Efficient Pseudo-random Number Generator Research Articles

Cryptographic Grade Chaotic Random Number Generator Based on Tent-Map

In recent years, there has been an increasing interest in employing chaotic-based random number generators for cryptographic purposes. However, many of these generators produce sequences that lack the necessary strength for cryptographic systems, such as Tent-Map. However, these generators still suffer from common issues when generating random numbers, including issues related to speed, randomness, lack of statistical properties, and lack of uniformity. Therefore, this paper introduces an efficient pseudo-random number generator, called State-Based Tent-Map (SBTM), based on a modified Tent-Map, which addresses this and other limitations by providing highly robust sequences suitable for cryptographic applications. The proposed generator is specifically designed to generate sequences with exceptional statistical properties and a high degree of security. It utilizes a modified 1D chaotic Tent-Map with enhanced attributes to produce the chaotic sequences. Rigorous randomness testing using the Dieharder test suite confirmed the promising results of the generated keystream bits. The comprehensive evaluation demonstrated that approximately 97.4% of the tests passed successfully, providing further evidence of the SBTM’s capability to produce sequences with sufficient randomness and statistical properties.

Construction of a New 2D Hyperchaotic Map with Application in Efficient Pseudo-Random Number Generator Design and Color Image Encryption

This paper proposes a new two-dimensional discrete hyperchaotic system and utilizes it to design a pseudo-random number generator (PRNG) and an efficient color image encryption algorithm. This hyperchaotic system has very complex dynamic properties and can generate highly random chaotic sequences. The complex hyperchaotic characteristics of the system are confirmed via bifurcation diagram, chaotic attractor, Lyapunov exponents, correlation analysis, approximate entropy and permutation entropy. Compared with some traditional discrete chaotic systems, the new chaotic system has a larger range of chaotic parameters and more complex hyperchaotic characteristics, making it more suitable for application in information encryption. The proposed PRNG can generate highly random bit sequences that can fully pass all NIST testing items. The proposed color image encryption algorithm achieves cross-channel permutation and diffusion of pixels in parallel. These strategies not only greatly improve the encryption speed of color images, but also enhance the security level of cipher images. The simulation experiments and security analysis results show that the algorithm has strong robustness against differential attacks, statistical attacks and interference attacks, and has good application potential in real-time secure communication applications of color images.

A resource efficient pseudo random number generator based on sawtooth maps for Internet of Things

AbstractThe strength of cryptographic keys rely on the random number generators (RNGs) to produce random seed values. Unfortunately there are not many RNGs options suitable for Internet of Things (IoTs) scenario, due to limited processing resources and bulk quantity of IoT data that needs to be secured. In this article, we studied sawtooth map which is a chaotic map. However, when implemented on a computer, the sawtooth map results on a non‐chaotic orbit due to the finite precision of computation. This can be avoided if we use the sawtooth map as the local map in a coupled map lattice (CML) system. We explore such coupled map systems for randomness through entropy and statistical analysis. Based on the results, we propose a lightweight hybrid pseudo random number generator (PRNG) based on sawtooth based CML system and SPONGENT hashing. The proposed PRNG is thoroughly tested against statistical attacks, entropy analysis, key space analysis and compared with existing state of the art solutions. The results provide evidence that the proposed PRNG produces random numbers that could produce sufficiently strong cryptographic keys for resource constrained IoT devices.

Hybrid Design of Pseudo Random Number Generator Using Shift Register FPGA and CMOS VLSI

The proliferation of digital systems in various applications necessitates the development of efficient pseudo-random number generators (PRNGs) for cryptographic and data processing purposes. In this study, we present a novel approach to PRNG design, leveraging a hybrid combination of Shift Register Field-Programmable Gate Arrays (FPGA) and Complementary Metal-Oxide-Semiconductor (CMOS) Very Large-Scale Integration (VLSI) technology. This hybrid design capitalizes on the strengths of both FPGA and CMOS VLSI to achieve enhanced performance and versatility. The FPGA-based component of the PRNG system offers configurability and parallelism, allowing for rapid and customizable PRNG generation. The CMOS VLSI component, on the other hand, ensures low power consumption and compact integration, ideal for embedded applications. By combining these two technologies, the PRNG achieves a delicate balance between flexibility and efficiency. We evaluate the hybrid PRNG design through rigorous testing and analysis, including statistical tests, spectral tests, and computational performance assessments. Our results demonstrate that the hybrid PRNG outperforms standalone FPGA or CMOS-based PRNGs in terms of randomness, uniformity, and speed, making it suitable for a wide range of applications in cryptography, secure communications, and data processing. The hybrid PRNG design presented in this study not only contributes to the advancement of PRNG technology but also offers a versatile solution for engineers and researchers seeking to tailor their PRNG systems to specific application requirements while optimizing performance and energy efficiency.

