Design Of Pseudorandom Number Generators Research Articles

Design of pseudorandom number generator based on a controllable multi-double-scroll chaotic system

The generation, implementation, and application of multi-scroll chaotic systems have been extensively studied due to their complex dynamic behaviors. This paper introduces a new controlled multi-double-scroll chaotic system and its corresponding implementation on a digital platform, the Field Programmable Gate Array (FPGA). The proposed system can generate 2N+1 and 2N+2 numbers of double-scroll attractors. In particular, the system has controllable multistability and multi-double-scroll complete amplitude control characteristics. The numerical analyses of Lyapunov exponents, bifurcation diagrams, phase diagrams, and basin of attraction show that the system exhibits complex dynamic behaviors. Furthermore, a new pseudo-random number generator (PRNG) is designed based on the multi-double-scroll chaotic system (MDSCS), in which a post-processing circuit is used to improve the quality of the generator. The PRNG has a high data throughput and uses only a small amount of resources in the target FPGA. The proposed PRNG uses less than 1% of the resources of the target FPGA and delivers a data bit throughput of 7.2 Gbps/s. To our best knowledge, it reaches the highest data throughput of PRNG based on continuous chaotic systems. The evaluation sequences are tested using generic randomness tests such as NIST SP800-22, TestU01, and Histograms. The experimental results show that the random sequences generated by our design have passed all the test items, which means that they will have excellent performance in the application.

A generalized framework for elliptic curves based PRNG and its utilization in image encryption

In the last decade, Elliptic Curves (ECs) have shown their efficacy as a safe fundamental component in encryption systems, mainly when used in Pseudorandom Number Generator (PRNG) design. This paper proposes a framework for designing EC-based PRNG and maps recent PRNG design techniques into the framework, classifying them as iterative and non-iterative. Furthermore, a PRNG is designed based on the framework and verified using the National Institute of Standards and Technology (NIST) statistical test suite. The PRNG is then utilized in an image encryption system where statistical measures, differential attack measures, the NIST statistical test suite, and system key sensitivity analysis are used to demonstrate the system's security. The results are good and promising as compared with other related work.

A new class of Hamiltonian conservative chaotic systems with multistability and design of pseudo-random number generator

• A new modeling method is employed to develop a class of high dimensional Hamiltonian conservative chaotic systems. • A new conservative hyperchaotic system is proposed and exhibits some behaviour previously unobserved. • Multistability including infinite-orbit and infinite-scroll is observed in the proposed systems. • For encryption, pseudo-random digital signal generators based on conservative chaotic systems are developed. Compared to dissipative chaotic system, conservative chaotic systems have some attractive features valuable for engineering applications, such as security communication. This paper proposes a method for constructing new high dimensional conservative chaotic systems, for instance 4 dimensional conservative chaotic systems and 5 dimensional conservative hyper-chaotic systems. The dynamic properties of the constructed systems are verified by the dynamical evolution map, equilibrium points, Lyapunov dimension, the volume of flow and the Hamiltonian energy. An interesting co-existence of quasi-period, chaos and hyper-chaos flows are observed in the developed conservative chaotic systems. With trigonometric transformation, parallel conservative chaotic systems are achieved with infinitely many scrolls. To accommodate the engineering application requirement, the security communication is considered as a case study. The proposed conservative chaotic systems passed the validation National Institute of Standard Statistic Test criteria for the pseudo-random property , which is the critical factor of security communication. Furthermore, the pseudo-random signal generator is developed using the Field Programmable Gate Array technique. Due to the complicated topology structure, such digital implementation was not commonly reported in literatures, instead most conservative chaotic systems were validated only by analog circuit simulation.

Design and FPGA Implementation of a Pseudorandom Number Generator Based on a Four-Wing Memristive Hyperchaotic System and Bernoulli Map

Random numbers are widely used in the fields of computer, digital signature, secure communication and information security. Especially in recent years, with the large-scale application of smart card and the demand of information security, the demand for high-quality random number generator is increasingly urgent. With the development of the theory of non-linear systems, the design of pseudorandom number generator (PRNG) for chaotic behavior of non-linear systems provides a new theoretical basis and implementation method. This paper presents a PRNG based on a no-equilibrium four-wing memristive hyperchaotic system (FWMHS) and its implementation on Field Programmable Gate Array (FPGA) board. In order to increase the output throughput and the statistical quality of the generated bit sequences, we propose the PRNG design which uses a dual entropy sources architecture with FWMHS and Bernoulli map. Simulation and experimental results verifying the feasibility of the FWMHS are also given. Then, the proposed PRNG system is modeled and simulated on the Vivado 2018.3 platform, and implemented on the Xilinx ZYNQ-XC7Z020 FPGA evaluation board. The maximum operating frequency has been achieved as 135.04 MHz with a speed of 62.5 Mbit/s. Finally, we have experimentally verified that the binary data obtained by this dual entropy sources architecture pass the tests of NIST 800.22, ENT and AIS.31 statistical test suites with XOR function post-processing for a high throughput speed. The security analysis is carried out by means of dynamical degradation, key space, key sensitivity, correlation and information entropy. Statistical tests and security analysis show that it has good pseudorandom characteristics and can be used in chaos-based cryptographic applications at hardware or software implementation.

Random number generators for MIMD parallel processors

We discuss and analyze issues related to the design of pseudorandom number generators (prn's) for MIMD (multiple instruction stream/multiple data stream) parallel processors, which are very well suited to Monte Carlo calculations. We are concerned with ensuring reproducibility of runs, providing very long sequences, and assuring an adequate degree of independence of the parallel streams. We consider the class of linear congruential generators x n+1,i ≡ ax n,1 + b i mod m and analyze the effect that different choices of b i have on the correlation properties between such streams. We derive a spectral test ν τ for t parallel linear congruential generators, a modification of Knuth's Algorithm S. From this, we prove a good lower bound for v 2 = min all pairs(i,j) ν 2( i, j) for certain choices of b i 's. The set of the largest r primes p i , i = 1, …, r, satisfying p i < √ m 2 , where m is the period length of each generator, gives a lower bound O(m 1 2 ) to the correlation between a pair of corresponding elements in any two streams. An alternative choice, b i = d i mod m for d = M 1 2 + 1 gives a bound O(m 1 2 (t − 1)) which will be satisfactory for small numbers of streams. Finally, we construct a spectral test for correlations between x n, i and x n+ k, i+ l , but derive no analytic prescriptions from it.