Pseudorandom Research Articles

Pseudo-Random Number Generation with β-Encoders

Pseudo-Random Number Generation with β-Encoders

Dynamic Analysis and FPGA Implementation of Fractional-Order Hopfield Networks with Memristive Synapse

Memristors have become important components in artificial synapses due to their ability to emulate the information transmission and memory functions of biological synapses. Unlike their biological counterparts, which adjust synaptic weights, memristor-based artificial synapses operate by altering conductance or resistance, making them useful for enhancing the processing capacity and storage capabilities of neural networks. When integrated into systems like Hopfield neural networks, memristors enable the study of complex dynamic behaviors, such as chaos and multistability. Moreover, fractional calculus is significant for their ability to model memory effects, enabling more accurate simulations of complex systems. Fractional-order Hopfield networks, in particular, exhibit chaotic and multistable behaviors not found in integer-order models. By combining memristors with fractional-order Hopfield neural networks, these systems offer the possibility of investigating different dynamic phenomena in artificial neural networks. This study investigates the dynamical behavior of a fractional-order Hopfield neural network (HNN) incorporating a memristor with a piecewise segment function in one of its synapses, highlighting the impact of fractional-order derivatives and memristive synapses on the stability, robustness, and dynamic complexity of the system. Using a network of four neurons as a case study, it is demonstrated that the memristive fractional-order HNN exhibits multistability, coexisting chaotic attractors, and coexisting limit cycles. Through spectral entropy analysis, the regions in the initial condition space that display varying degrees of complexity are mapped, highlighting those areas where the chaotic series approach a pseudo-random sequence of numbers. Finally, the proposed fractional-order memristive HNN is implemented on a Field-Programmable Gate Array (FPGA), demonstrating the feasibility of real-time hardware realization.

Enhanced Chaotic Pseudorandom Number Generation Using Multiple Bernoulli Maps with Field Programmable Gate Array Optimizations

Certain methods for implementing chaotic maps can lead to dynamic degradation of the generated number sequences. To solve such a problem, we develop a method for generating pseudorandom number sequences based on multiple one-dimensional chaotic maps. In particular, we introduce a Bernoulli chaotic map that utilizes function transformations and constraints on its control parameter, covering complementary regions of the phase space. This approach allows the generation of chaotic number sequences with a wide coverage of phase space, thereby increasing the uncertainty in the number sequence generation process. Moreover, by incorporating a scaling factor and a sine function, we develop a robust chaotic map, called the Sine-Multiple Modified Bernoulli Chaotic Map (SM-MBCM), which ensures a high degree of randomness, validated through statistical mechanics analysis tools. Using the SM-MBCM, we propose a chaotic PRNG (CPRNG) and evaluate its quality through correlation coefficient analysis, key sensitivity tests, statistical and entropy analysis, key space evaluation, linear complexity analysis, and performance tests. Furthermore, we present an FPGA-based implementation scheme that leverages equivalent MBCM variants to optimize the electronic implementation process. Finally, we compare the proposed system with existing designs in terms of throughput and key space.

Adaptive Measurement and Parameter Estimation for Low-SNR PRBC-PAM Signal Based on Adjusting Zero Value and Chaotic State Ratio

Accurately estimating the modulation parameters of pseudorandom binary code–pulse amplitude modulation (PRBC–PAM) signals damaged by strong noise poses a significant challenge in emitter identification and countermeasure. Traditionally, weak signal detection methods based on chaos theory can handle situations with low signal-to-noise ratio, but most of them are developed for simple sin/cos waveform and cannot face PRBC–PAM signals commonly used in ultra-low altitude performance equipment. To address the issue, this article proposes a novel adaptive detection and estimation method utilizing the in-depth analysis of the Duffing oscillator’s behaviour and output characteristics. Firstly, the short-time Fourier transform (STFT) is used for chaotic state identification and ternary processing. Then, two novel approaches are proposed, including the adjusting zero value (AZV) method and the chaotic state ratio (CSR) method. The proposed weak signal detection system exhibits unique capability to adaptively modify its internal periodic driving force frequency, thus altering the difference frequency to estimate the signal parameters effectively. Furthermore, the accuracy of the proposed method is substantiated in carrier frequency estimation under varying SNR conditions through extensive experiments, demonstrating that the method maintains high precision in carrier frequency estimation and a low bit error rate in both the pseudorandom sequence and carrier frequency, even at an SNR of −30 dB.

