Pseudorandom Research Articles

SIMECK-T: An Ultra-Lightweight Encryption Scheme for Resource-Constrained Devices

The Internet of Things produces vast amounts of data that require specialized algorithms in order to secure them. Lightweight cryptography requires ciphers designed to work on resource-constrained devices like sensors and smart things. A new encryption scheme is introduced based on a blend of the best-performing algorithms, SIMECK and TEA. A selection of software-oriented Addition–Rotation–XOR (ARX) block ciphers are augmented with a dynamic substitution security layer. The performance is compared against other lightweight approaches. The US National Institute of Standards and Technology (NIST) SP800-22 Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications and the German AIS.31 of the Federal Office for Information Security (BSI) are used to validate the output of the proposed encryption scheme. The law of iterated logarithm (LIL) for randomness is verified in all three forms. The total variance (TV), the Hellinger Distance (HD), and the root-mean-square deviation (RMSD) show values smaller than the required limit for 10.000 sequences of ciphertext. The performance evaluation is analyzed on a Raspberry PICO 2040. Several security metrics are compared against other ciphers, like χ2 and encryption quality (EQ). The results show that SIMECK-T is a powerful and fast, software-oriented, lightweight cryptography solution.

False Strange Attractors as Sources of Pseudo Randomness

False Strange Attractors as Sources of Pseudo Randomness

False Strange Attractors as Sources of Pseudo Randomness

Abstract In this work, the use of false chaotic attractors in enhancing the security of chaos-based encryption applications will be explored. False attractors result by rearranging the solution trajectories of a nonlinear dynamical system, leading to novel shapes in the 3D space. This way, a single solution trajectory of a chaotic system can be used to generate numerous new false trajectories. Examples of such attractors are provided for the Lorenz system, and a system with line equilibrium from Moysis et al. (2019). By formalizing the method of constructing false attractors, and generalizing it by adding a series of elementary operations, the key parameters of this procedure can be used as part of the secret key in symmetric encryption applications, effectively increasing the key space. Specifically, the key space increases significantly with respect to the simulation time, and the system’s dimension. Moreover, due to its fast implementation, this technique can be used as a less complex, but much lighter alternative to full scale permutation. The usability of the false attractors as sources of randomness is showcased through the design of a chaotic pseudo-random bit generator. The generator can output 64 bits per iteration, and is equally effective under any false attractor of the chaotic system.

High-speed secure stream cipher using synchronized chaos and the RC4 algorithm for optical communications.

A high-security, high-speed stream cipher for physical-layer-secure optical communication, based on optical-carrier-induced private chaos synchronization and RC4 algorithm, is proposed and numerically demonstrated. The high security and speed are achieved by combining physical true random numbers generated from synchronized chaos, used as the key for random DNA coding, with the RC4 pseudo-random numbers. Moreover, no third-party signal is required as the optical carrier itself serves as the common drive for chaos synchronization in semiconductor lasers. To ensure privacy, phase encryption with confidential dispersion components is deployed at the communicating parties to encrypt the driving signals. A secure stream cipher exceeding 100 Gb/s, leveraging approximately 4 Gb/s physical random numbers to achieve a rate 32 times higher, has been numerically demonstrated. Additionally, it is also noted that pseudo-random numbers generated from different seeds can be encoded using the same physical true random numbers to create parallel stream ciphers, making this approach well-suited for wavelength-division-multiplexed and space-division-multiplexed high-speed optical communications.

A class of n-D Hamiltonian conservative chaotic systems with three-terminal memristor: Modeling, dynamical analysis, and FPGA implementation.

