Pseudorandom Number Generator Research Articles

Efficient image encryption scheme using a nonlinear shift register and chaos

Powerful cryptographic systems require a qualified random number generator. This research purposes to provide a comprehensive comparative analysis done on several of the well-known pseudo-random number generators (PRNGs) regarding their efficiency and resilience against crypto-analytical threats. These generators consist of the basic 8-bit Non-Linear Feedback Shift Register (NLFSR), the logistic map (LM), and our proposed hybrid random number generator named NLFSR-LM, which combines through XOR operation the sequences of the NLFSR with the LM to achieve a high quality of randomness. The performance of the created generator is examined and subsequently compared according to statistical tests of randomness alongside cryptographic features in terms of key space, key sensitivity and resistance to numerous attacks. The proposed generator produced good results and exhibited several interesting properties, such as a high degree of security, a sufficiently large key space, and it provided better randomness than other frequently used PRNGs.

Design A Novel Image Encryption Algorithm Based on A PRNG with High Performance

This paper proposes a novel two-dimensional logistic map (2D-LM). Relative to the classical 2D logistic modulation map (2D-LMM), it has larger chaotic range and better chaos performance. In comparison with some 2D chaos maps, the proposed new 2D-LM also has unique advantages in the complexity of sequence. To further study its application, the novel image encryption algorithm is designed based on the proposed 2D-LM. The security tests show the higher anti-decryption ability of the design algorithm. Finally, we develop a FPGA test platform to realize the Pseudo-Random Number Generator (PRNG) based on the proposed 2D-LM. The experiment results show the feasibility of its industrial applications.

Fast, high-quality pseudo random number generators for heterogeneous computing

Random number generation is key to many applications in a wide variety of disciplines. Depending on the application, the quality of the random numbers from a particular generator can directly impact both computational performance and critically the outcome of the calculation. High-energy physics applications use Monte Carlo simulations and machine learning widely, which both require high-quality random numbers. In recent years, to meet increasing performance requirements, many high-energy physics workloads leverage GPU acceleration. While on a CPU, there exist a wide variety of generators with different performance and quality characteristics, the same cannot be stated for GPU and FPGA accelerators. On GPUs, the most common implementation is provided by cuRAND - an NVIDIA library that is not open source or peer reviewed by the scientific community. The highest-quality generator implemented in cuRAND is a version of the Mersenne Twister. Given the availability of better and faster random number generators, high-energy physics moved away from Mersenne Twister several years ago and nowadays MIXMAX is the standard generator in Geant4 via CLHEP. The MIXMAX original design supports parallel streams with a seeding algorithm that makes it especially suited for GPU and FPGA where extreme parallelism is a key factor. In this study we implement the MIXMAX generator on both architectures and analyze its suitability and applicability for accelerator implementations. We evaluated the results against “Mersenne Twister for a Graphic Processor” (MTGP32) on GPUs which resulted in 5, 13 and 14 times higher throughput when a 240, 17 and 8 sized vector space was used respectively. The MIXMAX generator coded in VHDL and implemented on Xilinx Ultrascale+ FPGAs, requires 50% fewer total Look Up Tables (LUTs) compared to a 32-bit Mersenne Twister (MT-19337), or 75% fewer LUTs per output bit. In summary, the state-of-the art MIXMAX pseudo random number generator has been implemented on GPU and FPGA platforms and the performance benchmarked.

Some Properties of a Discrete Lorenz System Obtained by Variable Midpoint Method and Its Application to Chaotic Signal Modulation

Various discretization effects caused by applying numerical integration techniques to continuous chaotic systems are broadly studied in nonlinear science. Along with the negative impact on the precision of the various finite-difference schemes, such effects may have surprisingly fruitful practical applications, e.g. pseudo-random number generation, image encryption with improved diffusion and confusion properties, chaotic path planning, and many others. One such application is chaos-based communication systems which gained attention in recent decades due to their high covertness and broadband transmission capability. A crucial problem in the design of chaotic communication systems is the modulation of carrier signals. Due to the noise-like properties of chaotic signals, they can barely be modulated using the same methods as conventional harmonic signals. Thus, developing new modulation techniques is of great interest in the field of chaotic communications. In this study, we investigate the discrete model of the Lorenz oscillator obtained using controllable midpoint numerical integration and develop a novel modulation technique for chaos-based communication systems. We discover and analyze the multistability phenomenon in the dynamics of the investigated finite-difference Lorenz model through bifurcation, the basin of attraction, and Lyapunov spectrum analysis procedures. Using a specially designed testbench, we explicitly show that the proposed modulation method outperforms commonly used parametric modulation and is nearly equal to the state-of-the-art symmetry-based modulation in terms of covertness and noise resistivity. In addition, the proposed modulation technique is much easier to implement using computer arithmetics, especially in fixed-point hardware. The reported results may be efficiently applied to designing advanced chaos-based communications systems or improving the characteristics of existing communication system architectures.

