Simulation and modeling approach for performance analysis of practical Quantum key distribution

With the technological development, the demand for secure communication is growing exponentially. Global secure communication have become crucial with increasing number of internet applications. Quantum Cryptography (QC) or Quantum Key Distribution (QKD) in that regime, promises an unconditional security based on laws of quantum principles. Free space QKD allows longer communication distances with practical secure key rates to aid secure global key distribution via satellites. This is encouraging many research groups to conduct QKD experimentation. But it is observed that such experiments are very complex and expensive. This paper thus attempts to establish a model for analysis of free space QKD through simulation. The model will be verified against experimental results available from different literature. It can be seen that the simulation approach stands effective for performance analysis of such complex systems. The developed model, test parameters like quantum bit error rate and secret key rate against mean photon number of laser pulses and quantum channel loss, and proves to fit well with the experimental results.

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.

Security of data transported in telecommunication networks is of primary importance for internet service providers (ISP) as data safety is at the basis of the mutual trust with customers. People were looking for theoretically secure transmission techniques since a long-time to ensure long-term confidentiality of data flows exchanged on these networks. Besides advanced encryption algorithms and the recently proposed post-quantum cryptography (PQC), a physics-based technology using quantum key distribution (QKD) was proposed a long time ago to approach this objective. QKD recently gained a renewed interest with many research programs worldwide supported by public authorities, and some pre-industrial QKD systems delivered to the market. However, some constraints of optical transport networks make sometimes complicated the deployment of such QKD systems in the field, such as the need of a dedicated fiber infrastructure for QKD, or the impossibility for a quantum key to pass through an optical amplifier. In this paper, we report the transmission of a coherent 400-Gbps dual-polarization 16QAM channel that transports QKD-secured 100-GbEthernet data stream with other fifty-four WDM channels at 100-Gbps over 184-km of standard single mode fiber (SSMF) through three QKD links (of 66-km, 50-km and 66-km, respectively) and two trusted nodes. On the two longest sections of the link, the quantum key and WDM signals are propagated on two different fibers, while on the shortest section of 50-km the QKD signal and WDM comb co-propagate on a same fiber. Secret key rates (SKR) and quantum bit error rate (QBER) are measured and reported on each of the three fiber sections. Various analyses are carried out on the co-propagation section of 50-km: the SKR / QBER sensitivity to the optical power of the WDM comb, or to the optical signal-to-noise ratio (OSNR) of the WDM channels co-propagating with the quantum signal is studied. The unique arrangement of the most advanced QKD and WDM technologies reported here constitutes, in our opinion, a world first, and demonstrates that QKD and WDM solutions can coexist in already deployed optical transport networks.

Quantum computing has the capability of parallel computing and is superior to classical computing in solving some specific problems. Once a large-scale quantum computer is developed, the security of classical cryptographic algorithms and protocols, which is based on the assumption of computational complexity, will be severely challenged. Quantum cryptography is a new cryptosystem; its security is based on the principles of quantum mechanics, and can resist the attack of quantum computing. This paper focuses on the nearly 40 years development of quantum cryptographic protocols, including quantum key distribution (QKD), quantum secure direct communication, quantum secret sharing, quantum identity authentication, two-party secure computation, and quantum private query, and summarizes the problems in the process of development. The analysis shows that the quantum cryptographic protocols are in an unbalanced state: QKD is far ahead of other protocols and other protocols are difficult to achieve breakthroughs. In the future, practical quantum protocols for digital signature and two-party secure computation are core issues that needs to be addressed urgently. Therefore, research on quantum and post-quantum cryptography should be conducted synchronously, cross-over study and talent cultivation for the quantum science and cryptography disciplines should be strengthened, and the examination and evaluation mechanism of relevant basic research needs to be optimized.

Absorption, scattering, and turbulence experienced in underwater channels severely limit the range of quantum communication links. In this paper, as a potential solution to overcome range limitations, we investigate a multi-hop underwater quantum key distribution (QKD) where intermediate nodes between the source and destination nodes help the key distribution. We consider the deployment of passive relays that simply redirect the qubits to the next relay node or the receiver without any measurement. Based on the near-field analysis, we present the performance of a relay-assisted QKD scheme in terms of quantum bit error rate and secret key rate in different water types and turbulence conditions. We further investigate the effect of system parameters such as aperture size and detector field of view on the performance. Our results demonstrate under what conditions relay-assisted QKD can be beneficial and what end-to-end transmission distances can be supported with a multi-hop underwater QKD system.

Chapter 6 - Quantum key distribution

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.