Pseudo-random Number Generator Using Knight’s Travel Path and Brightness Response of the Eye

Pseudo-random Number Generator Using Knight’s Travel Path and Brightness Response of the Eye

Synchronization of Gold sequences based on fast transform in a truncated basis of Walsh–Hadamard functions

Based on the analysis of the structures of isomorphic multiplicative groups of extended Galois fields, it is established that any cyclic shift of a pseudo-random Gold sequence can be transformed into a function belonging to the complete set of analogues of Rademacher functions of the corresponding dimension. This made it possible to develop a new algorithm for fast synchronization of Gold sequences based on the calculation of their discrete convolution using fast spectral transformation in a truncated basis of Walsh–Hadamard functions. The gain of the developed algorithm in terms of the number of arithmetic operations compared to the traditional method of calculating discrete convolution increases with increasing sequence length N and for N=511.1023 is approximately 3.4 times.

A high-quality visual image encryption algorithm utilizing the conservative chaotic system and adaptive embedding

Regarding the issue of encrypted images in the channel attracting the attention of attackers and making them vulnerable to attacks. This paper proposes a high-quality visual image encryption algorithm utilizing the conservative chaotic system, two-dimensional compressive sensing, optimization local of binary patterns, and adaptive embedding method. Firstly, a conservative chaotic system with excellent performance and resistance to reconstruction attacks is proposed. Secondly, the pseudo-random sequences generated by the chaotic system dynamically generate measurement matrices, which are optimized before compressing the image. Then, during the encryption process, by utilizing the newly proposed composite DNA computing rules, chaotic sequences dynamically encode and compute image information, which enriches the coding criteria and improves the security of encryption algorithms. Finally, in the information embedding stage, the newly proposed OLBP algorithm can identify important textured and non-textured regions of the host image, prioritize embedding non-textured regions, and then embed textured regions, which can improve the amount of information embedding and reduce damage to the host image. Experimental simulation and analysis exhibit that the encryption algorithm has high security, strong robustness and high efficiency. Meanwhile the imperceptible analysis of the steganographic images is exceed 52 dB, so the algorithm presents a high-quality visual effect of imperceptibility.

A Novel Parameter-Variabled and Coupled Chaotic System and Its Application in Image Encryption with Plaintext-Related Key Concealment.

The design of a chaotic system and pseudo-random sequence generation method with excellent performance and its application in image encryption have always been attractive and challenging research fields. In this paper, a new model of parameter-variabled coupled chaotic system (PVCCS) is established by interaction coupling between parameters and states of multiple low-dimensional chaotic systems, and a new way to construct more complex hyperchaotic systems from simple low-dimensional systems is obtained. At the same time, based on this model and dynamical DNA codings and operations, a new pseudo-random sequence generation method (PSGM-3DPVCCS/DNA) is proposed, and it is verified that the generated pseudo-random sequence of PSGM-3DPVCCS/DNA has excellent random characteristics. Furthermore, this paper designs a novel pixel chain diffusion image encryption algorithm based on the proposed parameter-variabled coupled chaotic system (PVCCS) in which the hash value of plaintext image is associated with the initial key to participate in the encryption process so that the encryption key is closely associated with plaintext, which improves the security of the algorithm and effectively resists the differential cryptanalysis risk. In addition, an information hiding method is designed to hide the hash value of plaintext image in ciphertext image so that the hash value does not need to be transmitted in each encryption, and the initial key can be reused, which solves the key management problem in application and improves the application efficiency of the encryption algorithm. The experimental analysis shows that the chaotic system constructed in this paper is creative and universal and has more excellent chaotic characteristics than the original low-dimensional system. The sequence generated by the pseudo-random sequence generation method has excellent pseudo-random characteristics and security, and the image encryption algorithm can effectively resist differential cryptanalysis risk, showing advanced encryption performance.

