Improving the efficiency of the steganographic method of data hiding with the application of iterative functions and noise addition

The development of computer and digital technology contributes to the growth of information flows transmitted through open and closed communication channels. In many cases, this information is confidential, financial, or commercial in nature and is of value to its owners. This requires the development of mechanisms to protect information from unauthorized access. There are two fundamental areas of secure data transmission over the open communication channels – cryptography and steganography. The fundamental difference between them is that cryptography hides from others the content of the message, and steganography hides the very fact of the message transmission. This paper is devoted to steganographic methods of data concealment, which are less researched than cryptographic, but have significant potential for use in a variety of applications. One of the important characteristics of most methods is their effectiveness. In general, efficiency is assessed in the context of solving specific problems. However, the most common criteria for the effectiveness of steganographic methods are the amount of hidden data and the method of transmitting the secret key to the receiving party, which will not allow the attacker to intercept it. Because media files make up a significant portion of network traffic, a digital image is chosen as the stegocontainer. It is proposed to determine the coordinates of the embedding location on the basis of iterative functions. The advantage of their use is the compactness of the description of the coordinates of the pixels in which the data will be hidden. In addition, it is proposed to use the Diffie-Gellman algorithm to transfer the parameters of iterative functions to the receiving side. This method of key distribution makes the steganographic method less vulnerable to being stolen by an attacker. The second performance criterion is the amount of hidden data. The paper found that the moderate addition of multiplicative noise makes it possible to increase the amount of hidden data without significantly reducing the visual quality of the stegocontainer. To analyze the distortions in the image-stegocontainer, which are due to the influence of noise and modification of the lower bits of pixels, the method of a quantitative assessment of visual quality is used, which is based on the laws of visual perception. Keywords: steganographic data hiding; hiding efficiency; iterative functions; Diffie-Gelman algorithm.

A Generalization of a Result for Iterative Functions in ℝn

The purpose of this paper is to generalize for real vector-valued functions of a result for real iterative functions and to give some applications for nonlinear system of equations.

Comparative Analysis of Compiler Performances and Program Efficiency

With the existence of several programming languages such as C/C++, Java, C#, LISP, Prolog, Python, Simula, F#, Go, Haskell, Scala, Ruby, Dart, Swift, Groovy etc. and diverse paradigms like structured, object-oriented, list, aspect-oriented, service-oriented, web, mobile and logic programming, there is a need to perform an exhaustive comparative analysis of diverse compilers and environments before making a choice of implementation technology in software engineering. Optimization of compilers helps to reduce execution time by making use of high speed processor registers, thereby, eliminating redundant computation. This paper reports some series of performance analysis done with some popular programming languages including Java, C++, Python and PHP. Programs involving recursive and iterative functions like factorial of large numbers and binary search of large arrays were run on the various platforms with the execution time recorded in milliseconds and represented in a chart. This can aid in making a selection of the appropriate language to use for a given application domain.

One-Point Optimal Family of Multiple Root Solvers of Second-Order

This manuscript contains the development of a one-point family of iterative functions. The family has optimal convergence of a second-order according to the Kung-Traub conjecture. This family is used to approximate the multiple zeros of nonlinear equations, and is based on the procedure of weight functions. The convergence behavior is discussed by showing some essential conditions of the weight function. The well-known modified Newton method is a member of the proposed family for particular choices of the weight function. The dynamical nature of different members is presented by using a technique called the “basin of attraction”. Several practical problems are given to compare different methods of the presented family.

Application of Fractal Growth Patterns in Housing Layout Design

In early phases of design, during the process of form-exploration, architects -- knowingly or unknowingly -- have used mathematics as their guiding tool to evolve a formal methodology of design. Fundamental compositional principles such as symmetry, rhythm and proportion are based on specific mathematical underpinnings. However, very often the designer comes across a situation where these underlying mathematical principles need to be overlapped or interfaced. Applying fractal concepts to the order can accommodate this complex diversity. Fractals allow us to provide a combination of order and surprise in a rhythmic composition using a specific mathematical geometry. Fractals are typically unit-based and, can thus allow exploration in architectural designs which have a ‘unit’ as a fundamental issue or necessity. The design of housing layout stands out prominently among such architectural problems and, can thus be one such instance in which fractals may be used as a design tool. Commonly seen organisational patterns in housing layout designs create rigidity and monotony, while others like clustered groups are too inconsistent and can create disorder. The research tries applying fractal ordering principles to strike a balance between these extremes by creating an orderly arrangement of houses with an underlying variation in the pattern. The traditional processes of creating housing layouts is quite cumbersome. With the mathematical power of computers, fractal ordering principles are used as Iterative functions to generate multiple design options. The research investigates the potential of the emergent patterns of fractals as an organisational principle in designing housing layouts, while limiting it based on site constraints, size and the transforming rules. In doing so, the objective is to explore the computational and mathematical basis of repetitive patterns in architectural order and compositions. The study also aims at developing a computer application, based on algorithms using fractals, which offers capabilities as a conceptual and organisational tool for a housing layout. The application is implemented, tested and its results are demonstrated using a live terrain data.

Another Simple Way of Deriving Several Iterative Functions to Solve Nonlinear Equations

We present another simple way of deriving several iterative methods for solving nonlinear equations numerically. The presented approach of deriving these methods is based on exponentially fitted osculating straight line. These methods are the modifications of Newton's method. Also, we obtain well-known methods as special cases, for example, Halley's method, super-Halley method, Ostrowski's square-root method, Chebyshev's method, and so forth. Further, new classes of third-order multipoint iterative methods free from a second-order derivative are derived by semidiscrete modifications of cubically convergent iterative methods. Furthermore, a simple linear combination of two third-order multipoint iterative methods is used for designing new optimal methods of order four.