Fiber-based quantum key distribution (QKD) systems are mature and commercialized, but their integration into existing optical networks is crucial for their widespread use, in particular in passive optical networks (PONs) if end-to-end quantum-secured communications are to be addressed. While discrete-variable QKD coexistence with classical channels is well-studied in point-to-point links, its performance in point-to-multipoint topologies like PONs has received less attention. We thus developed a numerical tool to estimate quantum-available bandwidth and maximum link lengths for QKD systems in single-fiber PON architectures in coexistence with GPON, XG-PON, NG-PON2, and HS-PON standards. The QKD channel performance is obtained by setting thresholds on the quantum bit error rate and the secret key rate, ultimately limited by spontaneous Raman scattering noise and high optical distribution network losses. We perform a comparison between the performance obtained assuming the asymptotic infinite-key generation rate or taking into account actual implementations in the finite-key regime. We evidence that proper design rules can be obtained as a function of both classical and quantum system parameters to support end-to-end quantum security services in existing optical networks.

Quantum cryptography is the art and science of exploiting quantum mechanical effects in order to perform cryptographic tasks. While the most well-known example of this discipline is quantum key distribution (QKD), there exist many other applications such as quantum money, randomness generation, secure two- and multi-party computation and delegated quantum computation. Quantum cryptography also studies the limitations and challenges resulting from quantum adversaries—including the impossibility of quantum bit commitment, the difficulty of quantum rewinding and the definition of quantum security models for classical primitives. In this review article, aimed primarily at cryptographers unfamiliar with the quantum world, we survey the area of theoretical quantum cryptography, with an emphasis on the constructions and limitations beyond the realm of QKD.

This chapter discusses quantum information science (QIS), quantum key distribution (QKD), and quantum teleportation. The new field of QIS encompasses several overlapping subdisciplines: quantum computing, quantum key distribution (also known as quantum cryptography), and quantum metrology (the measurement of small parameters and weak forces with ultra-high precision). In QIS, bits of information are encoded in quantum states, which themselves can be in superposition states and/or entanglement states. Generically, the 0 and 1 quantum bits are represented as qubits (quantum bits). QKD, or quantum cryptography, is a completely secure method of secret communication, and will remain so even if a quantum computer becomes available. Quantum teleportation is one of the more exotic features to have emerged from the field of QIS. It refers to the ability to transfer an unknown quantum state from one location to another, possibly very distant, location by using quantum entanglement.

Nowadays, a high level of security is required for the transmission of critical information. Quantum Key Distribution (QKD) systems are considered the best option to protect such information. Many studies have shown the efficiency of the QKD optical fiber inspired by M-ary pulse position modulation (MPPM). Free-Space Optical (FSO) links provide an efficient and effective data transmission system. However, cumulative effects of laser beam divergence, misalignment, and turbulence-induced fading on the received irradiance in the FSO link might allow an external eavesdropper located near the authorized receiver to break the transmission under certain conditions. This paper introduces the development of an FSO system based on the MPPM and the BB84 protocol (MPPM-BB84) over the Gamma-Gamma (GG) turbulence channel with pointing errors. Time Binning is implemented using MPPM to increase system security and reduce the quantum bit error rate (QBER). The system security is investigated under photon number splitting attack and excess noise. Closed-form expressions for asymptotic expressions of the average symbol error probability (SER), raw key rate (RKR), and secret key rate (SKR) are introduced. Moreover, the Monte-Carlo simulations are then used to prove the validity of the analytical results. The optimal values for the average photon number per pulse (to achieve the maximum RKR and SKR) for each symbol length can guarantee the stability of the FSO system under different weather conditions. Smaller symbol lengths are more tolerant of detector loss. The proposed system supports linking distances from 1 km to 3 km while keeping the SKR almost constant.

