Experimental measurement-device-independent quantum digital signatures

Implementing no-signaling correlations as a service

We deal with no-signaling correlations that include Bell-type quantum nonlocality. We consider a logical implementation using a trusted central server with encrypted connections to clients. We show that in this way it is possible to implement two-party no-signaling correlations in an asynchronous manner. While from the point of view of physics our approach can be considered as the computer emulation of the results of measurements on entangled particles, from the software engineering point of view it introduces a primitive in communication protocols that can be capable of coordinating agents without revealing the details of their actions. We present an actual implementation in the form of a Web-based application programming interface (RESTful Web API). We demonstrate the use of the API via the simple implementation of the Clauser-Horne-Shimony-Holt game.

Entanglement-based quantum digital signatures over a deployed campus network

The quantum digital signature protocol offers a replacement for most aspects of public-key digital signatures ubiquitous in today's digital world. A major advantage of a quantum-digital-signatures protocol is that it can have information-theoretic security, whereas public-key cryptography cannot. Here we demonstrate and characterize hardware to implement entanglement-based quantum digital signatures over our campus network. Over 25 hours, we collect measurements on our campus network, where we measure sufficiently low quantum bit error rates (<5% in most cases) which in principle enable quantum digital signatures at over 50 km as shown through rigorous simulation accompanied by a noise model developed specifically for our implementation. These results show quantum digital signatures can be successfully employed over deployed fiber. Moreover, our reported method provides great flexibility in the number of users, but with reduced entanglement rate per user. Finally, while the current implementation of our entanglement-based approach has a low signature rate, feasible upgrades would significantly increase the signature rate.

Experimental quantum e-commerce

E-commerce, a type of trading that occurs at a high frequency on the internet, requires guaranteeing the integrity, authentication, and nonrepudiation of messages through long distance. As current e-commerce schemes are vulnerable to computational attacks, quantum cryptography, ensuring information-theoretic security against adversary's repudiation and forgery, provides a solution to this problem. However, quantum solutions generally have much lower performance compared to classical ones. Besides, when considering imperfect devices, the performance of quantum schemes exhibits a notable decline. Here, we demonstrate the whole e-commerce process of involving the signing of a contract and payment among three parties by proposing a quantum e-commerce scheme, which shows resistance of attacks from imperfect devices. Results show that with a maximum attenuation of 25 dB among participants, our scheme can achieve a signature rate of 0.82 times per second for an agreement size of approximately 0.428 megabit. This proposed scheme presents a promising solution for providing information-theoretic security for e-commerce.

Measurement device hacking-free mutual quantum identity authentication over a deployed optical fiber

Quantum identity authentication serves as a crucial technology for secure quantum communication, but its security often faces challenges due to quantum hacking of measurement devices. This study introduces a measurement-device-independent mutual quantum identity authentication (MDI MQIA) scheme capable of ensuring secure user authentication, despite the use of measurement devices vulnerable to quantum hacking. To realize the MDI MQIA scheme, we proposed and applied a modified Bell state measurement based on linear optics, enabling the probabilistic measurement of all Bell states. Furthermore, the proposed experimental setup adopted a plug-and-play architecture, thus efficiently establishing the indistinguishability of two photons prepared by the communication members. Finally, we successfully performed a proof-of-principle experimental demonstration of the proposed scheme using a field-deployed fiber, achieving quantum bit error rates of less than 3%.

Optimization of the multivariate polynomial public key for quantum safe digital signature

Kuang, Perepechaenko, and Barbeau recently proposed a novel quantum-safe digital signature algorithm called Multivariate Polynomial Public Key or MPPK/DS. The key construction originated with two univariate polynomials and one base multivariate polynomial defined over a ring. The variable in the univariate polynomials represents a plain message. All but one variable in the multivariate polynomial refer to noise used to obscure private information. These polynomials are then used to produce two multivariate product polynomials, while excluding the constant term and highest order term with respect to the message variable. The excluded terms are used to create two noise functions. Then four produced polynomials, masked with two randomly chosen even numbers over the ring, form the Public Key. The two univariate polynomials and two randomly chosen numbers, behaving as an encryption key to obscure public polynomials, form the Private Key. The verification equation is derived from multiplying all of the original polynomials together. MPPK/DS uses a special safe prime to prevent private key recovery attacks over the ring, forcing adversaries to solve for private values over a sub-prime field and lift the solutions to the original ring. Lifting entire solutions from the sub-prime field to the ring is designed to be difficult based on security requirements. This paper intends to optimize MPPK/DS to reduce the signature size by a fifth. We added extra two private elements to further increase the complexity of the private key recovery attack. However, we show in our newly identified optimal attack that these extra private elements do not have any effect on the complexity of the private recovery attack due to the intrinsic feature of MPPK/DS. The optimal key-recovery attack reduces to a Modular Diophantine Equation Problem or MDEP with more than one unknown variables for a single equation. MDEP is a well-known NP-complete problem, producing a set with many equally-likely solutions, so the attacker would have to make a decision to choose the correct solution from the entire list. By purposely choosing the field size and the order of the univariate polynomials, we can achieve the desired security level. We also identified a new deterministic attack on the coefficients of two univariate private polynomials using intercepted signatures, which forms a overdetermined set of homogeneous cubic equations. To the best of our knowledge, the solution to such a problem is to brute force search all unknown variables and verify the obtained solutions. With those optimizations, MPPK/DS can offer extra security of 384 bit entropy at 128 bit field with a public key size being 256 bytes and signature size 128 or 256 bytes using SHA256 or SHA512 as the hash function respectively.

