKD, under the auspices of the European Telecommunication Standards Institute, described in the paper by Laenger and Lenhart in this Focus Issue, can be taken as a sign of the growing commercial interest.