The security of quantum cryptography relies on the foundations of quantum mechanics, in contrast to traditional public key cryptography which relies on the computational difficulty of certain mathematical functions, and cannot provide any indication of eavesdropping or guarantee of key security. The proposal present in this work develops a quantum key distribution model to safeguard security in large networks, in the directions of classical cryptography and quantum cryptography. Two three-party Quantum key distribution are used in this model, one with implicit user authentication and the other with explicit mutual authentication, are proposed to demonstrate the merits of the new combination. The performance of Quantum Key Distribution (QKD) systems have notably progressed since the early experimental demonstrations. The current evolutions in QKD research indicate that the pace of this progression is very likely to be maintained, if not increased, in the future years. In parallel to these improvements of QKD techniques, commercial products are also being developed, making QKD deployment a feasible alternative for securing real data networks. Deployment of a real QKD network is however far from being straightforward. It requires development of a network architecture connecting multiple users that may possibly be very far away from each other. Considering the fact that the existing QKD links are only point-to-point, and intrinsically limited in distance, deployment of a practical QKD network structure is a nontrivial problem. The proposed work describes the proposed architecture for a QKD network specify the requirements relevant to the network design, protocols, and services. The objective of this specification is to define the major components and their main features The proposal provides security against such attacks as man-in-the-middle, eavesdropping and replay. It also improves the efficiency of the quantum key distribution which contains the fewest number of communication rounds among existing Quantum key distributions. In this model two parties can share and use a long-term secret (repeatedly). To prove the security of the proposed schemes, this proposed model provides a primitive called the Unbiased-Chosen Basis (UCB) assumption with the quantum key in angular positions.

Quantum key distribution (QKD) allows two remote users to establish a secret key in the presence of an eavesdropper. The users share quantum states prepared in two mutually-unbiased bases: one to generate the key while the other monitors the presence of the eavesdropper. Here, we show that a general $d$-dimension QKD system can be secured by transmitting only a subset of the monitoring states. In particular, we find that there is no loss in the secure key rate when dropping one of the monitoring states. Furthermore, it is possible to use only a single monitoring state if the quantum bit error rates are low enough. We apply our formalism to an experimental $d=4$ time-phase QKD system, where only one monitoring state is transmitted, and obtain a secret key rate of $17.4 \pm 2.8$ Mbits/s at a 4 dB channel loss and with a quantum bit error rate of $0.045\pm0.001$ and $0.044\pm0.001$ in time and phase bases, respectively, which is 58.4 % of the secret key rate that can be achieved with the full setup. This ratio can be increased, potentially up to 100 %, if the error rates in time and phase basis are reduced. Our results demonstrate that it is possible to substantially simplify the design of high-dimension QKD systems, including those that use the spatial or temporal degrees-of-freedom of the photon, and still outperform qubit-based ($d = 2$) protocols.

We demonstrate that, with a fair comparison, the secret key rate of discrete-variable measurement-device-independent quantum key distribution (DV-MDI-QKD) with high-efficiency single-photon detectors and good system alignment is typically rather high and thus highly suitable for not only long distance communication but also metropolitan networks. The previous reservation on the key rate and suitability of DV-MDI-QKD for metropolitan networks expressed by Pirandola et al. [Nature Photon. 9, 397 (2015)] was based on an unfair comparison with low-efficiency detectors and high quantum bit error rate, and is, in our opinion, unjustified.

Recent advancements in reactor designs could offer new revolutionary capabilities, including remote monitoring, increased flexibility, and reduced operation and maintenance costs. Embracing new digital technologies would allow for operational concepts such as semiautonomous or near-autonomous control, and two-way communications for real-time integration with the upcoming smart electric grid. However, such continuous data transmission from and toward a reactor site could potentially introduce new challenges and vulnerabilities, necessitating the prioritization of cybersecurity. Conventional information technology–based encryption schemes, which rely mostly on computational complexity, have been shown to be vulnerable to cyberattacks. With the advent of quantum computing, practically any asymmetric encryption could be potentially compromised. For example, it has been shown that a RSA-2048 bit key could be broken in 8 h. To address this challenge, we explore the feasibility of quantum key distribution (QKD) to secure communications. QKD is a physical layer security scheme relying on the laws of quantum mechanics instead of mathematical complexity. QKD promises not only unconditional security but also detection of potential intrusion, as it allows the communication parties to become aware of eavesdropping. To test the proposed hypothesis, a novel simulation tool (NuQKD) was developed to allow for real-time simulation of the BB84 QKD protocol between two remote terminals. A reference scenario is proposed, generic enough to cover various internal and external communication links to a reactor site. Using NuQKD, the internal and external data links were modeled, and receiver operating characteristic curves were calculated for various QKD configurations. A performance analysis was conducted, demonstrating that QKD can provide adequate secret key rates with low false alarms and has the potential of addressing the nuclear industry’s high standards of confidentiality for distance lengths up to 75 km of fiberoptics. Using a conservative estimation, QKD can provide up to 21.5 kbps of secret key rate for a distance of 1 km and 14.4 kbps at 10 km. The target secret key rates for the corresponding links were estimated at 16 kbps and 80 bps, respectively, based on the analysis of real data from a PUR-1 fully digital reactor. Consequently, QKD is shown to be compatible with existing and future point-to-point reactor communication architectures. These results motivate further study of quantum communications for nuclear reactors.