Good Pseudo-random Number Generator Research Articles

DNA Image Encryption Scheme Based on a Chaotic LSTM Pseudo-Random Number Generator

Deoxyribonucleic Acid (DNA) coding technology is a new research field developed by the combination of computer science and molecular biology, that has been gradually applied in the field of image encryption in recent years. Furthermore, sensitivity to initial conditions, pseudo-random properties, and state ergodicity of coupled chaotic maps can help produce good pseudo-random number generators and meet the requirements of an image encryption system well. In this paper, an image encryption algorithm based on high-dimensional coupled chaotic maps and DNA coding is proposed. A pseudo-random sequence is generated by a long short-term memory (LSTM) architecture using the proposed maps and evaluated through a set of statistical tests to show the high performance of the proposed generator. All intensity values of an input image are converted to a binary sequence, which is scrambled globally by the high-dimensional coupled chaotic maps. The DNA operations are performed on the scrambled binary sequences instead of binary operations to increase the algorithm efficiency. Simulation results and performance analyses demonstrate that the proposed encryption scheme is extremely sensitive to small changes in secret keys, provides high security and can resist differential attack.

Study on upper limit of sample size for a two-level test in NIST SP800-22

NIST SP800-22 is one of the most widely used statistical testing tools for pseudorandom number generators (PRNGs). This tool consists of 15 tests (one-level tests) and two additional tests (two-level tests). Each one-level test provides one or more p-values. The two-level tests measure the uniformity of the obtained p-values for a fixed one-level test. One of the two-level tests categorizes the p-values into ten intervals of equal length, and apply a chi-squared goodness-of-fit test. This two-level test is often more powerful than one-level tests, but sometimes it rejects even good PRNGs when the sample size at the second level is too large, since it detects approximation errors in the computation of p-values. In this paper, we propose a practical upper limit of the sample size in this two-level test, for each of six tests appeared in SP800-22. These upper limits are derived by the chi-squared discrepancy between the distribution of the approximated p-values and the uniform distribution U(0, 1). We also computed a “risky” sample size at the second level for each one-level test. Our experiments show that the two-level test with the proposed upper limit gives appropriate results, while using the risky size often rejects even good PRNGs. We also propose another improvement: to use the exact probability for the ten categories in the computation of goodness-of-fit at the two-level test. This allows us to increase the sample size at the second level, and would make the test more sensitive than the NIST’s recommending usage.

Maximal length cellular automata in GF(q) and pseudo-random number generation

This work explores the randomness quality of maximal length cellular automata (CAs) in GF([Formula: see text]), where [Formula: see text]. A greedy strategy is chosen to select the candidate CAs which satisfy unpredictability criterion essential for a good pseudo-random number generator (PRNG). Then, performance of these CAs as PRNGs is empirically analyzed by using Diehard battery of tests. It is observed that, up to GF(11), increase in [Formula: see text] improves randomness quality of the CAs, but after that, it saturates. Finally, we propose an implementable design of a good PRNG based on a 13-cell maximal length cellular automaton over GF(11) which can compete with the existing well-known PRNGs.

Implementing 64-bit Maximally Equidistributed F 2 -Linear Generators with Mersenne Prime Period

CPUs and operating systems are moving from 32 to 64 bits, and hence it is important to have good pseudorandom number generators designed to fully exploit these word lengths. However, existing 64-bit very long period generators based on linear recurrences modulo 2 are not completely optimized in terms of the equidistribution properties. Here, we develop 64-bit maximally equidistributed pseudorandom number generators that are optimal in this respect and have speeds equivalent to 64-bit Mersenne Twisters. We provide a table of specific parameters with period lengths from 2 607 -1 to 2 44497 -1.

