## 1 Introduction  
With the increasing amount of data being shared electronically, the need for secure encryption schemes has become more critical than ever. Encryption schemes use mathematical functions to scramble data in a way that can only be decoded by authorized parties with the right decryption key. Designing a robust encryption scheme is essential for ensuring the confidentiality, integrity, and authenticity of sensitive information transmitted over networks or stored on devices. Numerous encryption schemes have been designed with the aim of reducing the likelihood of cyberattacks by ensuring the security of data. [PERSON] et al. [1] analyzed the security aspects concerning an image encryption system that relies on bit-plane extraction and multi chaos. They presented an algorithm that offers robust security and is highly resilient against chosen-plaintext attacks. [PERSON] et al. [2] developed an image encryption method utilizing an optimization approach. The underlying objective function of this approach considers both entropy and correlation, where a specific region called the core is chosen within the original image, and a parameter is computed to optimize the objective function over this core. [PERSON] [3] presented a novel method for encrypting images that incorporates both confusion and diffusion. This approach involves reorganizing the pixels of the image to generate a shuffled variant, followed by the process of diffusion achieved by XoRing the pixels using a secret key. [PERSON] et al. [4] introduced a novel encryption method that employs a two-dimensional logistic nested infinite collapse technique to securely transmit audio data via the internet. [PERSON] et al. [5] created a novel encryption technique for ensuring safe communication in asynchronous updating Boolean networks. The algorithm employs chaos-inspired approaches and an asynchronous updating mechanism. Their work made significant advances, such as the development of a unique two-dimensional completely parameterized sine map and an encoding method. These components enable the network to be transformed into a Boolean matrix and propagated as an image. [PERSON] et al. [6] developed a method for securing 3D image files by altering the starting state of a discrete system with the SHA-256 hash algorithm. To scramble and spread the coordinate values inside an image file, they used chaotic sequences, the Arnold matrix, and a DNA diffusion technique. [PERSON] et al. [7] designed a face encryption technique that utilizes chaos. The proposed algorithm is composed of three components: key generation through the application of hash and a two-dimensional logistic tent modular map, the extraction of facial images, and the encryption of the facial images. Furthermore, [PERSON] et al. [8] introduced a novel encryption approach designed specifically for three-dimensional models. The proposed technique involves the utilization of a two-dimensional chaotic system, formed by combining the logistic map and infinite collapse. Additionally, they [8] incorporated the principles of semi-tensor product theory into their encryption method. Nowadays, the security of text messages has gained significant attention due to the major concerns of users regarding the privacy and security of their communication channels, such as email and messaging apps, which are vulnerable to interception and hacking. Various schemes for securing text data have been developed, using a range of transformations including wavelet transforms, max-plus algebra-based wavelet transforms, and different mathematical structures, such as elliptic curves. In the design of cryptosystems, various types of transformations are significant, as they enable the conversion of plain data into encrypted data that are challenging to understand without having access to the secret key used for encryption [9]. Many researchers have used different types of transformations to design text encryption schemes [10; 11; 12; 13; 14; 15; 16; 17; 18]. [PERSON] et al.