Memristors are commonly used to introduce various chaotic systems and can be used to enhance their chaotic characteristics. However, due to the strict construction conditions of Hamiltonian systems, there has been limited research on the development of memristive Hamiltonian conservative chaotic systems (MHCCSs). In this work, a method for constructing three-terminal memristors is proposed, and the three-terminal memristors are incorporated into the Hamiltonian system, resulting in the development of a class of n-D MHCCS. Based on this method, we model a 4D MHCCS as a standard model for detailed dynamic analysis. The dynamic analysis reveals that the MHCCS exhibits complex dynamic behaviors, including conservativeness, symmetry, chaos depending on parameters, extreme multistability, and chaos under a wide parameter range. The dynamic analysis shows that MHCCS not only retains the favorable characteristics of a conservative system but also has more complex nonlinear dynamics due to the incorporation of memristors, thereby further enhancing its chaotic characteristics. Furthermore, the pseudo-random number generator based on the MHCCS has excellent randomness in terms of the NIST test. Finally, the physical realizability of the system is verified through Field Programmable Gate Array experiments. This study demonstrates that the constructed class of MHCCSs is a good entropy source that can be applied to various chaotic embedded systems, including secure communication, cryptographic system, and pseudo-random number generator.

Generation, evaluation and comparison of DNA-based (pseudo) random sequences

The object of this study is the methods and algorithms for computing, evaluating, and comparing DNA-based pseudorandom sequences (PRSs) and random sequences (RSs). This paper addresses the task of extracting (P)RSs with the required stochastic and statistical properties from a DNA noise source, experimentally validating these properties in compliance with the requirements of current international standards, as well as evaluating and comparing the sequences obtained for different DNA samples. The results are the developed algorithms for generating DNA-based (P)RSs, improved algorithms for their comparison, and proposals for the process of evaluating their properties. For the output of implemented algorithms, more than 96 % of the bit streams of sequences successfully pass all statistical tests, and the entropy per bit for RSs is close to 1. A special feature of the developed generation algorithms is the use of validated conditioning component – block cipher in CTR mode – which explains the possibility of obtaining unique random data with required properties. The peculiarity of the proposed evaluation algorithm is the complexity of the tests and checks used: complete assessment of statistical properties and entropy values. Special features of the improved comparison algorithms are resource saving and the ability to evaluate much larger data sets. This is due to the use of structures and data types that are better in terms of memory usage and flexible cryptographic primitives with different modes. The results could be practically applied to constructs where randomness is required: for computing the keys and system-wide parameters, when performing transformations as part of hash functions, while obtaining sequences of an arbitrary alphabet, in zero-knowledge protocols, etc.

Determining the stability of a fire truck tanker against overturning while driving through crossed forest terrain

The object of this study is to consider dynamic processes in the tank of a fire truck with different levels of water filling. The task to be solved is to determine the data on the fluctuation of the center of mass of a dynamic system, which consists of the water tank of a fire truck tanker truck, when it moves through rough forest terrain at different speeds. The data make it possible to predict the danger of a fire truck tipping over. In the process of solving the task, an estimation model of a fire truck tanker truck was built together with a water tank, using the LS-Dyna dynamic systems simulation software package. In order to reproduce the dynamic impact on the fire truck tanker with the water capacity exerted by the relief of the rugged forest area, the time dependences of the angles of current position of the fire truck tanker – roll angle, yaw, and pitch – were established. The resulting dependences were used as boundary conditions to reproduce the dynamic influence of the terrain. The turning angles of the water tank of a fire truck were determined depending on the unevenness of the terrain, the geometry of which was calculated by a pseudo-random number generator. Using the explicit method for integrating the dynamics equations, implemented in the code of the LS-Dyna software package, the patterns of fluctuations of the center of mass of the water tank of the fire truck tanker depending on the level of filling and speed of movement were defined. Using results from the mathematical modeling of dynamic processes in the fire truck tanker, a numerical algorithm was developed for this fire truck tanker to maintain its stability against overturning. Therefore, the results of this study have a direct practical application in the field of fire truck tanker design safety and could be used to improve and devise new technologies in this field

Mechanical analysis and function matrix projective synchronization of El-Nino chaotic system

Abstract This study explores the mechanical aspects of the El Niño system by transforming it into a Kolmogorov type system, characterized by four types of torques known as internal, inertial, dissipation, and external. Five scenarios by varying these torques to identify the factors that lead to chaos and their physical significance are also investigated. The interactions between kinetic, potential, and Hamiltonian energies are analyzed and depicted as how these energies interact with system parameters. The study also emphasizes the benefits of conservative chaos over dissipative chaos. Particularly, it has more applications like secure communications and pseudo-random number generation. The role of force interactions and exchanges, including Casimir energy in the generation of chaos is also identified. The transition from regular to irregular orbits, and then to more chaotic states is investigated through Casimir function. It concludes that all four types of torques are necessary to induce chaos in the El Niño chaotic system. Additionally, function matrix projective synchronization between identical El-Nino chaotic systems has achieved.