Developments in pseudo‐random number generators

Monte Carlo simulations have become a common practice to evaluate a proposed statistical procedure, particularly when it is analytically intractable. Validity of any simulation study relies heavily on the goodness of random variate generators for some specified distributions, which in turn is based on the successful generation of independent variates from the uniform distribution. However, a typical computer‐generated pseudo‐random number generator (PRNG) is a deterministic algorithm and we know that no PRNG is capable of generating a truly random uniform sequence. Since the foundation of a simulation study is built on the PRNG used, it is extremely important to design a good PRNG. We review some recent developments on PRNGs with nice properties such as high‐dimensional equi‐distribution, efficiency, long period length, portability, and efficient parallel implementations. WIREs Comput Stat 2017, 9:e1404. doi: 10.1002/wics.1404This article is categorized under: Algorithms and Computational Methods > Random Number Generation

Improving the pseudo-randomness properties of chaotic maps using deep-zoom

A generalized method is proposed to compose new orbits from a given chaotic map. The method provides an approach to examine discrete-time chaotic maps in a “deep-zoom” manner by using k-digits to the right from the decimal separator of a given point from the underlying chaotic map. Interesting phenomena have been identified. Rapid randomization was observed, i.e., chaotic patterns tend to become indistinguishable when compared to the original orbits of the underlying chaotic map. Our results were presented using different graphical analyses (i.e., time-evolution, bifurcation diagram, Lyapunov exponent, Poincaré diagram, and frequency distribution). Moreover, taking advantage of this randomization improvement, we propose a Pseudo-Random Number Generator (PRNG) based on the k-logistic map. The pseudo-random qualities of the proposed PRNG passed both tests successfully, i.e., DIEHARD and NIST, and were comparable with other traditional PRNGs such as the Mersenne Twister. The results suggest that simple maps such as the logistic map can be considered as good PRNG methods.

Pseudo-Random Number Generators for Vector Processors and Multicore Processors

Large scale Monte Carlo applications need a good pseudo-random number generator capable of utilizing both the vector processing capabilities and multiprocessing capabilities of modern computers in order to get the maximum performance. The requirements for such a generator are discussed. New ways of avoiding overlapping subsequences by combining two generators are proposed. Some fundamental philosophical problems in proving independence of random streams are discussed. Remedies for hitherto ignored quantization errors are offered. An open source C++ implementation is provided for a generator that meets these needs.

A PSEUDO-RANDOM NUMBER GENERATOR EMPLOYING MULTIPLE RÉNYI MAPS

The increasing risk along with the drastic development of multimedia data transmission has raised a big concern on data security. A good pseudo-random number generator is an essential tool in cryptography. In this paper, we propose a novel pseudo-random number generator based on the controlled combination of the outputs of several digitized chaotic Rényi maps. The generated pseudo-random sequences have passed both the NIST 800-22 Revision 1a and the DIEHARD tests. Moreover, simulation results show that the proposed pseudo-random number generator requires less operation time than existing generators and is highly sensitive to the seed.

A Bidirectional Generalized Synchronization Theorem -Based Chaotic Pseudorandom Number Generator

In order to design good pseudorandom number generator, using a bidirectional generalized synchronization theorem for discrete chaos system, this paper introduces a new 5 -dimensional bidirectional generalized chaos synchronization system (BGCSDS), whose prototype is a novel chaotic system . Numerical simulation showed that two pair variables of the BGCSDS achieve generalized chaos synchronization via a transform H. A chaos-based pseudorandom number generator (CPNG) was designed by the new BGCSDS . Using the FIPS-140-2 tests issued by the National Institute of Standard and Technology (NIST) verified the random ness of the 1000 binary number sequences generated via the CPNG and the RC4 algorithm respectively. The results showed all the tested sequences passed the FIPS-140-2 test s . The confidence interval analysis showe d the statistical properties of the randomness of the sequences generated via the CPNG and the RC4 algorithm do not have significant differences. So, t he CPNG is suitable to be used in the information security filed.

CONFIGURABLE CELLULAR AUTOMATA FOR PSEUDORANDOM NUMBER GENERATION

This paper proposes a generalized structure of cellular automata (CA) — the configurable cellular automata (CoCA). With selected properties from programmable CA (PCA) and controllable CA (CCA), a new approach to cellular automata is developed. In CoCA, the cells are dynamically reconfigured at run-time via a control CA. Reconfiguration of a cell simply means varying the properties of that cell with time. Some examples of properties to be reconfigured are rule selection, boundary condition, and radius. While the objective of this paper is to propose CoCA as a new CA method, the main focus is to design a CoCA that can function as a good pseudorandom number generator (PRNG). As a PRNG, CoCA can be a suitable candidate as it can pass 17 out of 18 Diehard tests with 31 cells. CoCA PRNG's performance based on Diehard test is considered superior over other CA PRNG works. Moreover, CoCA opens new rooms for research not only in the field of random number generation, but in modeling complex systems as well.