## 2 Background  
Image transmission has become commonplace in today's fast-moving technological age, and it is imperative that important images are stored and transmitted securely [14]. The growing study into privacy-preserving biometrics has given rise to many inquiries into the security of storing and transmitting biometric data, such as face, palmprint, and iris images. How to transmit images without damage and at the same time ensure that they are not tampered with or stolen is turning out to be a complex subject worth investigating. How to securely store and authenticate biometric images requires a great deal of cryptographic knowledge. Cryptographic systems can be divided into two main categories [15] in principle, which are Single-Key Systems and Dual-Key systems. The Dual-Key System was first introduced by [PERSON] and [PERSON] in New Directions in Cryptography [16] in 1976. With the Dual-Key System, each user has a chosen pair of keys, one that can be made public and the other that is secret. The Dual-Key System is therefore also known as a Public-Key Cryptosystem. Public-Key Cryptosystems can be used in public networks to enable secure communications and authenticate users. The cryptographic algorithms used in the proposed model belong to the Public-Key Cryptosystem because the environment and characteristics of the Public-Key Cryptosystem are consistent with the requirements of the application. The Public-Key Cryptosystem has the property that it is computationally infeasible to find the decryption key when the cryptographic algorithm and encryption key are known, which means that the sender and receiver do not need to share a secret key. The public key can be distributed freely, while the private key remains secret. Existing studies for privacy with biometric images mainly use image encryption algorithms, where image encryption mainly consists of the Arnold transform. Arnold Transform (also known as Arnold's Cat Map) is an image encryption algorithm based on the classical cryptographic system that essentially performs multiple matrix operations on the positions of pixels in an image of equal length and width pixel points, thus changing the position of the pixels in space in order to uniformly distribute the energy of the image [17]. The Arnold Transform is the most commonly used technique for mixing digital images [18]. [PERSON] et al. [19] proposed a new approach to color image encryption based on Arnold Transform (ART) and interference methods. [PERSON] et al. [14] extended the 2D Arnold Transform to a 3D Arnold Transform and a real-time secure symmetric encryption scheme. [PERSON] et al. [20] proposed an image encryption algorithm based on an improved Arnold transform and a chaotic pulse-coupled neural network. While all of these methods make good use of the Arnold Transform, using the Arnold Transform alone has significant security threats, is vulnerable to brute force enumeration cracking, and has some vulnerabilities. Another approach to encrypting privacy-preserving biometric images is to encrypt them using cryptographic algorithms alone. [PERSON] et al. [21] used the AES encryption algorithms to encrypt the biometric images and then convert them to QR Codes. The AES encryption algorithm was a popular symmetric encryption algorithm that used the same key for both encryption and decryption. Compared with AES encryption algorithms, the ElGamal Encryption Algorithm is based on the discrete logarithm problem and uses large primes as moduli, so it is very difficult to crack, and the ElGamal Encryption Algorithm is a Public-Key Cryptosystem with easier key management. After comparison, among the cryptographic algorithms, the ElGamal Encryption Algorithm is more compatible with the use of image encryption. [PERSON] et al. [22], [PERSON] et al. [23], and [PERSON] et al. [24] all proposed modifications to the ElGamal Encryption Algorithms and gave us some new ideas.