A Pseudorandom Sequence Generated over a Finite Field Using The Möbius Function

The aim of this paper is to generate and examine a pseudorandom sequence over a finite field using the Möbius function. In the main part of the paper, after generating a number of sequences using the Möbius function, we examine the sequences’ pseudorandomness using autocorrelation and prove that the second half of any sequence in $\mathbb{F}_{3^n}$ is the same as the first, but for the sign of the terms. I reach the conclusion, that it is preferable to generate sequences in fields of the form $\mathbb{F}_{3^n}$, thereby obtaining a sequence of the numbers $-1$,$0$,$1$, each of which appear in the same amounts. There is a variety of applications of the discussed pseudorandom generator and other generators such as cryptography or randomized algorithms.

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.

The Dynamic Analysis of a Novel Reconfigurable Cubic Chaotic Map and Its Application in Finite Field

Dynamic degradation occurs when chaotic systems are implemented on digital devices, which seriously threatens the security of chaos-based pseudorandom sequence generators. The chaotic degradation shows complex periodic behavior, which is often ignored by designers and seldom analyzed in theory. Not knowing the exact period of the output sequence is the key problem that affects the application of chaos-based pseudorandom sequence generators. In this paper, two cubic chaotic maps are combined, which have symmetry and reconfigurable form in the digital circuit. The dynamic behavior of the cubic chaotic map and the corresponding digital cubic chaotic map are analyzed respectively, and the reasons for the complex period and weak randomness of output sequences are studied. On this basis, the digital cubic chaotic map is optimized, and the complex periodic behavior is improved. In addition, a reconfigurable pseudorandom sequence generator based on the digital cubic chaotic map is constructed from the point of saving consumption of logical resources. Through theoretical and numerical analysis, the pseudorandom sequence generator solves the complex period and weak randomness of the cubic chaotic map after digitization and makes the output sequence have better performance and less resource consumption, which lays the foundation for applying it to the field of secure communication.

An enhanced correlation identification algorithm and its application on spread spectrum induced polarization data

In spread spectrum induced polarization (SSIP) data processing, attenuation of background noise from the observed data is the essential step that improves the signal-to-noise ratio (SNR) of SSIP data. The time-domain spectral induced polarization based on pseudorandom sequence (TSIP) algorithm has been proposed to improve the SNR of these data. However, signal processing in background noise is still a challenging problem. We propose an enhanced correlation identification (ECI) algorithm to attenuate the background noise. In this algorithm, the cross-correlation matching method is helpful for the extraction of useful components of the raw SSIP data and suppression of background noise. Then the frequency-domain IP (FDIP) method is used for extracting the frequency response of the observation system. Experiments on both synthetic and real SSIP data show that the ECI algorithm will not only suppress the background noise but also better preserve the valid information of the raw SSIP data to display the actual location and shape of adjacent high-resistivity anomalies, which can improve subsequent steps in SSIP data processing and imaging.

Cellular Automata and Their Generalizations in Cryptography. Part 1

The purpose of the article is an analytical review of the application of cellular automata and their generalizations in cryptography. Research method: an analysis of scientific publications on the topic of the article. Results: The review article analyzes the literature devoted to the use of classical cellular automata and their generalizations for the construction of cryptographic algorithms. The article consists of two parts. The first part is devoted to classical cellular automata and symmetric cryptographic algorithms based on them. It briefly discusses the history of the theory of cellular automata and its applications in various scientific disciplines. The review of the works of a number of authors who proposed symmetric cryptographic algorithms and pseudorandom sequence generators based on one-dimensional cellular automata is presented. The security of such cryptographic algorithms turned out to be insufficient. The following is a review of articles devoted to the use of two-dimensional cellular automata for constructing ciphers (this approach gave the best results). Multidimensional cellular automata are also mentioned. The second part of the article will be devoted to a review of works devoted to the use of generalized cellular automata in cryptography – on the basis of such automata, it is possible to create symmetric encryption algorithms and cryptographic hash functions that provide a high level of security and high performance in hardware implementation (for example, on FPGA), as well as having fairly low requirements for hardware resources. In addition, an attention will be paid to interesting connections of generalized cellular automata, in the context of their use in cryptography, with the theory of expander graphs. Attention will also be paid to the security of cryptographic algorithms based on generalized cellular automata. The works devoted to the implementation of various cryptographic algorithms based on generalized cellular automata on FPGA and GPU will be mentioned. In addition, an overview of asymmetric cryptographic algorithms based on cellular automata will be given. The questions about the belonging of some problems on cellular automata and their generalizations to the class of NP-complete problems, as well as to some other complexity classes, will also be considered.

An efficient data masking for securing medical data using DNA encoding and chaotic system

Data security is utmost important for ubiquitous computing of medical/diagnostic data or images. Along with must consider preserving privacy of patients. Recently, deoxyribose nucleic acid (DNA) sequences and chaotic sequence are jointly used for building efficient data masking model. However, the state-of-art model are not robust against noise and cropping attack (CA). Since in existing model most digits of each pixel are not altered. This work present efficient data masking (EDM) method using chaos and DNA based encryption method for securing health care data. For overcoming research challenges effective bit scrambling method is required. Firstly, this work present an efficient bit scrambling using logistic sine map and pseudorandom sequence using chaotic system. Then, DNA substitution is performed among them to resist against differential attack (DA), statistical attack (SA) and CA. Experiment are conducted on standard considering diverse images. The outcome achieved shows proposed model efficient when compared to existing models.