Quantum Key Distribution Protocol Research Articles

Multi-Protocol Relay Chaining for Large-Scale Quantum Key Distribution Networks

Abstract As the first stage of the quantum Internet, quantum key distribution (QKD) networks hold the promise of providing long-term security for diverse users. Most existing QKD networks have been constructed based on independent QKD protocols, and they commonly rely on the deployment of single-protocol trusted relay chains for long reach. Driven by the evolution of QKD protocols, large-scale QKD networking is expected to migrate from a single-protocol to a multi-protocol paradigm, during which some useful evolutionary elements for the later stages of the quantum Internet may be incorporated. In this work, we delve into a pivotal technique for large-scale QKD networking, namely multi-protocol relay chaining. A multi-protocol relay chain is established by connecting a set of trusted/untrusted relays relying on multiple QKD protocols between a pair of QKD nodes. The structures of diverse multi-protocol relay chains are described, based on which the associated model is formulated and the policies are defined for the deployment of multi-protocol relay chains. Furthermore, we propose three multi-protocol relay chaining heuristics. Numerical simulations indicate that the designed heuristics can effectively reduce the number of trusted relays deployed and enhance the average security level versus the commonly used single-protocol trusted relay chaining methods on backbone network topologies.

Research on Quantum Key, Distribution Key and Post-quantum Cryptography Key Applied Protocols for Data Science and Web Security

Currently, data security is one of the most concerning research topics. The traditional RSA encryption system has become vulnerable to quantum algorithms such as Grover and Shor, leading to the development of new security systems for the quantum. As a result, quantum cryptography is gaining importance as a key element of future communication security. This study focuses on quantum key distribution protocols for data quantum encryption, aiming to achieve quantum robustness in all stages of quantum cryptography communication processes. Quantum cryptography communication requires robust quantum encryption not only between end-nodes but also between all components. Therefore, this study demonstrates the process of end-to-end data quantum encryption and proves the overall quantum robustness in this process.

Efficient Implementation of Interior-Point Methods for Quantum Relative Entropy

Quantum relative entropy (QRE) programming is a recently popular and challenging class of convex optimization problems with significant applications in quantum computing and quantum information theory. We are interested in modern interior-point (IP) methods based on optimal self-concordant barriers for the QRE cone. A range of theoretical and numerical challenges associated with such barrier functions and the QRE cones have hindered the scalability of IP methods. To address these challenges, we propose a series of numerical and linear algebraic techniques and heuristics aimed at enhancing the efficiency of gradient and Hessian computations for the self-concordant barrier function, solving linear systems, and performing matrix-vector products. We also introduce and deliberate about some interesting concepts related to QRE such as symmetric quantum relative entropy. We design a two-phase method for performing facial reduction that can significantly improve the performance of QRE programming. Our new techniques have been implemented in the latest version (DDS 2.2) of the software package Domain-Driven Solver (DDS). In addition to handling QRE constraints, DDS accepts any combination of several other conic and nonconic convex constraints. Our comprehensive numerical experiments encompass several parts, including (1) a comparison of DDS 2.2 with Hypatia for the nearest correlation matrix problem, (2) using DDS 2.2 for combining QRE constraints with various other constraint types, and (3) calculating the key rate for quantum key distribution (QKD) channels and presenting results for several QKD protocols. History: Accepted by Giacomo Nannicini, Area Editor for Quantum Computing and Operations Research. Accepted for Special Issue. Funding: This work was supported by the National Science Foundation [Grant CMMI-2347120] and Discovery Grants from the Natural Sciences and Engineering Research Council of Canada. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2024.0570 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2024.0570 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

Postselection Technique for Optical Quantum Key Distribution with Improved de Finetti Reductions

