Cryptanalysis and Improvement for the Quantum Private Comparison Protocol Based on Triplet Entangled State and Single-Particle Measurement

Quantum private comparison (QPC) aims to accomplish the equality comparison of secret inputs from two users on the basis of not leaking their contents out. Recently, Chen et al. proposed the QPC protocol based on triplet GHZ state and single-particle measurement (Optics Communications 283, 1561–1565 (2010)). In this paper, they suggested the standard model of a semi-honest third party (TP) for the first time, and declared that their protocol is secure. Subsequently, Lin et al. pointed out that in Chen et al.’s protocol, one user can extract the other user’s secret without being discovered by performing the intercept-resend attack, and suggested two corresponding improvements (Optics Communications 284, 2412–2414 (2011)). However, Yang et al. first pointed out that the model of TP adopted by both Chen et al.’s protocol and Lin et al.’s improved protocols is unreasonable, and thought that a practical TP may also try any possible means to steal the users’ secrets except being corrupted by the adversary including the dishonest user (Quantum Inf Process 12, 877–885 (2013). In this paper, after taking the possible attacks from TP into account, we propose the eavesdropping strategy of TP toward Lin et al.’s improved protocols and suggest two feasible solutions accordingly.     

Intercept-Resend-Measure Attack Towards Quantum Private Comparison Protocol Using Genuine Four-Particle Entangled States and its Improvement

Recently, Jia et al. proposed the quantum private comparison protocol with the genuine four-particle entangled states (Jia et al., Int. J. Theor. Phys. 51(4), 1187–1194 (2012)). Jia et al. claimed that in this protocol, TP cannot obtain Alice and Bob’s secrets and only knows their comparison result. However, in this paper, we demonstrate that if TP is a genuine semi-honest third party, he can totally obtain Alice and Bob’s secrets by launching a particular intercept-resend-measure attack. After suggesting the intercept-resend-measure attack strategy from TP first, we put forward one corresponding improvement to prevent this attack.     

A Protocol for the Quantum Private Comparison of Equality with χ-Type State

We present a new quantum protocol for comparing the equal information with the help of a semi-honest third party (TP). Different from previous protocols, we utilize the four-particle χ-type states as the information carriers. Various kinds of outside attacks and participant attacks are discussed in detail. One party cannot learn the other’s private information. The TP cannot learn any information about the private information, even about the comparison result or the length of secret inputs.     

Semi-Quantum Private Comparison Using Single Photons

Recently, by using the BB84 quantum key distribution (QKD) protocol, Sun et al. put forward two quantum private comparison (QPC) protocols with a semi-honest third party (TP) and a malicious TP, respectively (Sun et al., Quantum Inf. Process. 14, 2125–2133, 2015). In this paper, we absorb the concept of semi-quantumness suggested by Boyer et al. (Phys. Rev. Lett. 99(14), 140501, 2007 and Phys. Rev. A 79(3), 032341, 2009) into Sun et al.’s QPC protocols and construct two corresponding SQPC protocols. The common interesting feature of the proposed SQPC protocols is that apart from the establishment of shared keys between different participants, the rest parts of the protocols are completely classical. The output correctness and the security of the proposed SQPC protocols are validated. Compared with the present SQPC protocols, the advantages of the proposed SQPC protocols lies in the following aspects: on the aspect of quantum resource, they employ single photons rather than Bell entangled states; with respect to quantum measurement for TP, they need single-photon measurements rather than Bell state measurements; as for quantum entanglement swapping, they do not need it at all; and the second proposed SQPC protocol takes effect under a malicious TP and makes TP know neither the genuine contents of secret inputs nor the comparison result.     

Improvements of Quantum Private Comparison Protocol Based on Cluster States

Quantum private comparison aims to determine whether the secrets from two different users are equal or not by utilizing the laws of quantum mechanics. Recently, Sun and Long put forward a quantum private comparison (QPC) protocol by using four-particle cluster states (Int. J. Theor. Phys. 52, 212–218, 2013). In this paper, we investigate this protocol in depth, and suggest the corresponding improvements. Compared with the original protocol, the improved protocol has the following advantages: 1) it can release the requirements of authenticated classical channels and unitary operations; 2) it can prevent the malicious attack from the genuine semi-honest TP; 3) it can enhance the qubit efficiency.     

Secure Quantum Private Comparison of Equality Based on Asymmetric W State

Recently, Liu et al. (Opt. Commun. 284:3160, 2011) proposed a protocol for quantum private comparison of equality (QPCE) based on symmetric W state. However, Li et al. (Eur. Phys. J. D 66:110, 2012) pointed out that there is a flaw of information leak, and they proposed a new protocol based on EPR pairs. While examining these two protocols, we find that there exists a same flaw: the third party (TP) can know the comparison result. In this paper, through introducing and constructing a special class of asymmetric W state, a secure QPCE protocol based on this asymmetric W state is presented. Analysis shows the present protocol can not only effectively avoid the information leak found by Li et al., but also ensure TP would not get any information about the comparison result.     

