For a long time, chaos was considered uncontrollable and unusable. However, over the past thirty years, researchers have formulated equations for certain chaotic phenomena, revealing a deterministic aspect to what initially seems random. The evolution of chaotic systems is characterized by strange attractors, which, despite their complex nature, do not allow precise long-term predictions of system behavior. The Lorenz attractor is the best-known example and was the first to be studied, though many other attractors with unusual shapes have since been discovered. The aim of this work is to perform a spectral analysis of the Lorenz attractor by examining the frequencies present in the time signals generated by the solutions of the Lorenz system of equations. To evaluate the frequency complexity of these signals, the discrete Fast Fourier Transform (FFT) is used to derive their frequency spectrum.

In an era of rapidly evolving communication methods, the exchange of sensitive information— such as personal data, financial records, and proprietary business knowledge—has become increasingly vulnerable to interception and misuse. As a result, organizations must adopt robust security measures and encryption technologies to safeguard their communications and maintain trust with their stakeholders. Whether it's military, financial, medical, personal, etc.—sharing information over the Internet and social networks has become an urgent necessity that cannot be ignored. This is where the importance of steganography technology, which is concerned with maintaining the confidentiality of information by camouflaging it, comes into play. This technology, which is a unique process, allows us to hide a secret message inside another file, often an image known as a camouflaged image. After entering the secret information into that image, the resulting image is called a "stego image." The goal of this process is to not reveal the secret information contained in the original file, making it difficult or even impossible to distinguish between the original copy and the document containing the secret message. There are many ways to achieve this, the most prominent of which is the LSB technique, which relies on the least significant bit. However, despite its effectiveness, this method suffers from a major limitation, which is the small size of the stored. information. Therefore, in this research, we decided to adopt a method that combines secret information processing and LSB technology with the aim of increasing the size of the stored information while maintaining image quality and confidentiality. This pursuit of excellence truly demonstrates how important innovation is to protecting our privacy in today's connected world.

In many applications of information processing, such as cryptography, generating random sequences presents many difficulties. In this paper, a new pseudo-random sequence is proposed, based on two chaotic systems, a logistic map and a seven-dimensional (7D) hyperchaotic system. The main process of the proposed generator is that it functions by using the logistic map to control the 7D hyperchaotic system, which exhibits random behavior to produce a pseudo-random sequence. Specifically, the logistic map is used to select one of the variables from the 7D hyperchaotic system. The variable selected at each iteration is used as a controller to fill the pseudo-random sequence, choosing from one of the other variables of the 7D hyperchaotic system. This means that in each iteration, the pseudo-random sequence takes a value from the 7D hyperchaotic system according to the logistic map and the selected variable of the 7D hyperchaotic system. This method allows the creation of a highly efficient pseudo-random generator through simple processes. Experimental and analysis results show that the proposed generator has good random characteristics, making it suitable for cryptography applications such as encryption algorithms.