The postselection technique is an important proof technique for proving the security of quantum key distribution protocols against coherent attacks via the uplift of any security proof against independent identically distributed collective attacks. In this work, we go through multiple steps to rigorously apply the postselection technique to optical quantum key distribution protocols. First, we place the postselection technique on a rigorous mathematical foundation by fixing a technical flaw in the original postselection paper. Second, we extend the applicability of the postselection technique to prepare-and-measure protocols by using a de Finetti reduction with a fixed marginal. Third, we show how the postselection technique can be used for decoy-state protocols by tagging the source. Finally, we extend the applicability of the postselection technique to realistic optical setups by developing a new variant of the flag-state squasher. We also improve existing de Finetti reductions, which reduce the effect of using the postselection technique on the key rate. These improvements can be more generally applied to other quantum information processing tasks. As an example to demonstrate the applicability of our work, we apply our results to the time-bin-encoded three-state protocol. We observe that the postselection technique performs better than all other known proof techniques against coherent attacks. Published by the American Physical Society 2024

Discrete modulation continuous variable quantum key distribution under fast fading channel

After decades of development, continuous variable quantum key distribution technology still cannot meet people’s needs for secure communication over long distances. Free-space quantum communication provides a new way for secure communication over long distances. However, because the communication connected in free space is inevitably affected by atmospheric turbulence, the transmission rate of the channel changes rapidly according to the probability distribution, making it difficult for the communication personnel to determine the transmission rate of the channel. At the same time, discrete modulated continuously variable quantum key Distribution protocol (DM-CVQKD) has certain advantages over Gauss modulated continuously variable quantum key Distribution protocol (GM-CVQKD) in the communication distance. Therefore, this paper analyzes the key rate of DM-CVQKD in this case (that is, in the fast attenuation channel), proves that it can resist the collective attack, and observes the relationship between the parameters and the key rate in the fast attenuation channel by numerical simulation and control variables. Finally, through the analysis of numerical simulation results, it is found that DM-CVQKD can still maintain a high key rate under certain conditions, which proves that long-distance free space quantum communication is feasible under certain conditions. At the same time, it was found that the performance of DM-CVQKD was affected by the extreme case where Eve completely controlled the instantaneous transmittance.

Mapping Guaranteed Positive Secret Key Rates for Continuous Variable Quantum Key Distribution.

The standard way to measure the performance of existing continuous variable quantum key distribution (CVQKD) protocols is by using the achievable secret key rate (SKR) with respect to one parameter while keeping all other parameters constant. However, this atomistic method requires many individual parameter analyses while overlooking the co-dependence of other parameters. In this work, a numerical tool is developed for comparing different CVQKD protocols while taking into account the simultaneous effects of multiple CVQKD parameters on the capability of protocols to produce positive SKRs. Using the transmittance, excess noise, and modulation amplitude parameter space, regions of positive SKR are identified to compare three discrete modulated (DM) CVQKD protocols. The results show that the M-QAM protocol outperforms the M-APSK and M-PSK protocols and that there is a non-linear increase in the capability to produce positive SKRs as the number of coherent states used for a protocol increases. The tool developed is beneficial for choosing the optimum protocol in unstable channels, such as free space, where the transmittance and excess noise fluctuate, providing a more holistic assessment of a protocol's capability to produce positive SKRs.

High-dimensional quantum key distribution using orbital angular momentum of single photons from a colloidal quantum dot at room temperature

High-dimensional quantum key distribution (HDQKD) is a promising avenue to address the inherent limitations of basic quantum key distribution (QKD) protocols. However, experimental realizations of HDQKD to date have relied on indeterministic photon sources that limit the achievable key rate. In this paper, we demonstrate a full emulation of a HDQKD system using a single colloidal giant quantum dot (gQD) as a deterministic, compact, and room-temperature single-photon source (SPS). We demonstrate a practical protocol by encoding information in a high-dimensional space (d = 3) of the orbital angular momentum of the photons. Our experimental configuration incorporates two spatial light modulators for encoding and decoding the spatial information carried by individual photons. Our experimental demonstration establishes the feasibility of utilizing high radiative quantum yield gQDs as practical SPSs for HDQKD. We also experimentally demonstrate surpassing the traditional d = 2 QKD capacity with comparable error rates, indicating a significant improvement in performance while maintaining reliability.