Cryptanalysis and Improvement of the Semi-quantum Secret Sharing Protocol

Recently, Xie et al. Int. J. Theor. Phys. 54, 3819–3824, (2015) proposed a Semi-quantum secret sharing protocol (SQSS). Yin et al. Int. J. Theor. Phys. 55: 4027–4035, (2016) pointed out that this protocol suffers from the intercept-resend attack. Yin et al. also proposed an improved protocol. However, we find out that Yin et al.’s paper has some problems, we analyze Yin et al.’s paper, then proposed the improved semi-quantum secret sharing protocol. Our protocol is more secure and efficient, most importantly, our protocol satisfies the condition of semi-quantum.     

An efficient protocol for the private comparison of equal information based on the triplet entangled state and single-particle measurement

The central theme of this paper is that we propose an efficient protocol for comparing the equal information with the help of a third party (TP). We assume that TP is semi-honest, i.e., TP executes the protocol loyally, keeps a record of all its intermediate computations and might try to steal the players’ private inputs from the record, but he cannot be corrupted by the adversary. The security of this protocol with respect to various kinds of attacks is discussed. Our protocol utilizes the triplet entangled states and the simple single-particle measurement. The particles carried the secret messages do not be repeatedly transmitted. The players’ messages are divided into many groups. Sometimes, the protocol is already successfully completed, but all data are not compared. Thus, many time and huge quantum resources can be saved.     

Information Leakage in Quantum Secret Sharing of Multi-Bits by an Entangled Six-Qubit State

In a recent paper Long et al. (J. Phys. A: Math. Theor. 45: 195303, 2012), a quantum secret sharing protocol was presented, in which the genuinely maximally entangled six-qubit states were used. According to the protocol, Alice could share three bits among three agents, which showed that it was more efficient than previous protocols. Here, we analyze it and point out that the information about the transmitted secret will be partly leaked out unknowingly. Through the classical public channel, 2/3 of Alice’s secret messages is leaked out to Bob₁ and Bob₂, and 1/3 secret messages is leaked out to Bob₃, respectively. This phenomenon should be strictly forbidden in a quantum secret sharing protocol.     

Quantum Teleportation of an Arbitrary N-qubit State via GHZ-like States

Recently Zhu (Int. J. Theor. Phys. 53, 4095, 2014) had shown that using GHZ-like states as quantum channel, it is possible to teleport an arbitrary unknown two-qubit state. We investigate this channel for the teleportation of an arbitrary N-qubit state. The strict proof through mathematical induction is presented and the rule for the receiver to reconstruct the desired state is explicitly derived in the most general case. We also discuss that if a system of quantum secret sharing of classical message is established, our protocol can be transformed to a N-qubit perfect controlled teleportation scheme from the controller’s point of view.     

Participant Attack and Improvement to Multiparty Quantum Secret Sharing Based on GHZ States

A multiparty quantum secret sharing protocol based on GHZ states was proposed by Hwang et al. (Phys. Scr. 83:045004, 2011). Its major advantage is high efficiency, but soon another paper (Liu and Pan in Phys. Scr. 84:045015, 2011) shown that the protocol is insecure for one dishonest agent and give a improvement of protocol. Here, we analyze the security of both protocols, and point out that both protocols would lead to all the secret information leakage under a special attack, which is different from the attack strategy proposed by the paper (Liu and Pan in Phys. Scr. 84:045015, 2011). Furthermore, we discuss the deep reason of this insecurity, and propose a novel and efficient secure protocol, which keep the important weakness of original protocol free, i.e., correlation-extractability. The security of our scheme is equivalent to that of BB84 protocol.     

Deterministic Secure Quantum Communication and Authentication Protocol based on Extended GHZ-W State and Quantum One-time Pad

A deterministic secure quantum communication and authentication protocol based on extended GHZ-W state and quantum one-time pad is proposed. In the protocol, state |φ^?〉 is used as the carrier. One photon of |φ^?〉 state is sent to Alice, and Alice obtains a random key by measuring photons with bases determined by ID. The information of bases is secret to others except Alice and Bob. Extended GHZ-W states are used as decoy photons, the positions of which in information sequence are encoded with identity string ID of the legal user, and the eavesdropping detection rate reaches 81%. The eavesdropping detection based on extended GHZ-W state combines with authentication and the secret ID ensures the security of the protocol.     

Improved Three-Party Quantum Secret Sharing Based on Bell States

Hwang et al. (Phys. Scr. 83:045004, 2011) proposed a high efficient multiparty quantum secret sharing by using Greenberger-Horne-Zeilinger (GHZ) states. But Liu et al. (Phys. Scr. 84:045015, 2011) analyzed the security of Hwang et al.’s protocol and found that it was insecure for Charlie who might obtain half of information about the dealer’s secret directly. They put forward an improved protocol by adding operation on photons in sequence S ₃. However, we point out Liu et al.’s protocol is not secure too if a dishonest participant Charlie carries out intercept-resend attack. And a further improved quantum secret sharing protocol is proposed based on Bell states in this paper. Our newly proposed protocol can stand against participant attack, provide a higher efficiency in transmission and reduce the complexity of implementation.     

