Ping-pong Protocol Research Articles

Security of a High Dimensional Two‐Way Quantum Key Distribution Protocol

AbstractTwo‐way quantum key distribution (QKD) protocols utilize bi‐directional quantum communication to establish a shared secret key. Due to the increased attack surface, security analyses remain challenging. Here a high‐dimensional variant of the Ping Pong protocol is investigated and an information theoretic security analysis in the finite‐key setting is performed. The main contribution in this work is to show a new proof methodology for two‐way quantum key distribution protocols based on the quantum sampling framework of Bouman and Fehr introduced in 2010 and also sampling‐based entropic uncertainty relations introduced by the authors in 2019. The Ping Pong protocol is only investigated here, but these methods may be broadly applicable to other QKD protocols, especially those relying on two‐way channels. Along the way, some fascinating benefits to high‐dimensional quantum states applied to two‐way quantum communication are also showed.

Ping-pong quantum key distribution with trusted noise: non-Markovian advantage

The ping-pong protocol adapted for quantum key distribution is studied in the trusted quantum noise scenario, wherein the legitimate parties can add noise locally. For a well-studied attack model, we show how non-unital quantum non-Markovianity of the added noise can improve the key rate. We also point out that this noise-induced advantage cannot be obtained by Alice and Bob by adding local classical noise to their post-measurement data.

An Improved Ping-Pong Protocol Using Three-Qubit Nonmaximally Nonorthogonal Entangled States

Abstract We analyse the ping-pong (PP) protocol [K. Bostrom and T. Felbinger, Phys. Rev. Lett. 89, 187902 (2002)] using different sets of partially entangled three-qubit states. Interestingly, our results show that the partially entangled nonorthogonal three-qubit states are more useful as resources in comparison to three-qubit maximally entangled Greenberger–Horne–Zeilinger (GHZ) states. The properties of orthogonal set of partially entangled states as resources for PP protocol, however, are similar to that of maximally entangled GHZ states – both the states are not preferable due to the vulnerability towards eavesdropping. On the other hand, partially entangled nonorthogonal basis set holds importance for transferring two-bit information, one each from a sender, to a single receiver. The protocol is further analysed for various eavesdropping attacks, and the results are compared with the use of two shared Bell pairs for two-bit information transfer. Surprisingly, the use of partially entangled nonorthogonal set of states is found to offer better qubit efficiency and increased security, as against the use of two separate maximally entangled Bell states with orthogonal basis. In addition, we also propose a mixed-state sharing protocol to further enhance the security of the PP protocol.

Ping-pong protocol based on the orbital angular momentum of light

Orbital angular momentum (OAM) is one of the photon’s degrees of freedom in infinite-dimensional Hilbert space. In this paper, we use this photon property to propose a modified version of the deterministic two-way quantum key distribution protocol, known as ping-pong protocol, based on the OAM of light. The advantage of the protocol is that it does not require Bell measurement for decoding the information being transmitted, which makes the protocol more flexible and feasible for practical applications. We propose an implementation setup and show how the channel capacity of the protocol can be easily increased. The security of the protocol is analyzed and the probability of detecting Eve in a general incoherent attack is obtained.

Decoherence can help quantum cryptographic security

In quantum key distribution, one conservatively assumes that the eavesdropper Eve is restricted only by physical laws, whereas the legitimate parties, namely the sender Alice and receiver Bob, are subject to realistic constraints, such as noise due to environment-induced decoherence. In practice, Eve too may be bound by the limits imposed by noise, which can give rise to the possibility that decoherence works to the advantage of the legitimate parties. A particular scenario of this type is one where Eve can't replace the noisy communication channel with an ideal one, but her eavesdropping channel itself remains noiseless. Here, we point out such a situation, where the security of the Ping-Pong protocol (modified to a key distribution scheme) against a noise-restricted adversary improves under a non-unital noisy channel, but deteriorates under unital channels. This highlights the surprising fact that, contrary to the conventional expectation, noise can be helpful to quantum information processing. Furthermore, we point out that the measurement outcome data in the context of the non-unital channel can't be simulated by classical noise locally added by the legitimate users.