Designing and Developing a Mobile Academic Platform for University

Academic consultation is a consultation activity between academic supervisors and students in the study and helps solve problems that accept students. The goal is that students who can complete their studies according to their interests and abilities. The implementation of academic consultation is regulated by each study program / faculty / university. The current academic guidance process at Multimedia Nusantara University does not control the students being guided. In addition, the current process of distributing student assistance is done manually by the head and vice of the study program. They divide the average number of students by the number of lecturers. With the random number algorithm, pseudo random number generator will help the division of students with automatic divide. The pseudo random number generator algorithm was chosen because it has the advantage of providing initial value of the process that is produced quickly, simply and saves storage. The design of this online academic consultation application will assist in the academic monitoring process anytime and anywhere. This application developed using flutter and can be use by students and supervisor. The result from this research was application successfully developed and received a score of 88 % for UEQ Questionare, which is categorized as excellent.

A New Cryptographic Key Planning Algorithm Based on Blum Blum Shub

The Blum Blum Shub (BBS) algorithm is one of the known powerful pseudo random number generators. This algorithm can be used for key generation. BBS is basically based on the product of two large prime numbers and a seed value. The selection of these values is a critical issue. In this study, a new approach is proposed to overcome this problem. In the proposed approach, a prime number pool is first created. At this point, the user sets a start and end value. The primes in this range are generated and stored in an array. Then, two primes are randomly selected from this prime number pool with chaotic maps. The positions of these prime numbers in the array are recorded. The seed value is taken as the sum of the positions of these two primes. In other words, the parameters to be selected will be randomly selected in the ranges that the user will enter at that moment. In this study, two random bit sequences were obtained in this way. These sequences are 1 million bits long. NIST SP 800-22 tests were applied to these sequences and the sequences successfully completed all tests.

Performance Testing of the Triple Modular Redundancy Mitigation Circuit Test Environment Implementation in Field Programmable Gate Array Structures

The logic structures implemented in Field Programmable Gate Arrays (FPGAs) are often critical and their correct operation is vital. FPGA devices are often used in areas where there is increased ionising radiation (space, medical diagnostics, aviation or nuclear power). There is therefore a need for mechanisms to correct radiation-induced errors. A common approach is the redundant implementation of particularly critical parts of the logic structure. By triplicating selected fragments, it is possible not only to detect potential errors but also to correct them. Such an approach is called triple modular redundancy (TMR), and its essence lies in the use of specialised voting circuits called voters, which allow the erroneous results of individual subcircuits to be eliminated by voting. The triplicate circuit under consideration, together with the voter, constitutes the mitigation structure. It becomes necessary to develop a test environment to assess the correct operation of these circuits. Also key is the efficiency of the implementation of these structures, which can be related to the occupation of logical resources or the power consumption of a given implementation. This paper demonstrates the essence of implementing a test environment to test the correctness of the mitigation of logic structures using TMR voters. An error injector mechanism using the Pseudo-Random Bit Sequence (PRBS) register is proposed, which introduces an element of randomness into the testing process. The aim of this research is to determine the implementation efficiency of the proposed test environment. In the experimental part, the implementation costs of the proposed solution were examined. The results indicate that between 66 and 109 LUT blocks were required to implement the error injector, corresponding to a relatively small increase in dynamic power consumption: by 22% for combinational circuits and by 37% for sequential circuits.

