## 2 Background
However, the use of a single cryptographic algorithm to guarantee security creates the problem of an excessive volume of keys, which makes the transmission of keys and ciphertexts difficult, and there are shortcomings in this type of approach. More cryptographic studies use image encryption algorithms and cryptographic algorithms nested together for encryption, which greatly improve algorithmic security. [PERSON] et al. [18] presented a hybrid technique of image encryption using the Arnold Transform and RSA algorithms. [PERSON] et al. [25] proposed RGB encryption based on symmetric keys while mixing Arnold Transform. From these papers, we came up with the idea that the ElGamal Encryption Algorithm has some advantages over the RSA Encryption Algorithm. [PERSON] et al. [26] proposed a more secure image encryption framework for sending image information over untrusted channels. [PERSON] et al. [27] proposed a scheme based on an improved elliptic curve cryptosystem and Arnold Transform that was suitable for large image encryption and provided high security while avoiding key exchange and distribution. [PERSON] et al. [28] proposed a novel asymmetric image encryption method that was based on the elliptic curve ElGamal Encryption Algorithm and chaos theory. [PERSON] et al. [29] and [PERSON] et al. [30] upgraded their algorithms based on elliptic curve encryption in combination with other image encryption techniques with good results. In this paper, we propose a new privacy-preserving biometric image encryption method based on these studies by combining an improved 3D Arnold Transform with the ElGamal Encryption Algorithm, which both simplifies the encryption and decryption algorithms and improves the security of the whole algorithm. Digital signatures are well established nowadays. [PERSON] explained the many basic methods of constructing a secure signature scheme in his book _Digital Signatures_[31]. Digital signatures have evolved from public key ciphers and have important applications in network security, including authentication, data integrity, non-repudiation, and anonymity. To ensure that encrypted images are not tampered with or corrupted during transmission, I used digital signature algorithms to sign and verify the encrypted images, ensuring data integrity and non-repudiation. [PERSON] [32] described a new digital signature based solely on traditional cryptographic functions such as DES, whose security did not depend on the difficulty of decomposition and avoided the high computational cost of modular operations. [PERSON] et al. [33] proposed a digital signature algorithm for verifying images that allowed some types of image modification (e.g., lossy compression) but prevented other types of manipulation (e.g., tampering) and extended signature-based authentication for images to the authentication of video sequences. [PERSON] et al. [34], [PERSON] et al. [35], [PERSON] et al. [36], and [PERSON] et al. [37] all proposed innovative digital signature schemes that were modified for traditional signature algorithms. Since the traditional ElGamal Digital Signature algorithm used only one random number and therefore had certain security flaws, in order to improve the security of the algorithm, [PERSON] et al. [38] proposed an improved ElGamal Digital Signature Scheme that was based on the hard-to-compute property of discrete logarithms over a finite field. In summary, the ElGamal Digital Signature Scheme has strong superiority in digital signatures. However, since digital signature algorithms are often accompanied by cryptographic algorithms, we need to consider the complexity, completeness, and fit of the whole process in addition to the integrity of the authentication. Although the above literature proposes very clever signature methods, they lack a degree of integration with the authentication of cryptographic algorithms.