Quantum cryptography in the security of cognitive radio networks

Cognitive radio networks face challenges from malicious users who aim to disrupt decision-making during spectrum sensing and decrease spectrum efficiency. The proposed model seeks to distinguish between the presence and absence of primary user signals using energy detection and also it introduces a quantum-inspired outlier detection mechanism for cognitive radio networks to enhance security and reliability during spectrum sensing by ignoring the identified outliers. It employs BB84 quantum key distribution (QKD) protocol and one time pad for secure transmission of secondary user (SU) local decisions to the fusion center (FC), ensuring data integrity and confidentiality. These decisions are transmitted securely establishing a shared secret key between SU and FC and arrives at a global decision. To make the model more robust, we proposed another novel model with a modified BB84 protocol and compared the results of both the models, offering a robust solution for enhancing the reliability and performance of cognitive radio networks with proven results from simulation.

Keep it secret, keep it safe: teaching quantum key distribution in high school

Quantum Key Distribution (QKD) is a cryptography protocol based on the fundamental principles of quantum physics (QP). Teaching this subject does not require extensive knowledge beyond these principles, making it suitable for inclusion in high school (HS) curricula. Despite its relevance, teaching QKD in HS is yet understudied. In this study, we collected responses from 12th-grade students from various schools that adopted and applied the Discipline-Culture vision of the physics curriculum. We assessed their understanding through conceptual and quantitative problems and examined their attitudes regarding the motivation to study this subject. We analyzed the responses using content analysis, identifying the challenges and affordances of teaching QKD. The challenges faced by students have been categorized into three themes: difficulties with QP, difficulties with the QKD protocol, and difficulties with the mathematics involved in this context. Despite these challenges, we found that teaching QKD reinforces students’ conceptual understanding of QP concepts and problem-solving skills. This work enhances educators’ ability to address the challenges of teaching QP and suggests that teaching QKD in HS strengthens students’ motivation to study QP.

Multi-party quantum key distribution protocol in quantum network

This study proposes a measurement property of graph states and applies it to design a mediated multiparty quantum key distribution (M-MQKD) protocol for a repeater-based quantum network in a restricted quantum environment. The protocol enables remote classical users, who cannot directly transmit qubits, to securely distribute a secret key with the assistance of potentially dishonest quantum repeaters. Classical users only require two quantum capabilities, while quantum repeaters handle entanglement transmission through single-photon measurements. The one-way transmission approach eliminates the need for additional defenses against quantum Trojan horse attacks, reducing maintenance costs compared to round-trip or circular transmission methods. As a result, the M-MQKD protocol is lightweight and easy to implement. The study also evaluates the security of the protocol and demonstrates its practicality through quantum network simulations.

Accelerating QKD post-processing by secure offloading of information reconciliation

While quantum key distribution (QKD) offers unparalleled security in communication, its real-world application is hindered by inherent physical constraints. The challenge lies predominantly in the cumbersome, energy-intensive nature of current QKD systems, which stems largely from the time-intensive post-processing stage. This paper investigates the feasibility of offloading the computationally intensive post-processing tasks, specifically focusing on information reconciliation (IR), to potentially untrusted servers.We present a novel scheme that leverages syndrome decoding techniques to efficiently transfer the IR step of QKD protocols to a single external server. Notably, this offloading is accomplished while maintaining the highest level of security, known as unconditional security. The proposed technique is bolstered by a comprehensive theoretical analysis and validated through experimental trials. These findings demonstrate the effectiveness of our approach in bridging the gap between the theoretical promise of QKD and its real-world deployment.

Simulations of distributed-phase-reference quantum key distribution protocols

Quantum technology can enable secure communication for cryptography purposes using quantum key distribution. Quantum key distribution protocol establishes a secret key between two users with security guaranteed by the laws of quantum mechanics. To define the proper implementation of a quantum key distribution system using a particular cryptography protocol, it is crucial to critically and meticulously assess the device’s performance due to technological limitations in the components used. We perform simulations on the ANSYS Interconnect platform to study the practical implementation of these devices using distributed-phase-reference protocols: differential-phase-shift and coherent-one-way quantum key distribution. Further, we briefly describe and simulate some possible eavesdropping attempts, backflash attack, trojan-horse attack and detector-blinding attack exploiting the device imperfections. The ideal simulations of these hacking attempts show how partial or complete secret key can be exposed to an eavesdropper, which can be mitigated by the implementation of discussed countermeasures.

