## 1 Introduction
[11] presented an encryption approach that encrypts plaintext with the Aboodh transform and then decrypts it with the inverse Aboodh transform. [PERSON] [12] developed a novel technique for encoding plaintext messages using Elzaki transform and decoding the messages using the inverse transform. [PERSON] et al. [13] presented a technique for encrypting and decrypting a message that employs an integral approach based on Mahgoub transformation and a modulo operator to ensure congruence. [PERSON] et al. [15] created a unique cryptographic idea that employs a natural transition to improve information security, particularly for sensitive data. The technique encodes and decodes sensitive data using a newly created mathematical algorithm that performs computations with either mod 26 or mod 63. [PERSON] et al. [16] presented a mathematical method for encrypting and decrypting data, using a transform known as the Kamal transform to encrypt the plaintext and its inverse transform for decryption. The congruence modulo operator is used as a security measure for protecting the sensitive data from unauthorized access. In addition, [PERSON] et al. [18] used the SEE integral transform for producing a distinct sequence from an algebraic equation obtained by applying the transform to the numerical values of the message letters. This SEE integral transform functions as a symmetrical cryptosystem that can be employed to encode plaintext, and its inverse is utilized to decipher the received cipher text and restore it to its original state. Furthermore, [PERSON] et al. [17] developed a scheme that is based on a complex Sadiq-Emad-Eman (SEE) integral transform. This method involves utilizing the complex SEE conversion to encode a message, and then decrypting the resulting ciphertext to recover the original information. The use of wavelet transforms in designing cryptosystems provides numerous notable advantages [19]. They allow for the creation of encryption schemes that are both secure and efficient, with low computational complexity. Furthermore, such encryption schemes can be made robust against attacks by using the multiple layers of security provided by wavelet transforms. There exist numerous cryptographic algorithms in the literature that rely on wavelet transforms as a key component, for instance, [20; 21; 22]. [PERSON] et al. [20] suggested a cryptographic technique that involves implementing the Daubechies wavelet transform. [PERSON] and [PERSON] [21] applied the Haar wavelet transform to safeguard images in wireless sensor networks. [PERSON] and [PERSON] [22] enhanced the protection of images through steganography, utilizing optimal wavelet coefficients. Max-plus algebra is a mathematical structure that involves two operations, namely maximization and addition, on the set of real numbers. This algebraic structure has been employed in various fields, such as cryptography. Incorporating max-plus algebra into the development of a cryptosystem has the potential to enhance its security and increase its ability to withstand attacks [14]. The application of max-plus algebra in wavelet transforms has led to the creation of various types of wavelet transforms, known as MP-wavelets. [PERSON] et al. [23] proposed three such types, namely Type I, Type II, and Type III, which use max-plus algebra in conjunction with the Haar wavelet transform. More recently, [PERSON] and [PERSON] [24] suggested a multi-image enhancement method that employs MP-wavelets. One of the benefits of MP-wavelets is that they do not require floating-point calculations, which eliminates the problem of round-off errors. Additionally, MP-wavelets are simple and efficient to compute. The use of elliptic curves (ECs) in cryptography is widespread due to their favorable mathematical properties, such as being non-linear and having a large group order, which makes them resilient to numerous cryptographic attacks. They have been standardized by the National Institute of Standards and Technology (NIST) and are extensively used in modern cryptographic systems [25].