Key rate of quantum key distribution with hashed two-way classical communication

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.

Covert communication methods are used in the communication with high security level. When it turns to quantum communication, covertness is also an important concern which is firstly discussed by Arrazola and Scarani (Phys Rev Lett, 117:250503, 2016). To make quantum key distribution (QKD) protocol more suitable in the scenarios need high security, we propose a covert QKD protocol with decoy-state method in this paper. The secure key rate and covertness of the covert decoy-state QKD are proved. We compare the performance of the covert decoy-state QKD with those of the original decoy-state QKD and covert QKD without decoy states in numerical simulations. It shows that (1) the covert decoy-state QKD can have a performance comparable to the original decoy-state QKD protocol besides its covertness; (2) the covert decoy-state QKD can have a considerable improvement of transmission distance over covert QKD without decoy states at the cost of a small change of covertness parameter. Furthermore, the statistical fluctuation due to the finite length of data is also taken into account based on the Gaussian analysis method.

Most quantum communications are resilient against eavesdropping attacks. But most protocols fail to address the problems of the poor rates of data transmission and key generation with the constraints of transmission distance and misattribution errors. To address these issues, we propose a new round-robin-differential-phase-shift (RRDPS) quantum key distribution (QKD) protocol to improve the transmission and key generation rates, secure transmission distance and misattribution errors. The new protocol named WDM-OAM-MDI-RRDPS QKD protocol is based on a combination of the wavelength division multiplexing (WDM) technique, Fibonacci-valued orbital angular momentum (OAM) theory, decoy state and measurement-device independent (MDI) method. It utilizes a series of coherent weak sources simultaneously and high-capacity Fibonacci-valued encoding technology. In our protocol, WDM technology can greatly increase the amount of information transmitted in optical fiber communication, and improve the transmission efficiency, the total secure bit rate and the key generation rate of QKD. The OAM theory can achieve basis independence and increase the information capacity per photon from one to five. Fibonacci-valued OAM states can be used to reduce misattribution errors. The decoy state and MDI method can be used to increase the transmission distance resilient to the Photon-number-splitting and detector blinding attacks.

Relativistic quantum key distribution (QKD) protocol is a kind of modified BB84 QKD protocol based on the principles of not only quantum mechanics but also special relativity. Its advantage compared with BB84 protocol is that all of the qubits could be used for key generation, and Alice and Bob are able to select any measuring bases. We prove its unconditional security against coherent attack via the method based on CSS codes: begin with a modified EPR based protocol which can be proved unconditionally secure, then reduce the protocol to a CSS codes based protocol. Finally, the CSS codes based protocol is demonstrated equivalent to the relativistic QKD protocol, and we arrived at the conclusion of the unconditional security of the final key.

Quantum key distribution (QKD) protocols aim at allowing two parties to generate a secret shared key. While many QKD protocols have been proven unconditionally secure in theory, practical security analyses of experimental QKD implementations typically do not take into account all possible loopholes, and practical devices are still not fully characterized for obtaining tight and realistic key rates. We present a simple method of computing secure key rates for any practical implementation of discrete-variable QKD (which can also apply to measurement-device-independent QKD), initially in the single-qubit lossless regime, and we rigorously prove its unconditional security against any possible attack. We hope our method becomes one of the standard tools used for analysing, benchmarking, and standardizing all practical realizations of QKD.

<sec>Measurement-device-independent quantum key distribution (MDI-QKD) protocol can effectively resist all possible attacks targeting the measurement devices in a quantum key distribution (QKD) system, thus exhibiting high security. However, due to the protocol’s high sensitivity to channel attenuation, its key generation rate and transmission distance are significantly limited in practical applications.</sec><sec>To improve the performance of MDI-QKD, researchers have proposed quantum-memory (QM)-assisted MDI-QKD protocol, which has enhanced the protocol's performance to a certain extent. Nevertheless, under finite-size conditions where the total number of transmitted pulses is limited, accurately estimating the relevant statistical parameters is still a challenge. As a result, existing QM-assisted MDI-QKD schemes still encounters issues such as low key rates and limited secure transmission distances.</sec><sec>To solve these problems, this work proposes a novel improved finite-size QM-assisted MDI-QKD protocol. By utilizing quantum memories to temporarily store early-arriving pulses and release them synchronously, the protocol effectively reduces the influence caused by channel asymmetry. Additionally, the protocol introduces a four-intensity decoy-state method to improve the estimation accuracy of single-photon components. Meanwhile, to mitigate the influence of finite-length effects on QM schemes, the proposed protocol combines a collective constraint model and a double-scanning algorithm to jointly estimate scanning error counts and vacuum-related counts. This approach enhances the estimation accuracy of the single-photon detection rate and phase error rate under finite-size conditions, thereby significantly improving the secure key rate of the MDI-QKD system.</sec><sec>Simulation results show that under the same experimental conditions, compared with the existing QM-assisted three-intensity decoy-state MDI-QKD protocol and the four-intensity decoy-state MDI-QKD protocol based on Heralded Single-photon Source (HSPS), the proposed protocol extends the secure transmission distance by more than 30 km and 100 km, respectively. This proves that under the same parameter settings, the proposed scheme exhibits significant advantages in both key rate and secure transmission distance. Therefore, this research provides important theoretical references and valuable benchmarks for developing long-distance, high-security quantum communication networks.</sec>