Quantum private comparison of arbitrary single qubit states based on swap test

By using swap test, a quantum private comparison (QPC) protocol of arbitrary single qubit states with a semi-honest third party is proposed. The semi-honest third party (TP) is required to help two participants perform the comparison. She can record intermediate results and do some calculations in the whole process of the protocol execution, but she cannot conspire with any of participants. In the process of comparison, the TP cannot get two participants' private information except the comparison results. According to the security analysis, the proposed protocol can resist both outsider attacks and participants' attacks. Compared with the existing QPC protocols, the proposed one does not require any entanglement swapping technology, but it can compare two participants' qubits by performing swap test, which is easier to implement with current technology. Meanwhile, the proposed protocol can compare secret integers. It encodes secret integers into the amplitude of quantum state rather than transfer them as binary representations, and the encoded quantum state is compared by performing the swap test. Additionally, the proposed QPC protocol is extended to the QPC of arbitrary single qubit states by using multi-qubit swap test.     

Quantum Private Comparison of Equality Based on Five-Particle Cluster State

A protocol for quantum private comparison of equality (QPCE) is proposed based on five-particle cluster state with the help of a semi-honest third party (TP). In our protocol, TP is allowed to misbehave on its own but can not conspire with either of two parties. Compared with most two-user QPCE protocols, our protocol not only can compare two groups of private information (each group has two users) in one execution, but also compare just two private information. Compared with the multi-user QPCE protocol proposed, our protocol is safer with more reasonable assumptions of TP. The qubit efficiency is computed and analyzed. Our protocol can also be generalized to the case of 2N participants with one TP. The 2N-participant protocol can compare two groups (each group has N private information) in one execution or just N private information.     

Quantum Private Comparison of Equality Based on Five-Particle Cluster State

A protocol for quantum private comparison of equality(QPCE) is proposed based on five-particle cluster state with the help of a semi-honest third party(TP). In our protocol, TP is allowed to misbehave on its own but can not conspire with either of two parties. Compared with most two-user QPCE protocols, our protocol not only can compare two groups of private information(each group has two users) in one execution, but also compare just two private information. Compared with the multi-user QPCE protocol proposed, our protocol is safer with more reasonable assumptions of TP. The qubit efficiency is computed and analyzed. Our protocol can also be generalized to the case of 2N participants with one TP. The 2N-participant protocol can compare two groups(each group has N private information)in one execution or just N private information.     

A Generalized Information Theoretical Model for Quantum Secret Sharing

An information theoretical model for quantum secret sharing was introduced by H. Imai et al. (Quantum Inf. Comput. 5(1), 69–80 2005), which was analyzed by quantum information theory. In this paper, we analyze this information theoretical model using the properties of the quantum access structure. By the analysis we propose a generalized model definition for the quantum secret sharing schemes. In our model, there are more quantum access structures which can be realized by our generalized quantum secret sharing schemes than those of the previous one. In addition, we also analyse two kinds of important quantum access structures to illustrate the existence and rationality for the generalized quantum secret sharing schemes and consider the security of the scheme by simple examples.     

Cryptanalysis and Improvement of a Multi-User Quantum Communication Network Using χ-Type Entangled States

The security of a multi-user quantum communication network protocol using χ-type entangled states (Chang et al., J. Korean Phys. Soc. 61:1–5, 2012) is analyzed. We find that, by using one χ-type state in this protocol, two participants can only share 2 bits of information, not 4 bits as the authors stated. In addition, we give a special attack strategy by which an eavesdropper can elicit half of the secret information without being detected. Finally, we improve the protocol to be secure against all the present attacks.     

Improvement of Efficient Multiparty Quantum Secret Sharing Based on Bell States and Continuous Variable Operations

Yuan et al. (Int. J. Theor. Phys. 51:3443, 2012) proposed a multiparty quantum secret sharing protocol using Bell states and continuous variable operations. Zhang and Qin (Int. J. Theor. Phys. 52:3953, 2013) showed that their protocol is not secure. In this paper, we will give an improvement of Yuan et al. protocol. Our improved protocol can stand against not only Zhang et al. attack strategies, but also the other ones efficiently.     

Quantum Private Comparison of Equal Information Based on Highly Entangled Six-Qubit Genuine State

Using the highly entangled six-qubit genuine state we present a quantum private comparison (QPC) protocol, which enables two users to compare the equality of two bits of their secrets in every round comparison with the assistance of a semi-honest third party (TP). The proposed protocol needs neither unitary operations nor quantum entanglement swapping technology, both of which may consume expensive quantum devices. Single particle measurements and Bell-basis measurements, which are easy to implement with current technologies, are employed by two users and TP in the proposed protocol, respectively. The proposed protocol can withstand all kinds of outside attacks and participant attacks. Moreover, none of information about the two users’ private secrets and the comparison result is leaked out to TP.