Kolam-Inspired Frequency Hopping: An Innovative Approach for Interference Reduction in Wireless Communication

The integration of cultural patterns into engineering applications opens new avenues for innovation and efficiency. This research explores the application of Kolam patterns, a traditional Indian art form characterized by its symmetry and periodicity, in frequency hopping for wireless communication systems. Kolam-inspired frequency hopping sequences are designed and compared with conventional pseudorandom sequences using key performance metrics, including Bit Error Rate (BER) and Signal-to-Interference Ratio (SIR). Simulations conducted under varying conditions of frequencies, number of users, hops, and Signal-to-Noise Ratio (SNR) reveal that Kolam-based sequences demonstrate superior interference management and lower error rates. The results underscore the potential of Kolam patterns to improve spectral efficiency and reliability in modern communication networks. This study paves the way for further exploration of cultural and mathematical patterns in optimizing wireless technologies.

Pseudo-random number generation with β-encoders

The [Formula: see text]-encoder is an analog circuit that converts an input signal [Formula: see text] into a finite bit stream [Formula: see text]. The bits [Formula: see text] are correlated and therefore are not immediately suitable for random number generation, but they can be used to generate bits [Formula: see text] that are (nearly) uniformly distributed. In this paper, we study two such methods. In the first part the bits [Formula: see text] are defined as the digits of the base-2 representation of the original input x. Under the assumption that there is no noise in the amplifier we then study a question posed by Jitsumatsu and Matsumura on how many bits [Formula: see text] are needed to correctly determine the first n bits [Formula: see text]. In the second part, we show this method fails for random amplification factors. Nevertheless, even in this case, nearly uniformly distributed bits can still be generated from [Formula: see text] using modern cryptographic techniques.

The use of chaotic pseudo random number and elliptic curve cryptosystem in an efficient OTP-based authentication scheme for online learning system

The use of chaotic pseudo random number and elliptic curve cryptosystem in an efficient OTP-based authentication scheme for online learning system

Effect of pseudo-random number on the security of quantum key distribution protocol

Abstract In the process of quantum key distribution (QKD), the communicating parties need to randomly determine quantum states and measurement bases. To ensure the security of key distribution, we aim to use true random sequences generated by true random number generators as the source of randomness. In practical systems, due to the difficulty of obtaining true random numbers, pseudo-random number generators are used instead. Although the random numbers generated by pseudo-random number generators are statistically random, meeting the requirements of uniform distribution and independence, they rely on an initial seed to generate corresponding pseudo-random sequences. Attackers may predict future elements from the initial elements of the random sequence, posing a security risk to quantum key distribution.This paper analyzes the problems existing in current pseudo-random number generators and proposes corresponding attack methods and applicable scenarios based on the vulnerabilities in the pseudo-random sequence generation process. Under certain conditions, it is possible to obtain the keys of the communicating parties with very low error rates, thus effectively attacking the quantum key system. This paper presents new requirements for the use of random numbers in quantum key systems, which can effectively guide the security evaluation of quantum key distribution protocols.

A novel multi-delay feedback digital chaos anti-degradation algorithm and its application in key generator

Abstract Under conditions of finite accuracy, chaotic systems will exhibit a sequence of dynamic degradation issues. Such chaotic systems cannot be considered strictly chaotic, and their applications will be significantly impacted. A control approach is given to handle this problem, which combines parameter perturbation and multi-delay dynamic feedback. This approach utilizes a pseudo-random sequence produced by a high-performance chaotic system to disturb the parameters, then loops back the output of the previous state to the input based on its activity. Numerical studies were conducted to verify the usefulness of this enhanced technique when used in both one-dimensional and two-dimensional chaotic systems. Using a two-dimensional chaotic system as an example, it was confirmed that the enhanced digital chaotic system is extremely responsive to little variations in the starting value. Subsequently, a key generator was created, which successfully passed the NIST randomness test. The experimental results demonstrate that the enhanced digital chaotic system has favorable chaotic properties within the constraints of low precision.