Correction to: A statistical significance test for spatio-temporal receptive field estimates obtained using spike-triggered averaging of binary pseudo-random sequences

Correction to: A statistical significance test for spatio-temporal receptive field estimates obtained using spike-triggered averaging of binary pseudo-random sequences

FPGA based implementation of a perturbed Chen oscillator for secure embedded cryptosystems

This paper introduces an enhancement to the Chen chaotic system by incorporating a constant perturbation term d\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$d$$\\end{document} to one of the state variables, aiming to improve the performance of pseudo-random number generators (PRNGs). The perturbation significantly enhances the system's chaotic properties, resulting in superior randomness and increased security. An FPGA-based realization of a perturbed Chen oscillator (PCO)-derived PRNG is presented, tailored for embedded cryptosystems and implemented on a Nexys 4 FPGA card featuring the XILINX Artix-7 XC7A100T-1CSG324C integrated chip. The Xilinx-based system generator (XSG) tool is utilized to generate a digital version of the new oscillator, minimizing resource utilization. Experimental results demonstrate that the PCO-generated data successfully passes the NIST and TestU01 test suites. Additionally, statistical tests with key sensitivity are performed, validating the suitability of the designed PRNG for cryptographic applications. This establishes the PCO as a straightforward and efficient tool for multimedia security.

A 5D super-extreme-multistability hyperchaotic map based on parallel-cascaded memristors

A new 5-dimensional discrete memristors-based hyperchaotic map (5DMHM) is constructed by introducing four charge-controlled discrete memristors (DMs, coupled through parallel-cascade mixing operation) into the sine map. This 5DMHM has 4-dimensional space fixed points and its stability distributions are partitioned in coupling strength, memristor initial condition, and parameter planes. The dynamics of the map are investigated by employing 2D dynamical behavior and the first Lyapunov exponent (LE) distribution. The super extreme multistability is discovered through the basin of attraction, the initial-value-dependent LE spectra, bifurcation diagrams, the mean value of state variables, and trajectory plots. Moreover, a high level of complexity can be observed by calculating the spectral entropy complexity for various parameter planes. Subsequently, a microcontroller-based digital circuit is designed to implement the 5DMHM. The security analysis of the pseudorandom number generator (PRNG) designed by the 5DMHM is presented and the PRNG passes the NIST SP800-22 test. The comparison of the 5DMHM with the recent maps indicates a higher performance in secure communication and image encryption.

An optimized watermarking scheme based on genetic algorithm and elliptic curve

Digital watermarking serves as a crucial tool for tracing copyright infringements and ensuring the authenticity and integrity of sensitive information. The fundamental concept involves embedding a watermark in the host information, ensuring its undetectability by unauthorized parties. The efficacy of a watermarking scheme mainly depends on achieving high levels of imperceptibility, robustness, and embedding capacity. These attributes are intricately linked to both the selection of the host information segment and the embedding factor. Existing schemes often (i) employ the entire host information for embedding, incurring computational expenses, and (ii) optimize the embedding factor without considering imperceptibility, robustness, and embedding capacity simultaneously, resulting in less secure watermarks. To address these limitations, we introduce a novel watermarking scheme leveraging elliptic curves (ECs) and genetic algorithms (GA). We model the choice of the embedding part by generating pseudo-random numbers over ECs, taking advantage of their proven sensitivity, security, and low computational complexity. Due to parallel search and adaptability to non-linear relationships of GA, the scheme employs genetic optimization with a multivariate objective function to establish a balance between imperceptibility, robustness, and embedding capacity for optimal watermarked generation. Rigorous analysis and comparisons demonstrate that our proposed scheme attains significantly higher imperceptibility, robustness, and embedding capacity compared to existing optimized schemes. Furthermore, our scheme exhibits a speed advantage, being up to 278 and 21 times faster than optimized and non-optimized schemes, respectively, thereby affirming its practical applicability.