Polarization purity and dispersion characteristics of nested antiresonant nodeless hollow-core optical fiber at near- and short-wave-IR wavelengths for quantum communications

Advancements in quantum communication and sensing require improved optical transmission that ensures excellent state purity and reduced losses. While free-space optical communication is often preferred, its use becomes challenging over long distances due to beam divergence, atmospheric absorption, scattering, and turbulence, among other factors. In the case of polarization encoding, traditional silica-core optical fibers, though commonly used, struggle with maintaining state purity due to stress-induced birefringence. Hollow core fibers, and in particular nested antiresonant nodeless fibers (NANF), have recently been shown to possess unparalleled polarization purity with minimal birefringence in the telecom wavelength range using continuous-wave (CW) laser light. Here, we investigate a 1-km NANF designed for wavelengths up to the 2-μm waveband. Our results show a polarization extinction ratio between ~−30 dB and ~−70 dB across the 1520 to 1620 nm range in CW operation, peaking at ~−60 dB at the 2-μm design wavelength. Our study also includes the pulsed regime, providing insights beyond previous CW studies, e.g., on the propagation of broadband quantum states of light in NANF at 2 μm, and corresponding extinction-ratio-limited quantum bit error rates (QBER) for prepare-measure and entanglement-based quantum key distribution (QKD) protocols. Our findings highlight the potential of these fibers in emerging applications such as QKD, pointing towards a new standard in optical quantum technologies.

Advanced error correction method for quantum key distribution in IoT systems

The secure distribution of keys is essential to ensuring the privacy and integrity of data in Internet of Things (IoT) systems. Quantum Key Distribution (QKD) protocols, such as BB84, use principles from quantum mechanics to establish secure communication channels. However, errors that occur during the transmission of qubits can compromise the reliability of the shared key. This paper presents a new method for error correction that integrates Convolutional Neural Networks (CNNs) into the BB84 protocol for QKD in IoT systems. By harnessing the exceptional pattern recognition capabilities of CNNs, our approach learns hierarchical representations from preprocessed quantum channel data to effectively identify and correct errors. Extensive simulations demonstrate the high performance of our CNN-based method in reducing the Quantum Bit Error Rate (QBER). This contribution significantly enhances the security and reliability of key distribution, offering a promising solution for robust quantum communication in IoT environments.

Enhancing Quantum Key Distribution Protocols for Extended Range and Reduced Error

Abstract this paper proposes an optimized Quantum Key Distribution (QKD) protocol using entanglement swapping techniques to extend transmission range and improve error correction. Additionally, integrates an advanced error correction technique which is Low Density Parity Check (LDPC) and multi-hop quantum repeaters for more enhancement of the protocol performance. Hybrid Quantum Classical Error Correction Methods is applied ensuring compatibility and optimal performance and to manage the increased complexity. Simulations prove that 25% improvement in transmission distance with entanglement swapping. 50% improvement with advanced error correction and a 100% improvement with multi-hop quantum repeaters compared to existing protocols. These discoveries are supported by both theoretical analysis and simulation results, indicating significant decreases in error rates and extensions in maximum transmission distances. Comparative analysis made with existing protocols and that demonstrated the superiority of proposed approach in terms of extended secure communication distance, higher key generation rate and improved resilience to attacks.