Genetic Algorithm (GA) may be used to analyses the security of Quantum Key Distribution (QKD) protocols. It evaluates on multiple QKD protocol such as, comparing it to known bounds and also discovering new results. It also shows how it can be used to analyze the security of complicated QKD protocols requiring the adversary to interact with the users. It may also be used to detect security flaws in protocols. This algorithm can be a useful tool in QKD research and design. The genetic algorithm can be used to analyses the security of the quantum cryptographic protocols. This paper handles the different types of attacks like photon loss and multi-photon attacks. Analysis can be done on these protocols namely BB84, B92, SARGO4, Semi-Quantum protocol, Mediated Semi-Quantum protocols. The attacks can be handled by using genetic algorithm is the main intention of this work.

The security of quantum communication using a weak coherent source requires\nan accurate knowledge of the source's mean photon number. Finite calibration\nprecision or an active manipulation by an attacker may cause the actual emitted\nphoton number to deviate from the known value. We model effects of this\ndeviation on the security of three quantum communication protocols: the\nBennett-Brassard 1984 (BB84) quantum key distribution (QKD) protocol without\ndecoy states, Scarani-Acin-Ribordy-Gisin 2004 (SARG04) QKD protocol, and a\ncoin-tossing protocol. For QKD, we model both a strong attack using technology\npossible in principle, and a realistic attack bounded by today's technology. To\nmaintain the mean photon number in two-way systems, such as plug-and-play and\nrelativistic quantum cryptography schemes, bright pulse energy incoming from\nthe communication channel must be monitored. Implementation of a monitoring\ndetector has largely been ignored so far, except for ID Quantique's commercial\nQKD system Clavis2. We scrutinize this implementation for security problems,\nand show that designing a hack-proof pulse-energy-measuring detector is far\nfrom trivial. Indeed the first implementation has three serious flaws confirmed\nexperimentally, each of which may be exploited in a cleverly constructed\nTrojan-horse attack. We discuss requirements for a loophole-free implementation\nof the monitoring detector.\n

Quantum key distribution (QKD) protocols allow for information theoretically secure distribution of (classical) cryptographic key material. However, due to practical limitations the performance of QKD implementations is somewhat restricted. For this reason, it is crucial to find optimal protocol parameters, while guaranteeing information theoretic security. The performance of a QKD implementation is determined by the tightness of the underlying security analysis. In particular, the security analyses determines the key-rate, i.e., the amount of cryptographic key material that can be distributed per time unit. Nowadays, the security analyses of various QKD protocols are well understood. It is known that optimal protocol parameters, such as the number of decoy states and their intensities, can be found by solving a nonlinear optimization problem. The complexity of this optimization problem is typically handled by making a number of heuristic assumptions. For instance, the number of decoy states is restricted to only one or two, with one of the decoy intensities set to a fixed value, and vacuum states are ignored as they are assumed to contribute only marginally to the secure key-rate. These assumptions simplify the optimization problem and reduce the size of search space significantly. However, they also cause the security analysis to be non-tight, and thereby result in sub-optimal performance. In this work, we follow a more rigorous approach using both linear and nonlinear programs describing the optimization problem. Our approach, focusing on the decoy-state BB84 protocol, allows heuristic assumptions to be omitted, and therefore results in a tighter security analysis with better protocol parameters. We show an improved performance for the decoy-state BB84 QKD protocol, demonstrating that the heuristic assumptions typically made are too restrictive. Moreover, our improved optimization frameworks shows that the complexity of the performance optimization problem can also be handled without making heuristic assumptions, even with limited computational resources available.

Shor and Preskill (see Phys. Rev. Lett., vol.85, p.441, 2000) have provided a simple proof of security of the standard quantum key distribution scheme by Bennett and Brassard (1984) by demonstrating a connection between key distribution and entanglement purification protocols (EPPs) with one-way communications. Here, we provide proofs of security of standard quantum key distribution schemes, Bennett and Brassard and the six-state scheme, against the most general attack, by using the techniques of two-way entanglement purification. We demonstrate clearly the advantage of classical post-processing with two-way classical communications over classical post-processing with only one-way classical communications in quantum key distribution (QKD). This is done by the explicit construction of a new protocol for (the error correction/detection and privacy amplification of) Bennett and Brassard that can tolerate a bit error rate of up to 18.9%, which is higher than what any Bennett and Brassard scheme with only one-way classical communications can possibly tolerate. Moreover, we demonstrate the advantage of the six-state scheme over Bennett and Brassard by showing that the six-state scheme can strictly tolerate a higher bit error rate than Bennett and Brassard. In particular, our six-state protocol can tolerate a bit error rate of 26.4%, which is higher than the upper bound of 25% bit error rate for any secure Bennett and Brassard protocol. Consequently, our protocols may allow higher key generation rate and remain secure over longer distances than previous protocols. Our investigation suggests that two-way entanglement purification is a useful tool in the study of advantage distillation, error correction, and privacy amplification protocols.