An Experiment in Ping-Pong Protocol Verification by Nondeterministic Pushdown Automata

An experiment is described that confirms the security of a well-studied class of cryptographic protocols (Dolev-Yao intruder model) can be verified by two-way nondeterministic pushdown automata (2NPDA). A nondeterministic pushdown program checks whether the intersection of a regular language (the protocol to verify) and a given Dyck language containing all canceling words is empty. If it is not, an intruder can reveal secret messages sent between trusted users. The verification is guaranteed to terminate in cubic time at most on a 2NPDA-simulator. The interpretive approach used in this experiment simplifies the verification, by separating the nondeterministic pushdown logic and program control, and makes it more predictable. We describe the interpretive approach and the known transformational solutions, and show they share interesting features. Also noteworthy is how abstract results from automata theory can solve practical problems by programming language means.

Game-theoretic perspective of Ping-Pong protocol

We analyse Ping-Pong protocol from the point of view of a game. The analysis helps us in understanding the different strategies of a sender and an eavesdropper to gain the maximum payoff in the game. The study presented here characterizes strategies that lead to different Nash equilibriums. We further demonstrate the condition for Pareto optimality depending on the parameters used in the game. Moreover, we also analysed LM05 protocol and compared it with PP protocol from the point of view of a generic two-way QKD game with or without entanglement. Our results provide a deeper understanding of general two-way QKD protocols in terms of the security and payoffs of different stakeholders in the protocol.

Quantum secret sharing protocol with communication channel checking

The new quantum protocol of secret sharing between two subjects, which is based on the ping-pong protocol of quantum secure direct communication, is proposed. This protocol is based on scheme of transmission of the qubits by blocks, which is well known from publications. However, in contrast to this scheme in the proposed protocol the data transmission in a random way alternates with channel check on eavesdropping. Thereby the need for periodic storage of considerable number of qubits disappears. It will let to implement the procedure of secret sharing with assisting state-of-the-art technology of quantum information science. The proposed secret sharing protocol, which also uses the earlier developed by co-author the method of enhancement of the ping-pong protocols security, provides the high level of security to the outer malefactor’s eavesdropping attack. It is the advantage of this protocol over the appropriate classical (non-quantum) schemes.

Eavesdropping on quantum secure direct communication in quantum channels with arbitrarily low loss rate

Quantum attacks that provide an undetectable eavesdropping of the ping-pong protocol operating over lossy quantum channels have already been demonstrated by Wojcik (Phys Rev Lett 90(15):157901, 2003) and Zhang et al. (Phys Lett A 333(12):46---50, 2004). These attacks provide a maximum information gain of 0.311 bits per protocol cycle as long as the induced loss rate remains acceptable. Otherwise, the skipping of some protocol cycles is advised to stay within an accepted loss limit. Such policy leads to a reduction in information gain proportional to the number of skipped cycles. The attack transformation parametrized by the induced loss ratio is proposed. It provides smaller reduction in information gain when the losses accepted by the communicating parties are too low to mount the most effective attack. Other properties of the attack remain the same.

A General Scheme for Information Interception in the Ping-Pong Protocol

The existence of undetectable eavesdropping of dense coded information has been already demonstrated by Pavičić for the quantum direct communication based on the ping-pong paradigm. However, (a) the explicit scheme of the circuit is only given and no design rules are provided; (b) the existence of losses is implicitly assumed; (c) the attack has been formulated against qubit based protocol only and it is not clear whether it can be adapted to higher dimensional systems. These deficiencies are removed in the presented contribution. A new generic eavesdropping scheme built on a firm theoretical background is proposed. In contrast to the previous approach, it does not refer to the properties of the vacuum state, so it is fully consistent with the absence of losses assumption. Moreover, the scheme applies to the communication paradigm based on signal particles of any dimensionality. It is also shown that some well known attacks are special cases of the proposed scheme.

