Abstract In this paper, we put forward a multi-party quantum private comparison (MQPC) protocol with two semi-honest third parties (TPs) by adopting d -dimensional Bell states, which can judge the size relationship of private integers from more than two users within one execution of protocol. Each TP is permitted to misbehave on her own but cannot collude with others. In the proposed MQPC protocol, TPs are only required to apply d -dimensional single-particle measurements rather than d -dimensional Bell state measurements. There are no quantum entanglement swapping and unitary operations required in the proposed MQPC protocol. The security analysis validates that the proposed MQPC protocol can resist both the outside attacks and the participant attacks. The proposed MQPC protocol is adaptive for the case that n users want to compare the size relationship of their private integers under the control of two supervisors. Furthermore, the proposed MQPC protocol can be used in the strange user environment, because there are not any communication and pre-shared key between each pair of users.
Abstract In this paper, we put forward a multi-party quantum private comparison (MQPC) protocol with two semi-honest third parties (TPs) by adopting d -dimensional Bell states, which can judge the size relationship of private integers from more than two users within one execution of protocol. Each TP is permitted to misbehave on her own but cannot collude with others. In the proposed MQPC protocol, TPs are only required to apply d -dimensional single-particle measurements rather than d -dimensional Bell state measurements. There are no quantum entanglement swapping and unitary operations required in the proposed MQPC protocol. The security analysis validates that the proposed MQPC protocol can resist both the outside attacks and the participant attacks. The proposed MQPC protocol is adaptive for the case that n users want to compare the size relationship of their private integers under the control of two supervisors. Furthermore, the proposed MQPC protocol can be used in the strange user environment, because there are not any communication and pre-shared key between each pair of users.
Abstract In this paper, we utilize d-dimensional Bell states to construct a multi-party semiquantum private comparison (MSQPC) protocol with two supervisors, which can determine the size relationship of more than two classical users’ private inputs under the control of two supervisors within one round implementation. The two supervisors, i.e., one quantum third party (TP) and one classical TP, are both semi-honest, which means that they can misbehave at their own wishes but are not permitted to conspire with anyone else. Neither quantum entanglement swapping nor unitary operations are required in the proposed MSQPC protocol. The security analysis certifies that the proposed MSQPC protocol can overcome both the outside attacks and the participant attacks.
A feasible multi-party quantum private comparison (MQPC) protocol based on d -dimensional Bell states was proposed. In the protocol, all participants can independently encrypt their privacies and send them to a semi-honest quantum third party (TP) through authenticated channels. Then, the TP can determine the size relationship among all participants’ privacies without gaining access to the private information. We verified correctness and effectiveness of the proposed protocol with some examples. In addition, compared with other similar protocols, it is not necessary to perform unitary operation on particles and only single-particle measurement is required. Furthermore, the relatively high qubit efficiency is promised. The security analysis verifies that the proposed protocol can counteract external and internal attacks in theory.
In this paper, we propose a novel semiquantum private comparison (SQPC) protocol of the size relationship based on d-level single-particle states. This protocol can compare the size relationship of different privacy messages from two classical users with the help of a semi-honest third party (TP), who is permitted to misbehave on her own, but cannot be in collusion with anyone else. The correctness analysis shows that this protocol can gain correct comparison results. The security analysis results reveal that this protocol can resist some famous outside attacks and participant attacks. This protocol only adopts d-level single-particle states as the initial quantum resource, only requires the TP to perform d-level single-particle measurements, and makes the accurate comparison results inaccessible to the TP. Compared with the only existing SQPC protocol of size relationship (Quantum Inf. Process. 20, 124 (2021)), the proposed protocol has advantages in experimental preparation of initial quantum resource, TP’s experimental measurements, and TP’s knowledge about the comparison results.
Abstract In this paper, we propose two multi-party quantum private comparison protocols based on the properties of the d-dimensional GHZ state. Protocol 1 is designed to compare the equality of multiple participants’ secrets with the help of a semi-honest third party TP. The semi-honest TP will follow the protocol honestly, but he may attempt to learn additional information from the protocol execution. In this protocol, multiple participants encode their secret information into the corresponding particles in turn through unitary operations, thereby achieving the comparison of the equality of their multiple secrets in a single execution. This protocol has a wide range of applications. For example, by combining the basic model framework of this protocol with the Chinese Remainder Theorem, we propose Protocol 2. In this protocol, multiple participants compare the size relationships of their multiple secrets with the help of a semi-honest third party TP. Therefore, based on the same basic model framework, the two protocols proposed in this paper can be applied respectively to the comparison of the equality and the size relationships of multiple participants’ secrets. Importantly, the two protocols do not require pre-shared keys. Security analysis shows that the proposed protocols can resist various attacks, including entangle-measure attack, intercept-resend attack, third party attacks, and participant attacks.
Abstract In this paper, by utilizing d -dimensional single-particle states, three semiquantum cryptography protocols, i.e., the multi-party semiquantum private comparison (MSQPC) protocol, the multi-party semiquantum multiplication (MSQM) protocol and the multi-party semiquantum summation (MSQS) protocol, can be achieved simultaneously under the assistance of two semi-honest quantum third parties (TPs). Here, the proposed MSQPC scheme is the only protocol which is devoted to judging the size relationship of secret integers from more than two semiquantum participants without a pre-shared key. And the proposed MSQM protocol absorbs the innovative concept of semiquantumness into quantum multiplication for the first time, which can calculate the modulo d multiplication of private inputs from more than two semiquantum users. As for the proposed MSQS protocol, it is the only semiquantum summation protocol which aims to accomplish the modulo d addition of more than three semiquantum users’ private integers. Neither quantum entanglement swapping nor unitary operations are necessary in the three proposed protocols. The security analysis verifies in detail that both the external attacks and the internal attacks can be resisted in the three proposed protocols.
In this paper, a novel semiquantum private comparison (SQPC) protocol based on single kind of Bell entangled states is proposed, which allows two classical parties to judge the equality of their private inputs securely and correctly under the help of a semi-honest third party (TP) who possesses complete quantum capabilities. TP is allowed to misbehave on her own but cannot conspire with anyone else. Our protocol does not need to share secret keys among different participants in advance, and needs neither unitary operations nor quantum entanglement swapping. Moreover, our protocol only needs to prepare single kind of Bell entangled states as initial quantum resource. Detailed security analysis turns out that our protocol is secure against various outside and participant attacks. Compared with most of the existing SQPC protocols based on Bell entangled states, our protocol is more feasible in practice.