Dynamics and implementation of a functional neuron model with hyperchaotic behavior under electromagnetic radiation

Prolonged exposure to electromagnetic radiation (EMR) may be hazardous to human health and plays a key role in the medical diagnosis of some diseases. And this effect can be better demonstrated by constructing a neuron model of EMR. Flux-controlled memristors can estimate the effects of EMR on neurons. In this work, a discrete flux-controlled memristor is used to estimate the behavior of EMR. Furthermore, the memristor is introduced into a neuron model to explore the effects of EMR on the behavior of neurons. The rich and interesting complex dynamical behavior of the model is investigated using analytical methods from nonlinear theory, including plotting bifurcation diagrams, Lyapunov exponent spectra (LEs) and complexity. By modulating the electromagnetic induction strength k of the memristor, it was observed that the introduction of EMR is able to generate hidden hyperchaotic attractors and initial-boosted behavior. The constructed neuron model is implemented based on a DSP platform. Pseudo random number generators (PRNGs) are further designed and the NIST test results illustrate the excellent random performance of the sequences generated by the neuron model. The properties exhibited in the neuron model under EMR provide a reference solution for EMR in the diagnosis and treatment of certain diseases.

SMETHODS FOR REDUCING THE PAPR OF FBMC SIGNALS BASED ON A DISCRETE-NONLINEAR SPROTT SYSTEM IMPLEMENTED OVER A FINITE GALOIS FIELD

In this article, we provide a comparative analysis of various methods for reducing the peak factor of Filter bank Multicarrier signals in a multiplexing system with a filter bank using the discrete-nonlinear Sprott system implemented over a finite Galois field. The methods of partial transmission sequence, scrambling, and a combined method, which includes both methods, are considered. Each method is based on the use of a pseudorandom sequence, the formation of which is provided by generators based on a discrete nonlinear Sprott system. As a result of the work, the peak factor for each method is estimated and an additional cumulative distribution function is also presented. In addition, the influence of the number of iterations and windows used in the partial transmission sequence method on the peak factor was estimated. The results obtained in the course of the study can be applied in the design of information transmission systems.

Photonic compressive sensing of microwave signals with enhanced compression ratio and frequency range via optical pulse random mixing.

We propose and demonstrate a photonic compressive sensing (PCS) scheme for microwave signals using optical pulse random mixing, significantly enhancing both the compression ratio and operating frequency range. Unlike continuous-wave laser-based PCS systems, our approach mitigates the non-ideal characteristics of the pseudo-random binary sequence (PRBS), such as sloped edges and amplitude jitters, resulting in a more ideal compression process. Additionally, the high harmonic components of the optical pulses further facilitate wideband downconversion, improving the system's operating frequency range. In a proof-of-concept experiment, a dual-tone signal within the 4 GHz range is successfully recovered with a compression ratio of 20. Moreover, single-tone signals beyond the first Nyquist zone, at 7.17 GHz, 11.26 GHz, and 14.6 GHz, are effectively reconstructed with a compression ratio of 40. The proposed PCS system offers a simple, highly efficient solution for wideband spectrum identification, surpassing the performance of conventional continuous-wave-based PCS systems.

Construction of Flexible Deterministic Sparse Measurement Matrix in Compressed Sensing Using Legendre Sequences.

Compressed sensing (CS) is an innovative signal acquisition and reconstruction technology that has broken through the limit of the Nyquist sampling theory. It is widely employed to optimize the measurement processes in various applications. One of the core challenges of CS is the construction of a measurement matrix. However, traditional random measurement matrices are often impractical. Additionally, many existing deterministic binary measurement matrices fail to provide the required flexibility for practical applications. In this study, inspired by the observation that pseudo-random sequences share similar properties with random sequences, we constructed a deterministic sparse measurement matrix with a flexible measurement number based on an pseudo-random sequence-the Legendre sequence. Empirical analysis of the phase transition and an assessment of the practical features of the proposed measurement matrix were conducted. We validated the effectiveness of the proposed measurement matrix on randomly synthesized signals and images. The results of our simulations reveal that our proposed measurement matrix performs better than several other measurement matrices, particularly in terms of accuracy and efficiency.

