Improvement of Quantum Protocols for Secure Multi-Party Summation
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Improvement of Quantum Protocols for Secure Multi-Party Summation Gan Zhi-Gang 1 Received: 3 May 2020 / Accepted: 21 July 2020/ # Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract
Secure multi-party quantum summation is an important branch of secure multi-party quantum computation. Recently, Ji et al. suggested a secure multi-party quantum summation scheme based on the entanglement swapping between the d-level Bell state and the d -level n+1-particle cat state (Quantum Inf Process (2019)18:168). In this paper, it is pointed out that Ji et al.’s secure multi-party quantum summation scheme has a security loophole, i.e., the third party (TP) can obtain the secret numbers of n communicants without being discovered. Then, in order to avoid this security loophole, an improvement is suggested by adopting the method of encrypting the secret integers of n communicants with a pre-shared private key sequence among them. Keywords Secure multi-party quantum summation . Participant attack . Entanglement swapping
PACS 03.67.Dd; 03.67.Hk; 03.67.Pp
1 Introduction In modern cryptography, secure multi-party computation is a fundamental and important problem, and has successfully aroused the intensive interests of researchers. Different from classical secure multi-party computation, whose security is based on the complexity of computation, quantum secure multi-party computation can have the unconditional security in theory, which is relied on the physical principles of quantum mechanics. Secure multi-party quantum summation, which aims to compute the summation of secret inputs from different communicants without leaking out their genuine contents, is an important branch of secure multi-party quantum computation. Until now, several secure multi-party
* Gan Zhi-Gang [email protected]
1
College of Information & Electronic Engineering, Zhejiang Gongshang University, Hangzhou 310018, People’s Republic of China
International Journal of Theoretical Physics
quantum summation schemes [1–10] have been designed from different quantum technologies. For example, Zhang et al. [7] put forward a multi-party quantum summation without a trusted third party based on single particles. Yang and Ye [8] suggested a secure multi-party quantum summation based on quantum Fourier transform. Ji et al. [9] suggested a secure multi-party quantum summation scheme based on the entanglement swapping between the d level Bell state and the d –level n+1-particle cat state. They claim that this scheme is secure against both the outside attack and the participant attack. Duan [10] proposed a multi-party quantum summation within a d -level quantum system based on qudit shifting operation. However, it is pointed out in this paper that Ji et al.’s secure multi-party quantum summation scheme [9] has a security loophole, i.e., the third party (TP) can obtain the secret numbers of n communicants without being discovered. In order to avoid this security loophole, this paper proposes an improvement with the method of encrypting the secret
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