Twin-Field Quantum Digital Signature with Fully Discrete Phase Randomization

Quantum digital signatures (QDS) are able to verify the authenticity and integrity of a message in modern communication. However, the current QDS protocols are restricted by the fundamental rate-loss bound and the secure signature distance cannot be further improved. We propose a twin-field quantum digital signature (TF-QDS) protocol with fully discrete phase randomization and investigate its performance under the two-intensity decoy-state setting. For better performance, we optimize intensities of the signal state and the decoy state for each given distance. Numerical simulation results show that our TF-QDS with as few as six discrete random phases can give a higher signature rate and a longer secure transmission distance compared with current quantum digital signatures (QDSs), such as BB84-QDS and measurement-device-independent QDS (MDI-QDS). Moreover, we provide a clear comparison among some possible TF-QDSs constructed by different twin-field key generation protocols (TF-KGPs) and find that the proposed TF-QDS exhibits the best performance. Conclusively, the advantages of the proposed TF-QDS protocol in signature rate and secure transmission distance are mainly due to the single-photon interference applied in the measurement module and precise matching of discrete phases. Besides, our TF-QDS shows the feasibility of experimental implementation with current devices in practical QDS system.

Four-intensity measurement-device-independent quantum key distribution protocol with modified coherent state sources

We propose a scheme of double-scanning 4-intensity MDI-QKD protocol with the modified coherent state (MCS) sources. The MCS sources can be characterized by two positive parameters, ξ and c. In all prior works, c was set to be the same for all sources. We show that the source parameter c can be different for the sources in the X basis and those in the Z basis. Numerical results show that removing such a constraint can greatly improve the key rates of the protocol with MCS sources. In the typical experiment conditions, comparing with the key rates of WCS sources, the key rates of MCS sources can be improved by several orders of magnitude, and the secure distance is improved by about 40 km. Our results show that MCS sources have the potential to improve the practicality of the MDI-QKD protocol.

Secure and practical multiparty quantum digital signatures

Quantum digital signatures (QDSs) promise information-theoretic security against repudiation and forgery of messages. Compared with currently existing three-party QDS protocols, multiparty protocols have unique advantages in the practical case of more than two receivers when sending a mass message. However, complex security analysis, numerous quantum channels and low data utilization efficiency make it intractable to expand three-party to multiparty scenario. Here, based on six-state non-orthogonal encoding protocol, we propose an effective multiparty QDS framework to overcome these difficulties. The number of quantum channels in our protocol only linearly depends on the number of users. The post-matching method is introduced to enhance data utilization efficiency and make it linearly scale with the probability of detection events even for five-party scenario. Our work compensates for the absence of practical multiparty protocols, which paves the way for future QDS networks.

Twin-field quantum digital signatures

Digital signature is a key technique in information security, especially for identity authentications. Compared to classical correspondence, quantum digital signatures (QDSs) provide a considerably higher level of security. At present, its performance is limited by key generation protocols, which are fundamentally limited in terms of channel capacity. Based on the idea of twin-field quantum key distribution, this Letter presents a twin-field QDS protocol and details a corresponding security analysis. In its distribution stage, a specific key generation protocol, the sending-or-not-sending twin-field protocol, has been adopted. Besides, we present a systematic model to evaluate the performance of a QDS protocol and compare the performance of our protocol to other typical QDS protocols. Numerical simulation results show that the new protocol exhibits outstanding security and practicality compared to other existing protocols. Therefore, our protocol paves the way toward real-world applications of QDSs.