Demonstration of microwave single-shot quantum key distribution

Security of modern classical data encryption often relies on computationally hard problems, which can be trivialized with the advent of quantum computers. A potential remedy for this is quantum communication which takes advantage of the laws of quantum physics to provide secure exchange of information. Here, quantum key distribution (QKD) represents a powerful tool, allowing for unconditionally secure quantum communication between remote parties. At the same time, microwave quantum communication is set to play an important role in future quantum networks because of its natural frequency compatibility with superconducting quantum processors and modern near-distance communication standards. To this end, we present an experimental realization of a continuous-variable QKD protocol based on propagating displaced squeezed microwave states. We use superconducting parametric devices for generation and single-shot quadrature detection of these states. We demonstrate unconditional security in our experimental microwave QKD setting. The security performance is shown to be improved by adding finite trusted noise on the preparation side. Our results indicate feasibility of secure microwave quantum communication with the currently available technology in both open-air (up to ~ 80 m) and cryogenic (over 1000 m) conditions.

Enhancing Performance of Continuous-Variable Quantum Key Distribution (CV-QKD) and Gaussian Modulation of Coherent States (GMCS) in Free-Space Channels under Individual Attacks with Phase-Sensitive Amplifier (PSA) and Homodyne Detection (HD).

In recent research, there has been a significant focus on establishing robust quantum cryptography using the continuous-variable quantum key distribution (CV-QKD) protocol based on Gaussian modulation of coherent states (GMCS). Unlike more stable fiber channels, one challenge faced in free-space quantum channels is the complex transmittance characterized by varying atmospheric turbulence. This complexity poses difficulties in achieving high transmission rates and long-distance communication. In this article, we thoroughly evaluate the performance of the CV-QKD/GMCS system under the effect of individual attacks, considering homodyne detection with both direct and reverse reconciliation techniques. To address the issue of limited detector efficiency, we incorporate the phase-sensitive amplifier (PSA) as a compensating measure. The results show that the CV-QKD/GMCS system with PSA achieves a longer secure distance and a higher key rate compared to the system without PSA, considering both direct and reverse reconciliation algorithms. With an amplifier gain of 10, the reverse reconciliation algorithm achieves a secure distance of 5 km with a secret key rate of 10-1 bits/pulse. On the other hand, direct reconciliation reaches a secure distance of 2.82 km.

Security Analysis of the BB84 Protocol in IoT Networks

The Internet of Things (IoT) has experienced rapid growth, resulting in a proliferation of interconnected devices in domains such as smart homes, cities, and healthcare applications. Ensuring secure communication within IoT networks is crucial for protecting privacy and data. The BB84 protocol, a quantum key distribution (QKD) protocol, shows promise in enhancing IoT communication security. This paper presents a comprehensive security analysis of the BB84 protocol in IoT networks, examining key aspects including entropy, execution time, quantum bit error rate (QBER), and cryptographic key generation efficiency. The analysis aims to evaluate the protocol's resilience against potential attacks and its suitability for securing IoT communications. We delve into the evaluation of entropy levels in the key generation process to ensure strong cryptographic properties. We also examine the correlation between execution time and QBER to determine the protocol's efficiency and ability to counter timing-based attacks. Additionally, we analyze the efficiency of the keys generated by the BB84 protocol, taking into consideration factors such as key size, generation rate, and computational overhead. These evaluations allow us to assess the protocol's suitability for resource-constrained IoT devices

State-of-the-art analysis of quantum cryptography: applications and future prospects

Quantum computing provides a revolution in computational competences, leveraging the principles of quantum mechanics to process data in fundamentally novel ways. This paper explores the profound implications of quantum computing on cryptography, focusing on the vulnerabilities it introduces to classical encryption methods such as RSA and ECC, and the emergence of quantum-resistant algorithms. We review the core principles of quantum mechanics, including superposition and entanglement, which underpin quantum computing and cryptography. Additionally, we examine quantum encryption algorithms, particularly Quantum Key Distribution (QKD) protocols and post-quantum cryptographic methods, highlighting their potential to secure communications in the quantum era. This analysis emphasizes the urgent need for developing robust quantum-resistant cryptographic solutions to safeguard sensitive information against the imminent threats posed by advancing quantum technologies.

Implementation of coherent one way protocol for quantum key distribution up to an effective distance of 145 km

Implementation of coherent one way protocol for quantum key distribution up to an effective distance of 145 km