Strengthening Quality of Chaotic Bit Sequences

We discuss chaos and its quality as measured through the 0-1 test for chaos. When the 0-1 test indicates deteriorating quality of chaos, because of the finite precision representations of real numbers in digital implementations, then the process may eventually lead to a periodic sequence. A simple method for improving the quality of a chaotic signal is to mix the signal with another signal by using the XOR operation. In this paper, such mixing of weak chaotic signals is considered, yielding new signals with improved quality (with K values from the 0-1 test close to 1). In some sense, such a mixing of signals could be considered as a two-layer prevention strategy to maintain chaos. That fact may be important in those applications when the hardware resources are limited. The 0-1 test is used to show the improved chaotic behavior in the case when a continuous signal (for example, from the Chua, Rössler or Lorenz system) intermingles with a discrete signal (for example, from the logistic, Tinkerbell or Henon map). The analysis is presented for chaotic bit sequences. Our approach can further lead to hardware applications, and possibly, to improvements in the design of chaotic bit generators. Several illustrative examples are included.

Noise Assisted Image Encryption and Decryption using 2-D Chaotic System

In this paper, a new two-dimensional (2-D) chaos-based color image encryption and decryption scheme is proposed in which the noise signal is selected randomly to set the initial values for a chaotic system which also enhances the security of the system. The 256-bit hash value of noise is transformed into one-time initial values for the state variables of this proposed chaotic system. XOR operation is further carried out to diffuse the pixels. Finally, statistical and security analyses are performed for understanding the effectiveness of the proposed system. Experimental results confirm that the proposed chaos-based cryptosystem is efficient and suitable for information (image) transmission in a highly secured way.

ESSM: Formal Analysis Framework for Protocol to Support Algebraic Operations and More Attack Capabilities

The strand space model has been proposed as a formal method for verifying the security goals of cryptographic protocols. However, only encryption and decryption operations and hash functions are currently supported for the semantics of cryptographic primitives. Therefore, we establish the extended strand space model (ESSM) framework to describe algebraic operations and advanced threat models. Based on the ESSM, we add algebraic semantics, including the Abelian group and the XOR operation, and a threat model based on algebraic attacks, key-compromise impersonation attacks, and guess attacks. We implement our model using the automatic analysis tool, Scyther. We demonstrate the effectiveness of our framework by analysing several protocols, in particular a three-factor agreement protocol, with which we can identify new attacks while providing trace proofs.

Yosida Complementarity Problem with Yosida Variational Inequality Problem and Yosida Proximal Operator Equation Involving XOR-Operation

Due to the importance of Yosida approximation operator, we generalized the variational inequality problem and its equivalent problems by using Yosida approximation operator. The aim of this work is to introduce and study a Yosida complementarity problem, a Yosida variational inequality problem, and a Yosida proximal operator equation involving XOR-operation. We prove an existence result together with convergence analysis for Yosida proximal operator equation involving XOR-operation. For this purpose, we establish an algorithm based on fixed point formulation. Our approach is based on a proximal operator technique involving a subdifferential operator. As an application of our main result, we provide a numerical example using the MATLAB program R2018a. Comparing different iterations, a computational table is assembled and some graphs are plotted to show the convergence of iterative sequences for different initial values.

Secret Image-Sharing Scheme Based on Multinode Authentication in the Internet of Things

Internet of things (IoT) has been developed and applied rapidly because of its huge commercial value in recent years. However, security problem has become a key factor restricting the development of IoT. The nodes of IoT are easy to be impersonated or replaced when attacked, which leads to the mistake of the uploaded data, the abnormal use of the application, and so on. Identifying the authenticity of the data submitted by the nodes is the top priority. We propose a scheme to verify the authenticity of multinode data. In this scheme, the authenticity of node data is checked through visual secret recovery and XOR operation together. The least significant bit (lsb) operation converts data from nodes into a bit, which improves the efficiency of data verification and reduces the risk of data leakage. This scheme achieves the purpose of verifying the data provided by the node, which avoids malicious attacks from illegal nodes. By analyzing the experiment result and comparing with other works, our scheme has the advantages of high verification efficiency, lightweight storage of nodes, and security verification.