Quantum direct communication protocol strengthening against Pavičić’s attack

A quantum circuit providing an undetectable eavesdropping of information in message mode, which compromises all two-state [Formula: see text]-[Formula: see text] quantum direct communication (QDC) protocols, has been recently proposed by Pavičić [Phys. Rev. A 87 (2013) 042326]. A modification of the protocol’s control mode is proposed, which improves users’ 25% detection probability of Eve to 50% at best, as that in ping-pong protocol. The modification also improves the detection probability of Wójcik’s attack [Phys. Rev. Lett 90 (2003) 157901] to 75% at best. The resistance against man-in-the-middle (MITM) attack as well as the discussion of security for four Bell state protocols is presented. As a result, the protocol security is strengthened both theoretically and practically, and quantum advantage of superdense coding is restored.

An improved control mode for the ping-pong protocol operation in imperfect quantum channels

Quantum direct communication (QDC) can bring confidentiality of sensitive information without any encryption. A ping-pong protocol, a well-known example of entanglement-based QDC, offers asymptotic security in a perfect quantum channel. However, it has been shown (Wójcik in Phys Rev Lett 90(15):157901, 2003. doi: 10.1103/PhysRevLett.90.157901 ) that it is not secure in the presence of losses. Moreover, legitimate parities cannot rely on dense information coding due to possible undetectable eavesdropping even in the perfect setting (Pavičić in Phys Rev A 87(4):042326, 2013. doi: 10.1103/PhysRevA.87.042326 ). We have identified the source of the above-mentioned weaknesses in the incomplete check of the EPR pair coherence. We propose an improved version of the control mode, and we discuss its relation to the already-known attacks that undermine the QDC security. It follows that the new control mode detects these attacks with high probability and independently on a quantum channel type. As a result, an asymptotic security of the QDC communication can be maintained for imperfect quantum channels, also in the regime of dense information coding.

Robust quantum secure direct communication and authentication protocol against decoherence noise based on six-qubit DF state**Project supported by the National Natural Science Foundation of China (Grant No. 61402058), the Science and Technology Support Project of Sichuan Province of China (Grant No. 2013GZX0137), the Fund for Young Persons Project of Sichuan Province of China (Grant No. 12ZB017), and the Foundation of

By using six-qubit decoherence-free (DF) states as quantum carriers and decoy states, a robust quantum secure direct communication and authentication (QSDCA) protocol against decoherence noise is proposed. Four six-qubit DF states are used in the process of secret transmission, however only the |0′⟩ state is prepared. The other three six-qubit DF states can be obtained by permuting the outputs of the setup for |0′⟩. By using the |0′⟩ state as the decoy state, the detection rate and the qubit error rate reach 81.3%, and they will not change with the noise level. The stability and security are much higher than those of the ping–pong protocol both in an ideal scenario and a decoherence noise scenario. Even if the eavesdropper measures several qubits, exploiting the coherent relationship between these qubits, she can gain one bit of secret information with probability 0.042.

Consistent eavesdropping attack of two eavesdroppers on the ping-pong protocol with GHZ-triplets of qubits

In this paper has been analyzed the eavesdropping attackof two eavesdroppers on the ping-pong protocol withthree-qubit entangled Greenberger – Horne – Zeilingerstates. The expression for probability of attack detectionby legitimate users at attack of two eavesdroppers dependingon probabilities of detection them attacks separatelyare obtained. It is shown that an increase in thenumber of attackers in the quantum channel leads to anincrease in the probability of detecting these attacks bylegitimate users. The expressions for the maximum eavesdroppers'amount of information during a consistentattack of two eavesdroppers on the ping-pong protocolwith GHZ-triplets are obtained. It is indicated that themaximum eavesdroppers' amount of information determinedby the same expression as in the case of oneeavesdropper's attack, only the expression for the probabilityof attack detection is changed. It is shown that theping-pong protocol with GHZ-triplets is vulnerable toeavesdropping attack of two eavesdroppers not morethan to one eavesdropper's attack. It is shown that resultsof paper could be extend to the ping-pong protocols withn-qubit GHZ-states at any n.

