## 2 Related Works  
Ever since [PERSON] et al. [10] brought up the first solution using a private matching mechanism to prevent the leakage of unnecessary information between two parties, a number of authors have subsequently proposed different private matching mechanisms. These mechanisms typically conform to the different requirements of such parties in PM or are the results of fine-tuning to achieve low overhead in terms of computational cost and to enhance the search precision. However, most of these schemes suffer from drawbacks. Keeping this in view, we will present related works pertaining to PM and its drawbacks. Works within the context of image private matching will also be highlighted. The important factors in the field of PM are the protocol of private set union (PSU), [4; 11; 12], and private set intersection (PSI) [10; 13; 14; 15], respectively. [PERSON] et al. [16] revealed that these techniques do not provide adequate privacy on the server end and, thus, a server could compromise privacy. In [16], a scenario is proposed where users are allowed to learn only the magnitude of the shared values instead of the exact values. Such a scenario uses the Private Set Union Cardinality (PSI-CA) and a third-party server. [PERSON] et al. [17] proposed a system to search encrypted images databases stored on a server maintained by a third-party service provider. Under both [16; 17], the server should not know its stored data. Our work obviates the use of any third party for security purposes. [PERSON] et al. [18] applied private information retrieval (PIR) techniques to protect the privacy of the query image when searching over a public database. However, such a method assumes that the database is public when such database is supposed to be private. The proposed methods in [16; 17; 18] are also not suitable for evaluating similarity. These approaches can achieve an exact match, thereby limiting the ability to develop efficient solutions. In [19], [PERSON] et al. proposed a method for private matching using double encryption under the assumption that \(x\in X,E(E^{\prime}(x))=E^{\prime}(E(x))\), where \(E\) is the encryption function. To determine the common elements between two parties, the authors proposed using the crypto-hash function. Initially, such a function should be decided between the parties involved. Thus, this approach encourages a curious party to utilize a brute force attempt using the same hash function to determine uncommon elements over a finite domain of elements. In our work, we avoid the use of any hash function to prevent a curious user from obtaining additional information. The schemes put forward by [PERSON] et al. [20] emphasized secure image search over encrypted datasets and the maintenance of data security, through Min-Hash and order preserving encryption. Their scheme is useful in implementation for an image search process based on bag-of-features (BOF), but has inferior search precision up to 20% compared with those using the Fisher vector as a foundation [21; 22]. Despite the alternative protected search being proposed by [PERSON] et al. [23], offering extended protection and embedding in secure BOF, this proposal greatly reduces the effectiveness of search efficiency when put alongside [20] (see the analysis in [23]). Specifically, to enhance the search precision, [PERSON] et al. [21] implemented the Fisher vector within the search system, and demonstrated that the scheme based on a Fisher vector can achieve better performance compared to schemes based on BOF in terms of search precision. Following [21], developed Fisher vector based image search methods are suggested to further improve search precision in various instances [22]. Under both [21; 22], the Fisher vector was based on scale-invariant feature transform (SIFT), which is used to extract local feature vectors. Our work uses the SURF method that produces fewerlocal features and also can be bettered in terms of feature extraction processing speed [6; 7] compared with the SIFT method used by [21; 22].