Efficient quantum digital signatures without symmetrization step

Quantum digital signatures (QDS) exploit quantum laws to guarantee non-repudiation, unforgeability and transferability of messages with information-theoretic security. Current QDS protocols face two major restrictions, including the requirement of the symmetrization step with additional secure classical channels and the quadratic scaling of the signature rate with the probability of detection events. Here, we present an efficient QDS protocol to overcome these issues by utilizing the classical post-processing operation called post-matching method. Our protocol does not need the symmetrization step, and the signature rate scales linearly with the probability of detection events. Simulation results show that the signature rate is three orders of magnitude higher than the original protocol in a 100-km-long fiber. This protocol is compatible with existing quantum communication infrastructure, therefore we anticipate that it will play a significant role in providing digital signatures with unconditional security.

280-km experimental demonstration of a quantum digital signature with one decoy state

A quantum digital signature (QDS) guarantees the unforgeability, nonrepudiation, and transferability of signature messages with information-theoretic security, and hence has attracted much attention recently. However, most previous implementations of QDS showed relatively low signature rates and/or short transmission distance. In this Letter, we report a proof-of-principle phase-encoding QDS demonstration using only one decoy state. First, such a method avoids the modulation of the vacuum state, thus reducing experimental complexity and random number consumption. Moreover, incorporated with low-loss asymmetric Mach-Zehnder interferometers and a real-time polarization calibration technique, we have successfully achieved a higher signature rate, e.g., 0.98 bit/s at 103 km, and to date, a record-breaking, to the best of our knowledge, transmission distance of over 280-km installed fibers. Our work represents a significant step towards real-world applications of QDS.

Experimental demonstration of single-shot quantum and classical signal transmission on single wavelength optical pulse

Advances in highly sensitive detection techniques for classical coherent communication systems have reduced the received signal power requirements to a few photons per bit. At this level one can take advantage of the quantum noise to create secure communication, using continuous variable quantum key distribution (CV-QKD). In this work therefore we embed CV-QKD signals within classical signals and transmit classical data and secure keys simultaneously over 25 km of optical fibre. This is achieved by using a novel coherent displacement state generator, which has the potential for being used in a wide range of quantum optical experiments. This approach removes the need for separate channels for quantum communication systems and allows reduced system bandwidth for a given communications specification. This demonstration therefore demonstrates a way of implementing direct quantum physical layer security within a conventional classical communications system, offering a major advance in term of practical and low cost implementation.

Experimental Demonstration of High-Rate Measurement-Device-Independent Quantum Key Distribution over Asymmetric Channels

Measurement-device-independent quantum key distribution (MDI-QKD) can eliminate all detector side channels and it is practical with current technology. Previous implementations of MDI-QKD all used two symmetric channels with similar losses. However, the secret key rate is severely limited when different channels have different losses. Here we report the results of the first high-rate MDI-QKD experiment over asymmetric channels. By using the recent 7-intensity optimization approach, we demonstrate>10×higher key rate than the previous best-known protocols for MDI-QKD in the situation of large channel asymmetry, and extend the secure transmission distance by more than 20-50 km in standard telecom fiber. The results have moved MDI-QKD towards widespread applications in practical network settings, where the channel losses are asymmetric and user nodes could be dynamically added or deleted.

A New Quantum Blind Signature Scheme with BB84-State

The blind signature is widely used in cryptography applications because it can prevent the signer from gaining the original message. Owing to the unconditional security, the quantum blind signature is more advantageous than the classical one. In this paper, we propose a new provable secure quantum blind signature scheme with the nonorthogonal single-photon BB84-state and provide a new method to encode classical messages into quantum signature states. The message owner injects a randomizing factor into the original message and then strips the blind factor from the quantum blind signature signed by the blind signer. The verifier can validate the quantum signature and announce it publicly. At last, the analytical results show that the proposed scheme satisfies all of the security requirements of the blind signature: blindness, unforgeability, non-repudiation, unlinkability, and traceability. Due to there being no use of quantum entanglement states, the total feasibility and practicability of the scheme are obviously better than the previous ones.

Sending-or-not-sending twin-field quantum key distribution in practice

Recently, the twin field quantum key distribution (TF-QKD) protocols have been investigated extensively. In particular, an efficient protocol for TF-QKD with sending or not sending the coherent state has been given in. Here in this paper, we present results of practical sending-or-not-sending (SNS) twin field quantum key distribution. In real-life implementations, we need consider the following three requirements, a few different intensities rather than infinite number of different intensities, a phase slice of appropriate size rather than infinitely small size and the statistical fluctuations. We first show the decoy-state method with only a few different intensities and a phase slice of appropriate size. We then give a statistical fluctuation analysis for the decoy-state method. Numerical simulation shows that, the performance of our method is comparable to the asymptotic case for which the key size is large enough. Our method can beat the PLOB bound on secret key capacity. Our results show that practical implementations of the SNS quantum key distribution can be both secure and efficient.

