# Privacy Protection Based on Special Identifiers of Intersection Base Computing Technology
###### Abstract  
Private Set Intersection Cardinality (PSI-CA) and Private Set Union Cardinality (PSU-CA) are two cryptographic primitives whereby two or more parties are able to obtain the cardinalities of the intersection and the union of their respective private sets, and the privacy of their sets is preserved. In this paper, we propose a new privacy protection intersection cardinality protocol, which can quickly deal with set inequality and asymmetry problems and can obtain 100% correct results, and, in terms of efficiency, we are much faster than using the polynomial method. Our protocol adopts the Paillier addition homomorphic encryption scheme and applies the identifier guidance technology, using identifier determination, to the semi-homomorphic encryption ciphertext environment, excluding a large number of different options and quickly finding the base of the intersection of two sides. semi-homomorphic encryption; PSI; MPC; PSI-CA +
Footnote †: journal: Applied  
0000-0001-9999-4000-0000-0000-0000-0000-0000-00000-0000-00000-00000-00000-00000-00000-00000-00000-00000-00000-000000-00000-00000-000000-0  
for many privacy computing scenarios in reality. For example, in a social network, two users can calculate their degree of social compatibility by comparing the proportion of their mutual friends without revealing their specific friends. In health, customers with private genetic data can confidently interact with public risk genetic databases to know their probability of contracting a disease. The purpose of this article is to discuss the related protocols for solving the PSI-CA/PSU-CA problem. In general, all privacy computing problems can theoretically be solved with common secure computing protocols (e.g., GMW protocol [1], obfuscated circuit [2]).But these generic schemes require high computing and communication costs. Therefore, for specific secure computing problems, we usually use dedicated efficient protocols. Specifically, for solving the PSI-CA/PSU-CA problem, from the accuracy of the output results to classify, we can be divided into the following two categories. 1. The first type of protocol is the perfect computation protocol, which outputs accurate results. Taking the work in literature [3; 4; 5; 6; 7; 8] as an example, it uses the evaluation method of fuzzy polynomials, selects a polynomial to represent the input set, and combines the intersection of the evaluation set using homomorphic encryption technology. 2. The second type of protocol is the imperfect calculation protocol, and the output result of the protocol [9; 10] allows a certain amount of error. When faced with a small amount of data, it is often difficult to strike a good balance between efficiency and availability with this type of protocol, and it is often abandoned because of the large errors. **Our contribution:**  
Although imperfect computing protocols have good applications in many application scenarios, imperfect protocols tend to perform particularly poorly for certain small data sets, because in the case of small data sets, imperfect computing protocols may lead to consistent matching errors at a certain probability, so as to completely affect the final results. The efficiency gap between an imperfect protocol and a perfect protocol is not particularly obvious, but the accuracy is obviously different. Therefore, this paper constructs a class of perfect computing protocol for small data sets. Our contributions are as follows:  
1. We propose a new privacy protection intersection cardinality protocol, and this protocol can quickly obtain the union of both sides. 2. This protocol has extremely strong compatibility for the intersection of two sets of elements, it can accept any type of data, without knowing any information from either side, and can be 100% accurate in calculating the intersection base of both privacy sets. 3. The protocol only needs two rounds of communication to complete, and the efficiency in the offline phase is much better than for the polynomial intersection cardinality protocol.