The twin-field quantum key distribution (TF-QKD) protocol and its variants can overcome the well-known rate-loss bound without quantum repeaters, which have attracted significant attention. Generally, to ensure the security of these protocols, weak coherent states with continuous randomized phases are always assumed in the test mode. However, this assumption is difficult to meet in practice. To bridge the gap between theory and practice, we propose two alternative discrete-phase-randomized (DPR)-twin-field quantum key distribution protocols, which remove the phase sifting procedure in the code mode. Simulation results show that when compared with previous discrete-phase-randomized-twin-field quantum key distribution protocols, our modified protocols can significantly improve the secret key rate in the low channel loss range, which is very promising for practical twin-field quantum key distribution systems.

Measurement-device-independent quantum key distribution (MDI-QKD) protocol has been demonstrated as a viable solution to detector side-channel attacks. One of the main advantages of MDI-QKD is that the security can be proved without making any assumptions about how the measurement device works. The price to pay is the relatively low secure key rate comparing with conventional quantum key distribution (QKD), such as the decoy-state BB84 protocol. Recently a new QKD protocol, aiming at bridging the strong security of MDI-QKD with the high efficiency of conventional QKD, has been proposed. In this protocol, the legitimate receiver employs a trusted linear optics network to encode information on photons received from an insecure quantum channel, and then performs a Bell state measurement (BSM) using untrusted detectors. One crucial assumption made in most of these studies is that the untrusted BSM located inside the receiver's laboratory cannot send any unwanted information to the outside. Here, we show that if the BSM is completely untrusted, a simple scheme would allow the BSM to send information to the outside. Combined with Trojan horse attacks, this scheme could allow Eve to gain information of the quantum key without being detected. To prevent the above attack, either countermeasures to Trojan horse attacks or some trustworthiness to the "untrusted" BSM device is required.

We propose a quantum key distribution (QKD) protocol that is carried out in an indefinite causal order (ICO). In QKD, one considers a setup in which two parties, Alice and Bob, share a key with one another in such a way that they can detect whether an eavesdropper, Eve, has learnt anything about the key. To our knowledge, in all QKD protocols proposed until now, Eve is detected by publicly comparing a subset of Alice and Bob’s key and checking for errors. We find that a consequence of our protocol is that it is possible to detect eavesdroppers without publicly comparing any information about the key. Indeed, we prove that it is not possible for eavesdroppers, performing any individual attack, to extract useful information about the shared key without inducing a nonzero probability of being detected. We also prove the security of this protocol against a class of individual eavesdropping attacks. The role ICO plays in causing unusual phenomena in quantum technologies is an important question. By considering it we find a two-way QKD protocol that exhibits a similar private detection feature, albeit with some interesting differences. After noting some implications of these differences and discussing some of the practicalities of our protocol, we conclude that this work is best considered as a first step in applying quantum cryptographic ideas in an ICO.

We prove the unconditional security of a quantum key distribution (QKD) protocol on a noisy channel against the most general attack allowed by quantum physics. We use the fact that in a previous paper we have reduced the proof of the unconditionally security of this QKD protocol to a proof that a corresponding Quantum String Oblivious Transfer (String-QOT) protocol would be unconditionally secure against Bob if implemented on top of an unconditionally secure bit commitment scheme. We prove a lemma that extends a security proof given by Yao for a (one bit) QOT protocol to this String-QOT protocol. This result and the reduction mentioned above implies the unconditional security of our QKD protocol despite our previous proof that unconditionally secure bit commitment schemes are impossible.

We consider a continuous-variable (CV) quantum key distribution (QKD) protocol over free-space channels, which is simpler and more robust than typical CV QKD protocols. It uses a bright laser, squeezed and modulated in the amplitude quadrature, and self-homodyne detection. We consider a scenario, where the line of sight is classically monitored to detect active eavesdroppers, so that we can assume a passive eavesdropper. Under this assumption, we analyze security of the QKD protocol in the composable finite-size regime. Proper modulation of the squeezed laser to the shot-noise level can completely eliminate information leakage to the eavesdropper and also eliminate the turbulence-induced noise of the channel in the amplitude quadrature. Under these conditions, estimation of the eavesdropper's information is no longer required. The protocol is extremely robust to modulation noise and highly loss-tolerant, which makes it a promising candidate for satellite-based continuous-variable quantum communication.