Image Encryption Algorithm Based on a Novel 4D Chaotic System

In this paper, a novel four-dimensional chaotic system has been created, which has characteristics such as high sensitivity to the initial conditions and parameters. It also has two a positive Lyapunov exponents. This means the system is hyper chaotic. In addition, a new algorithm was suggested based on which they constructed an image cryptosystem. In the permutation stage, the pixel positions are scrambled via a chaotic sequence sorting. In the substitution stage, pixel values are mixed with a pseudorandom sequence generated from the 4D chaotic system using XOR operation. A simulation has been conducted to evaluate the algorithm, using the standardized tests such as information entropy, histogram, number of pixel change rate, unified average change intensity, and key space. Experimental results and performance analyses demonstrate that the proposed encryption algorithm achieves high security and efficiency.

Implementation of the method of figurative transformations to minimizing symmetric Boolean functions

This paper reports a study that has established the possibility of improving the effectiveness of the method of figurative transformations in order to minimize symmetrical Boolean functions in the main and polynomial bases. Prospective reserves in the analytical method were identified, such as simplification of polynomial function conjuncterms using the created equivalent transformations based on the method of inserting the same conjuncterms followed by the operation of super-gluing the variables. The method of figurative transformations was extended to the process of minimizing the symmetrical Boolean functions with the help of algebra in terms of rules for simplifying the functions of the main and polynomial bases and developed equivalent transformations of conjuncterms. It was established that the simplification of symmetric Boolean functions by the method of figurative transformations is based on a flowchart with repetition, which is the actual truth table of the assigned function. This is a sufficient resource to minimize symmetrical Boolean functions that makes it possible to do without auxiliary objects, such as Karnaugh maps, cubes, etc. The perfect normal form of symmetrical functions can be represented by binary matrices that would represent the terms of symmetrical Boolean functions and the OR or XOR operation for them. The experimental study has confirmed that the method of figurative transformations that employs the 2-(n, b)-design, and 2-(n, x/b)-design combinatorial systems improves the efficiency of minimizing symmetrical Boolean functions. Compared to analogs, this makes it possible to enhance the productivity of minimizing symmetrical Boolean functions by 100‒200 %. There are grounds to assert the possibility of improving the effectiveness of minimizing symmetrical Boolean functions in the main and polynomial bases by the method of figurative transformations. This is ensured, in particular, by using the developed equivalent transformations of polynomial function conjuncterms based on the method of inserting similar conjuncterms followed by the operation of super-gluing the variables.

Image confusion and diffusion based on multi-chaotic system and mix-column

In this paper, a new image encryption algorithm based on chaotic cryptography was proposed. The proposed scheme was based on multiple stages of confusion and diffusion. The diffusion process was implemented twice, first, by permuting the pixels of the plain image by using an Arnold cat map and, the second time by permuting the plain image pixels via the proposed permutation algorithm. The confusion process was performed many times, by performing the XOR operation between the two resulted from permuted images, subtracted a random value from all pixels of the image, as well as by implementing the mix column on the resulted image, and by used the Lorenz key to obtain the encrypted image. The security analysis tests that used to exam the results of this encryption method were information entropy, key space analysis, correlation, histogram analysis UACI, and NPCR have shown that the suggested algorithm has been resistant against different types of attacks.

A Secure Three-Factor Anonymous User Authentication Scheme for Internet of Things Environments

Internet of Things (IoT) is composed of various kinds of devices such as cars, electrical appliances, machines and sensors. With IoT technologies, devices can exchange information through the network, people are allowed to get information collected by devices without interacting with them, and automatic operations for devices are realized. Because of the variety of IoT devices, some of them possess limited computational capability. On the other hand, data transmission in IoT networks is usually through a public channel. To ensure efficiency and security for IoT environments, Lee et al. proposed a three-factor authentication scheme with hash function and XOR operation. They claimed their scheme possessed superior properties and could resist common attacks. After analyzing their scheme, we find that their scheme is vulnerable to five flaws. In this paper, how these found flaws threaten Lee et al.’s scheme is shown in detail. Then, we propose an improvement to overcome the found flaws and preserve the advantages by employing ECC.