A Generic Model of the Pseudo-Random Generator Based on Permutations Suitable for Security Solutions in Computationally-Constrained Environments.

Symmetric cryptography methods have an important role in security solutions design in data protection. In that context, symmetric cryptography algorithms and pseudo-random generators connected with them have strong influence on designed security solutions. In the computationally constrained environment, security efficiency is also important. In this paper we proposed the design of a new efficient pseudo-random generator parameterized by two pseudo-random sequences. By the probabilistic, information-theoretic and number theory methods we analyze characteristics of the generator. Analysis produced several results. We derived sufficient conditions, regarding parameterizing sequences, so that the output sequence has uniform distribution. Sufficient conditions under which there is no correlation between parameterizing sequences and output sequence are also derived. Moreover, it is shown that mutual information between the output sequence and parameterizing sequences tends to zero when the generated output sequence length tends to infinity. Regarding periodicity, it is shown that, with appropriately selected parameterizing sequences, the period of the generated sequence is significantly longer than the periods of the parameterizing sequences. All this characteristics are desirable regarding security applications. The efficiency of the proposed construction can be achieved by selection parameterizing sequences from the set of efficient pseudo-random number generators, for example, multiple linear feedback shift registers.

KISS: A bit too simple

KISS (‘Keep it Simple Stupid’) is an efficient pseudo-random number generator originally specified by G. Marsaglia and A. Zaman in 1993. G. Marsaglia in 1998 posted a C version to various USENET newsgroups, including sci.crypt. Marsaglia himself has never claimed cryptographic security for the KISS generator, but others have made the intellectual leap and claimed that it is of cryptographic quality. In this paper we show a number of reasons why the generator does not meet some of the KISS authors’ claims, why it is not suitable for use as a stream cipher, and that it is not cryptographically secure. Our best attack requires about 70 words of generated output and a few hours of computation to recover the initial state. In early 2011, G. Marsaglia posted a new version of KISS, which falls to a simple divide-and-conquer attack.

A Novel Pseudo-Random Number Generator for Cryptographic Applications

Background: Pseudo random numbers have indispensable role in designing cryptography systems such as key stream in stream ciphers. Efficiency of most crypto systems are in depend on the quality of secret key generated by a pseudo random number generator. Improvements/Methods: In the present paper, an efficient pseudo random number generator is presented for cryptographic applications. The algorithm is based on controlling distribution of generated random numbers with the chaotic henon congruential generator. Statistical Analyses: Statistical tests and histograms are performed over the proposed generator and the results confirm the improvements over the proposed algorithms. According to the results of statistical tests, proposed algorithms generate pseudo random numbers with acceptable independency and uniformity and random sequences with long enough period. Applications: Key streams in stream cipher system can be considered as the most important applications of pseudo random numbers. With this regard proposed generators are statistically proved as proper key stream generator for designing stream cipher systems.

An Efficient Noise Generator for Validation of Channels Equalizers

This paper develops an efficient pseudo-random number generator for validation of digital communication channels and secure disc. Drives. Simulation results validates the effectiveness of the random number generator.

Efficient, perfect polynomial random number generators

Let N be a positive integer and let P ε ℤ [x] be a polynomial that is nonlinear on the set ℤ N of integers modulo N. If, by choosing x at random in an initial segment of ℤ N , P(x) (mod N) appears to be uniformly distributed in ℤ N to any polynomial-time observer, then it is possible to construct very efficient pseudorandom number generators that pass any polynomial-time statistical test. We analyse this generator from two points of view. A complexity theoretic analysis relates the perfectness of the generator to the security of the RSA-scheme. A statistical analysis proves that the least-significant bits of P(x) (mod N) are statistically random.