Stacks of quantum cryptography protocols

In the paper the stack of protocols of quantum key distribution, based on the protocol with single qubits transmission (ВВ84 protocol), is in details analysed. Based on this analysis the full protocols stack of quantum secure direct communication on a basis of the ping-pong protocol is developed. The developed stack includes such basic protocols: privacy amplification, error correction coding, and quantum information transfer. At the same time developed stack of protocols of quantum secure communication is suitable at use of any variant of the ping-pong protocol as the base. The basic differences between stacks of protocols of quantum key distribution and quantum secure direct communication, which are caused by different purpose of these protocols, different types of the transferred information and accordingly different requirements to their security are considered.

Security of modified Ping-Pong protocol in noisy and lossy channel.

The “Ping-Pong” (PP) protocol is a two-way quantum key protocol based on entanglement. In this protocol, Bob prepares one maximally entangled pair of qubits, and sends one qubit to Alice. Then, Alice performs some necessary operations on this qubit and sends it back to Bob. Although this protocol was proposed in 2002, its security in the noisy and lossy channel has not been proven. In this report, we add a simple and experimentally feasible modification to the original PP protocol, and prove the security of this modified PP protocol against collective attacks when the noisy and lossy channel is taken into account. Simulation results show that our protocol is practical.

Single-Photon Secure Quantum Dialogue Protocol Without Information Leakage

Combining the idea of ping-pong protocol with Controlled-NOT operation, we propose a secure quantum dialogue protocol based on single-photonss. Bob obtains the information of the encrypted quantum state by performing Controlled-NOT operation on the auxiliary particle and the encrypted single-photonss. Unlike the previous quantum dialogue protocols based on single-photonss, the proposed protocol not only overcomes information leakage but also possesses an acceptable efficiency.

A quantum secure direct communication protocol based on four-qubit cluster state

We propose a quantum secure direct communication protocol utilizing four-qubit cluster state to enhance the efficiency of eavesdropping detection. In the security analysis, by applying the method of the entropy theory, we contrast our scheme to another two strategies, the Ping-pong protocol and the protocol using two particles of Einstein-Podolsky-Rosen pair as detection particles. The comparison results show that if the eavesdropper obtains the same amount of information, the presented quantum protocol strategy will have a larger detection probability than the other two. At last, the security of the proposed protocol is discussed. The analysis results indicate that the protocol in this paper is more secure. Copyright © 2013 John Wiley & Sons, Ltd.

Analyses of the consistent eavesdropping attack of several eavesdroppers on the ping-pong protocol with entangled pairs of qubits

In this paper the analyses of the eavesdropping attack of two or more eavesdroppers on the original ping-pong protocol with entangled pairs of qubits is carried out. General recursive expression for probability d of attack detection for any number n of eavesdroppers that allows to calculate this probability through the corresponding probability when n – 1 eavesdroppers attack is obtained. It is shown that an increase in the number of attackers in the quantum channel leads to an increase in the probability of detecting these attacks by legitimate users. The expressions for the maximum eavesdroppers' amount of information during a consistent attack of two and three eavesdroppers are obtained. It is indicated that the maximum eavesdroppers' amount of information determined by the same expression as in the case of one eavesdropper's attack, only the value of d is varying. It is shown that the ping-pong protocol with pairs of entangled qubits is vulnerable to eavesdropping attack of several eavesdroppers not more than to one eavesdropper's attack.

SECURITY ENHANCED DIRECT QUANTUM COMMUNICATION WITH HIGHER BIT-RATE

A scheme for deterministic secure direct communication based on ping-pong protocol without restricting the security control only to a distinct control mode and debate via classical channel is proposed. It utilizes an entangled pair of qubits and presents a higher bit-rate transfer of information together with a higher security than ping-pong protocol. The security of protocol is enhanced by introducing a control factor for each message mode. It is explicitly showed that the protocol has a high degree of security against a class of individual attacks, and successfully resolves the famous Wojcik attack.