Enhancing security and randomness in cryptography and non-cryptographic applications with ORNA algorithm

Abstract In this paper, we advocate for using PRNGs to generate long sequences of statistically random numbers, also known as pseudorandom numbers. It has several practical applications, including cryptography, weather-based stimulation, procedural environment noise generation in games and casinos, and scientific simulations of real-world problems, like city traffic systems that use it to stimulate cars. One distinctive feature of our approach is the PRNG algorithm we propose; this algorithm has successfully produced statistically sound long-term sequences. The properties of the PRNG are assessed using several statistical methods. Our work presents the Oscillating Random Number Algorithm (ORNA), a new kind of random number generator, and examines both the statistical tests proposed by NIST and the results that ORNA has generated. The following also describes the several preceding algorithms developed, including the Mersenne Twister Algorithm (MT19937) and the Permuted Congruential Algorithm (PCG128), and compares ORNA’s graphical efficiency to theirs. In this work, we compared ORNA to MT19937 and PCG128, and found that ORNA excels according to all 16 statistical tests. ORNA has three primary benefits, namely, superior statistical performance, quicker code execution, and simpler code implementation due to the algorithm’s reduced complexity.

Drone-Captured Wildlife Data Encryption: A Hybrid 1D–2D Memory Cellular Automata Scheme with Chaotic Mapping and SHA-256

In contemporary wildlife conservation, drones have become essential for the non-invasive monitoring of animal populations and habitats. However, the sensitive data captured by drones, including images and videos, require robust encryption to prevent unauthorized access and exploitation. This paper presents a novel encryption algorithm designed specifically for safeguarding wildlife data. The proposed approach integrates one-dimensional and two-dimensional memory cellular automata (1D MCA and 2D MCA) with a bitwise XOR operation as an intermediate confusion layer. The 2D MCA, guided by chaotic rules from the sine-exponential (SE) map, utilizes varying neighbor configurations to enhance both diffusion and confusion, making the encryption more resilient to attacks. A final layer of 1D MCA, controlled by pseudo-random number generators, ensures comprehensive diffusion and confusion across the image. The SHA-256 hash of the input image is used to derive encryption parameters, providing resistance against plaintext attacks. Extensive performance evaluations demonstrate the effectiveness of the proposed scheme, which balances security and complexity while outperforming existing algorithms.

Random Numbers for Machine Learning: A Comparative Study of Reproducibility and Energy Consumption

Pseudo-Random Number Generators (PRNGs) have become ubiquitous in machine learning (ML) technologies because they are interesting for numerous methods. In the context of ML, multiple stochastic streams, produced in black boxes for methods such as stochastic gradient descent or dropout, can produce a lack of repeatability, impacting the ability to debug and explain results. The field of machine learning holds the potential for substantial advancements across various domains. However, despite the growing interest, persistent concerns include issues related to reproducibility and energy consumption. Reproducibility is crucial for robust scientific inquiry and explainability, while energy efficiency underscores the imperative to conserve finite global resources. This study delves into the investigation of whether the leading Pseudo-Random Number Generators (PRNGs) employed in machine learning languages, libraries, and frameworks uphold statistical quality and numerical reproducibility when compared to the original C implementation of the respective PRNG algorithms. Additionally, we aim to evaluate the time efficiency and energy consumption of various implementations. Our experiments encompass Python, NumPy, TensorFlow, and PyTorch, utilizing the Mersenne Twister, Permuted Congruential Generator (PCG), and Philox algorithms. Remarkably, we verified that the temporal performance of machine learning technologies closely aligns with that of C-based implementations, with instances of achieving even superior performances. On the other hand, it is noteworthy that ML technologies consumed only 10% more energy than their C-implementation counterparts. However, while statistical quality was found to be comparable, achieving numerical reproducibility across different platforms for identical seeds and algorithms was not achieved.