Modelling the Lengths of Quantitative Motifs in Pseudorandom Integer Sequences

This study explores the behaviour of quantitative motifs in random numerical data, focussing on the property of length. One hundred and twenty sequences of pseudorandom integers were generated and segmented into quantitative motifs using the standard definition. The length–frequency relationship was modelled in each case using the Zipf-Alekseev function. Different combinations of sequence length, integer range, and pseudorandom number generator were trialled. The model-fitting was successful in all cases (𝑅2 1 > 0.9 in 118/120 cases and > 0.8 in 2/120), and the model parameters fell in the same range as those obtained in a previous textual study of motifs. Integer range was the main factor affecting the parameter values, with sequence length affecting the degree of spread. Further comparisons between textual and random data are needed, as well as a theoretical explanation of why motifs in random data demonstrate lawful behaviour. In future textual motif studies, particular attention needs to be paid to possible dependencies on value range and text length.

Four Novel Dual Discrete Memristor-Coupled Hyperchaotic Maps

Unlike the high-dimensional hyperchaotic system based on a continuous memristor, the low-dimensional map coupled by discrete memristor (DM) and traditional chaotic map can also generate hyperchaos. However, the hyperchaotic map constructed by two DMs has not attracted much attention. To this end, a generalized two-dimensional dual DM-coupled hyperchaotic mapping model is reported in this paper, and four specific maps are provided. The proposed maps have line invariant points, which can be interpreted as allowing arbitrary real values for the initial condition associated with the DM, and the stability is investigated in detail. Furthermore, the coupling strength-dependent and initial condition-dependent complex dynamics of four maps are studied by numerical simulations, and the dynamical performance is evaluated from the perspective of quantitative analysis. It is shown that the considered maps are capable of exhibiting the three characteristic fingerprints of memristors in arbitrary parameter spaces, and this characteristic has gained attention for the first time. In particular, the complete control of the considered maps by variable substitution is performed, which can generate arbitrary switched hyperchaotic behaviors. In addition, four pseudo-random number generators are designed based on the proposed maps, and the randomness is tested by using the NIST SP800-22 software. In general, the proposed maps can not only generate abundant dynamical behaviors, but also enrich the DM circuits and provide a reference for applications based on chaos. Finally, the developed digital hardware circuit implementation platform verifies the results of the numerical method.

Analysis and Guidelines for Different Designs of Pseudo Random Number Generators

Analysis and Guidelines for Different Designs of Pseudo Random Number Generators

Design of a Multiple Pseudorandom Number Generator Combined Chaotic System With RNS and Its Application to Secure Image Processing

Design of a Multiple Pseudorandom Number Generator Combined Chaotic System With RNS and Its Application to Secure Image Processing

A Hierarchical Multiscenario H.265/HEVC Video Encryption Scheme

With the pervasive application of video streaming, the security of streaming media information continually faces new challenges. Most existing encryption methods employ uniform criteria for encrypting all scenarios, leading to unnecessary mutual inhibition of algorithm security and coding efficiency. Furthermore, several encryption algorithms are inadequate for high-resolution videos. A novel, independently hierarchical video cryptosystem for H.265/high efficiency video coding (HEVC) is proposed that develops a scene-adaptive encryption strategy tailored for multiscenario videos. Additionally, we fully consider the seeds of pseudo-random number generators, syntax components in compressed codes, and scenario indicators. We analyze the visibility of encrypted videos in different scenarios and the encryption performance of various syntax parameters based on the integration of encryption for three distinct scenario categories to further enhance encryption efficiency and security. The method’s versatility is demonstrated using a diverse array of videos with significant and insignificant inter-frame motion information across varying resolutions. The experimental results from the video datasets indicate that our scheme effectively balances security and coding efficiency. Furthermore, the scene-adaptive approach can be tailored flexibly according to subscriber needs.

Study of the set of initial values of pseudorandom number generators based on floating point arithmetic

Study of the set of initial values of pseudorandom number generators based on floating point arithmetic

Hardware random numbers generator based on microcontroller

The work considers the principles of development and organization of the random number generation system using a hardware generator of true random numbers. An analysis of noise sources for a hardware generator of true random numbers has been carried out. The architecture of the random and pseudo-random number generation system, the structure of the hardware part, and the interaction protocol of the system elements have been developed. Hardware and software of the system are implemented. An analysis of numbers sequences randomness degree obtained in different modes was carried out using a NIST statistical tests suite and visual tests. Recommendations for using the system are given.