Phase self-aligned continuous-variable measurement-device-independent quantum key distribution

Continuous-variable measurement-independent-device quantum key distribution (CV-MDI-QKD) can offer high secure key rate at metropolitan distance and remove all side channel loopholes of detection as well. However, there is no in-field experimental demonstration of CV-MDI-QKD due to the remote distance phase-locking techniques challenge. Here, we present a new optical scheme to overcome this difficulty and also removes the requirement of two identical independent lasers. Furthermore, we give an alternate but detailed proof of the minimized key rate condition to extract the secure key rate. We anticipate that our new scheme can be used to demonstrate the in-field CV-MDI-QKD experiment and build the CV-MDI-QKD network with untrusted source.

Practical quantum digital signature with a gigahertz BB84 quantum key distribution system

Quantum digital signature (QDS) can guarantee message integrity and non-repudiation with information-theoretical security, and it has attracted more attention recently. Since proposed by Andersson et al. [Phys. Rev. A93, 032325 (2016)PLRAAN1050-294710.1103/PhysRevA.93.032325], a quantum digital signature protocol using an insecure channel has been realized with several different quantum key distribution (QKD) systems. Here we report an experimental QDS based on a BB84 QKD system. An asymmetric Faraday-Sagnac-Michelson interferometer structure has been designed in our system, which is intrinsically stable against channel disturbance. The innovatory structure supports the system to work at high speed and, in practice, the repetition rate is in gigahertz. A 0.044 bit/s signature rate has been attained with a 25 dB channel loss composed of a 25 km installed fiber with additional optical attenuation in a 10^-10 security level. Thus, our QDS device is stable and highly efficient. This Letter provides a further step for the practical application of QDS.

Photonic quantum information processing: a review

Photonic quantum technologies represent a promising platform for several applications, ranging from long-distance communications to the simulation of complex phenomena. Indeed, the advantages offered by single photons do make them the candidate of choice for carrying quantum information in a broad variety of areas with a versatile approach. Furthermore, recent technological advances are now enabling first concrete applications of photonic quantum information processing. The goal of this manuscript is to provide the reader with a comprehensive review of the state of the art in this active field, with a due balance between theoretical, experimental and technological results. When more convenient, we will present significant achievements in tables or in schematic figures, in order to convey a global perspective of the several horizons that fall under the name of photonic quantum information.

Measurement-Device-Independent Quantum Key Distribution over asymmetric channel and unstable channel

We show that a high key rate of Measurement-Device-Independent Quantum Key Distribution (MDIQKD) over asymmetric and unstable quantum channel can be obtained by full optimization and compensation. Employing a gradient optimization method, we make the full optimization taking both the global optimization for the 12 independent parameters and the joint constraints for statistical fluctuations. We present a loss-compensation method by monitoring the channel loss for an unstable channel. The numerical simulation shows that the method can produce high key rate for both the asymmetric channel and the unstable channel. Compared with the existing results of independent constraints, our result here improves the key rate by 1 to tens of times in typical experimental conditions.

Large scale quantum key distribution: challenges and solutions [Invited]

Quantum key distribution (QKD) together with one time pad encoding can provide information-theoretical security for communication. Currently, though QKD has been widely deployed in many metropolitan fiber networks, its implementation in a large scale remains experimentally challenging. This letter provides a brief review on the experimental efforts towards the goal of global QKD, including the security of practical QKD with imperfect devices, QKD metropolitan and backbone networks over optical fiber and satellite-based QKD over free space.

Biased three-intensity decoy-state scheme on the measurement-device-independent quantum key distribution using heralded single-photon sources

At present, most of the measurement-device-independent quantum key distributions (MDI-QKD) are based on weak coherent sources and limited in the transmission distance under realistic experimental conditions, e.g., considering the finite-size-key effects. Hence in this paper, we propose a new biased decoy-state scheme using heralded single-photon sources for the three-intensity MDI-QKD, where we prepare the decoy pulses only in X basis and adopt both the collective constraints and joint parameter estimation techniques. Compared with former schemes with WCS or HSPS, after implementing full parameter optimizations, our scheme gives distinct reduced quantum bit error rate in the X basis and thus show excellent performance, especially when the data size is relatively small.