## 1 Introduction  
The recent explosion of the World Wide Web and increasing interest from various multimedia fields has seen a concurrent significant elevation of the importance of digital images. The increased requirements placed on efficient private image matching (PIM) techniques in various applications interacting with reality have coincided with this. These applications may include social media [1,2] business community [3], e-health [4], and criminal suspect identification, etc. In the context of private image retrieval, similar images are usually brought together such that similar images can be retrieved efficiently once a query image is sent. In general, the PIM method refers to a process whereby a pair of parties determines their common matching values or similarities, whilst maintaining privacy for their own data. Hence, PIM only requires the magnitude of similarity, rather, content similarity. According to [5], private matching (PM) can be classified into three scenarios. In the first scenario, the parties involved, namely _[PERSON]_ and _[PERSON]_, must both learn the final results of PM as a result of the so-called symmetric PM. The second scenario involves a non-symmetric PM where only one party learns if a commonality of values exists. The third scenario seeks to determine the number of common elements rather than whether values match exactly. All of these requirements have been met and addressed using different PM protocols. We employ the second scenario in a secure manner to meet the requirements of actual security applications. Simply stated, in some cases, protecting the privacy of images during the matching process is necessary. Consider the following example to determine the importance of a security issue. Suppose a security agency is searching for data related to a potential terrorist suspect. The agency may wish to check whether images related to the suspect can be found in local police databases. However, for security purposes, neither the agency nor the local police want to reveal their images unless a need to share exists. One way to identify such a need is to detect similarities between the agency's query (in the form of images) and the local police's image collections. Once the need for sharing information is verified, the agency and local police can exchange only shared information. During the process of identifying similar images, the best choice for both parties is to not disclose the query image and the database, and have the former learn only of the existence of any commonality of image matching values (second scenario). Specifically, in image matching cases used for searching an image related to terrorist suspects, the effectiveness of a security agency may be reliant on the speed and accuracy with which a process of finding a matching image can be undertaken. The timeliness and accuracy with which such a security agency may acquire this information can have real-world effects. For this reason, it is important that a robust and fast system be constructed to secure and quickly scan sizable amounts of data, which is as effective and complex as images' plaintext searches. Such a process is referred to as secure and efficient private image matching (SEPIM). Most image matching (IM) approaches define an image representation and a distance metric that reduce the amount of data stored per image and the time cost of database search. Feature vectors (descriptors) of each image in the database are extracted and stored. During the matching, the descriptors of the query image are compared against their counterparts in the database to determine the most relevant image. However, keeping descriptors in their clear text may reveal information on some objects in the image. Thus, such descriptors should be encrypted in such a way that their distances are preserved without decryption. In this paper, we address the question of how to search for similar images between two parties in a privacy-preserving manner without losing image confidentiality.