Comparative Analysis of Pseudorandom Number Generators: Mersenne Twister, Middle Square Method, and Linear Congruential Generator through Dieharder Tests

Comparative Analysis of Pseudorandom Number Generators: Mersenne Twister, Middle Square Method, and Linear Congruential Generator through Dieharder Tests

On a Vernam cipher scheme based on elliptic curve L-functions

In this paper, we present a new Vernam-like cryptosystem based on the L-functions attached to elliptic curves. Actually, we show that for infinitely many elliptic curves, the coefficients of the L-series can be considered as a secure cryptographic cipher key when combined with linear and classical pseudo-random number generators. Hence, fast and widely known classical generators, like linear congruential generators, should be reintroduced into our list of cryptographic design choices.

Pseudo-Random Number Generators for Stochastic Computing (SC): Design and Analysis

Pseudo-Random Number Generators for Stochastic Computing (SC): Design and Analysis

A Process based Algorithm for Random Number Generation

Background: Random number generation plays a crucial role in various scientific, computational, cryptographic applications and stochastic processes. This paper introduces a novel algorithm designed to address the demand for high-quality random numbers with improved statistical properties. The proposed Algorithm uses the elements of hardware-based entropy to generate random numbers for efficiency and unpredictability. Methods: Pseudo-random numbers are sequences derived from algorithms known as pseudo-random number generators (PRNGs). These generators use an initial value, or seed, to produce sequences that exhibit statistical properties akin to truly random numbers.Results:For the z-test statistic and the corresponding p-value in the above five samples we found that p-value is not less than α = 0.05, therefore we fail to reject the null hypothesis. Conclusions: Module U behaves as a Random number generation algorithm. Further, we can test the module U for large samples and we can use module U for simulation of different Random processes to verify it’s correctness.

Various pseudo random number generators based on memristive chaos map model

Various pseudo random number generators based on memristive chaos map model

Comparison of two new chaos-based pseudorandom number generators implemented in microcontroller

Chaos-based encryption algorithms uses a pseudorandom number generator (PRNG) to generate chaotic dynamics to carry out the processes to encrypt different types of information. One of the main problems is that some chaotic systems do not present high randomness and uniformity in time series affecting directly the security of the chaos-based cryptosystem. In this work, we proposed two new 2D hyperchaotic maps designed from 1D chaotic maps to use in the design of two new PRNGs for cryptographic applications. The proposed PRNGs were implemented in Renesas RA4M1 32-bit microcontroller for first time in the literature. The chaotic sequences with double-precision floating-point format are also validated with different randomness and security analyses such as the Lyapunov exponent, key space, histograms, autocorrelation, information entropy and the NIST SP800-22 test. In addition, a comparison of the results with similar schemes in the literature about design, security and performance is made. The results achieved in this work can help scholars and designers to improve the effectiveness in randomness of new chaos-based PRNGs for cryptographic applications.

Pseudorandom number generation derived from Josephson junction stimulated by Wien bridge oscillator embedded in the microcontroller

Pseudorandom number generation derived from Josephson junction stimulated by Wien bridge oscillator embedded in the microcontroller

Enhancing logistic chaotic map for improved cryptographic security in random number generation

The use of chaotic maps for cryptography is advantageous due to their desirable characteristics, including complexity, unpredictability, sensitivity to initial values and control parameters, and ergodicity. However, most chaos-based systems have limitations that make them impractical, such as low efficiency, insufficient security, and small keyspace. To overcome these challenges, this paper proposes an enhanced logistic map (ELM), a one-dimensional digital chaotic map based on the logistic map and anterior perturbation method. The ELM map leverages perturbations of chaotic states, leading to enhanced randomness, data distribution, and low correlation, with improved security properties. The ELM map is simple yet capable of generating large chaotic behavior. The findings show that the ELM map is highly secure and can be used in various cryptographic applications. A new pseudorandom number generator (PRNG) is also proposed based on a combination of ELM chaotic maps. The resulting PRNG is highly dependent on the chaotic properties of the maps and the combination rule. Statistical analysis shows that the proposed method is statistically secure, highlighting the potential of the ELM map for other cryptographic applications.

Realization of a pseudo-random number generator utilizing two coupled Izhikevich neurons on an FPGA platform

Realization of a pseudo-random number generator utilizing two coupled Izhikevich neurons on an FPGA platform