Quantum Protocols for Private Set Intersection Cardinality and Union Cardinality Based on Entanglement Swapping

Quantum private set intersection cardinality (PSI-CA) and private set union cardinality (PSU-CA) are two specific primitives of classical secure multi-party computation. Because of the appearance of quantum algorithms such as Shor’s algorithm, the secure multi-party computation protocols based on cl...

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Bibliographic Details
Published in:International journal of theoretical physics 2021, Vol.60 (9), p.3514-3528
Main Authors: Wang, Yongli, Hu, Peichu, Xu, Qiuliang
Format: Article
Language:English
Subjects:
Algorithms
Computation
Elementary Particles
Intersections
Mathematical analysis
Mathematical and Computational Physics
Mathematical problems
Physics
Physics and Astronomy
Protocol
Quantum entanglement
Quantum Field Theory
Quantum mechanics
Quantum Physics
Theoretical
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Summary:Quantum private set intersection cardinality (PSI-CA) and private set union cardinality (PSU-CA) are two specific primitives of classical secure multi-party computation. Because of the appearance of quantum algorithms such as Shor’s algorithm, the secure multi-party computation protocols based on classical mathematical problems such as large integer factorization and discrete logarithm have been threatened potentially. Thus, as one of the most powerful resources, quantum mechanics is widely used to construct various secure multi-party computation protocols for the reason that it can provide unconditional security. In this paper, based on entanglement swapping between d -level Bell states and d -level cat states, a quantum protocol is built to perform the calculations of private set intersection cardinality and private set union cardinality. With the help of a semi-honest third party who does not collude with any participant, the proposed protocol can simultaneously calculate intersection cardinality and union cardinality of the private sets held by multiple participants who do not trust each other without revealing the intersection, the union and the sets themselves. The protocol can resist attacks from external, semi-honest TP and participants, even though m − 1 participants collude together ( m is the number of participants). In addition, the algorithm in the protocol is deterministic.
ISSN:0020-7748
1572-9575
DOI:10.1007/s10773-021-04925-7