An Improved Multi-Chaotic Public Key Algorithm Based on Chebyshev Polynomials

Due to the similar characteristics of chaotic systems and cryptography, public key encryption algorithms based on chaotic systems are worth in-depth research and have high value for the future. Chebyshev polynomials have good properties and are often used in the design of public key algorithms. This paper improves the Bose Multi-Chaotic Public Key Cryptographic Algorithm (BMPKC) by applying Chebyshev polynomials. The proposed algorithm (CMPKC-) introduces the selective coefficient based on the properties of Chebyshev polynomials, allowing the special functions that need to be negotiated in the original system to be freely and randomly chosen as Chebyshev polynomials, and can also be expanded to m levels. The improved cryptographic algorithm also utilizes chaotic hash functions and logistic mapping to generate pseudo-random sequences and overcomes shortcomings of the Bose algorithm by iteratively iterating the selected Chebyshev polynomials based on the number of 0s or 1s in the pseudo-random sequence, thus providing better security. Analysis and software testing results indicate that this algorithm has strong robustness against brute force attacks, achieving a higher attack time for breaking the private key compared to the CEPKC, BMPKC, and CMPKC algorithms. Compared to the CMPKC algorithm, our proposal algorithm achieves better performance in the encryption and decryption phases. Furthermore, we combine this Multi-Chaotic System Key Exchange Protocol with the Advanced Encryption Standard (AES) algorithm, while providing a demonstration, offering more possibilities for practical applications of this system.

Encryption algorithm based on improved four-dimensional chaotic system and dynamic DNA encoding

An image encryption algorithm is proposed based on the combination of genetic (DNA) random coding and chaotic mapping. An image encryption algorithm based on an improved new four-dimensional chaotic system and DNA coding is proposed to address the problem that a single coding method is prone to selecting plaintext attacks. Based on a four-dimensional chaotic system existing in the literature, a new four-dimensional hyperchaotic system is obtained through improvement. The initial value of the system is generated based on SHA-256, zigzag transform. The input key and four pseudo-random chaotic sequences are generated iteratively. DNA chunking encoding, arithmetic operation, and decoding are implemented for the image disrupted based on the zigzag transform. The two-dimensional matrix constituted based on the Chaotic Sequence of Chebyshev to obtain the scrambled and diffused ciphertext image. Simulation experiments and security performance analysis show that the algorithm enhances the correlation between the key and the plaintext, the randomness of the encryption process, and effectively improves the anti-attack capability [H. Chen, J. Zhao et al., Appl. Res. Comput. 10, 0434 (2021)]. In this paper, 512 × 512 × 3 peppers color images are used for testing, and the correlation coefficients of adjacent pixels of the encrypted images are all close to 0, and the information entropy is all more significant than 7.997, which is relative to the theoretical value of 8. The experimental results show that the proposed algorithm improves the security of the ciphertext, increases the critical space, and, at the same time, resists various attack methods.

Image encryption algorithm based on multiple chaotic systems and improved Joseph block scrambling

Abstract With the rapid development of digital information technology, images are increasingly used in various fields. To ensure the security of image data, prevent unauthorized tampering and leakage, maintain personal privacy, and protect intellectual property rights, this study proposes an innovative color image encryption algorithm. Initially, the Mersenne Twister algorithm is utilized to generate high-quality pseudo-random numbers, establishing a robust basis for subsequent operations. Subsequently, two distinct chaotic systems, the autonomous non-Hamiltonian chaotic system and the tent-logistic-cosine chaotic mapping, are employed to produce chaotic random sequences. These chaotic sequences are used to control the encoding and decoding process of the DNA, effectively scrambling the image pixels. Furthermore, the complexity of the encryption process is enhanced through improved Joseph block scrambling. Thorough experimental verification, research, and analysis, the average value of the information entropy test data reaches as high as 7.999. Additionally, the average value of the number of pixels change rate (NPCR) test data is 99.6101%, which closely approaches the ideal value of 99.6094%. This algorithm not only guarantees image quality but also substantially raises the difficulty of decryption.

Lightweight Pseudo Random Number Generator for Embedded Systems

Lightweight Pseudo Random Number Generator for Embedded Systems

Characteristics of 3D coupled map lattice and its application in pseudo-random number generator

Characteristics of 3D coupled map lattice and its application in pseudo-random number generator