The Raybit Model and the Assessment of its Quality in Comparison with the Logit and Probit Models

2017 ◽  
Vol 64 (3) ◽  
pp. 305-322
Author(s):  
Jan Purczyński ◽  
Kamila Bednarz-Okrzyńska
Keyword(s):  
Cumulative Distribution Function ◽  
Random Number ◽  
Random Number Generator ◽  
The Other ◽  
Cumulative Distribution ◽  
Number Generator ◽  
Probit Models ◽  
Proposed Model ◽  
Logit And Probit Models

A new model for a dependent variable taking the value 0 or 1 (binary, dichotomous) was proposed. The name of the proposed model – the raybit model – stems from the fact that the probability corresponds to the Rayleigh cumulative distribution function. The assessment of the quality of selected models was conducted with the use of four definitions of error: MSE, MAE, WMSE, WMAE. Two computational examples were considered, which proved that the raybit model yields smaller values of error than the logit and probit models. Computer simulations were conducted using a random number generator with a binomial distribution. They proved that for the values of the theoretical probabilityfor the interval Pi ∈ [0; 0.8] the raybit model outperforms the other two models yielding a smaller value of error.

Pseudo-random number generation using a 3-state cellular automaton

2017 ◽  
Vol 28 (06) ◽  
pp. 1750078 ◽  
Author(s):  
Kamalika Bhattacharjee ◽  
Dipanjyoti Paul ◽  
Sukanta Das
Keyword(s):  
Cellular Automaton ◽  
Random Number ◽  
Random Number Generator ◽  
Random Number Generation ◽  
Number Generator ◽  
Number Generation ◽  
Pseudo Random Number ◽  
Empirical Tests ◽  
Pseudo Random Number Generator

This paper investigates the potentiality of pseudo-random number generation of a 3-neighborhood 3-state cellular automaton (CA) under periodic boundary condition. Theoretical and empirical tests are performed on the numbers, generated by the CA, to observe the quality of it as pseudo-random number generator (PRNG). We analyze the strength and weakness of the proposed PRNG and conclude that the selected CA is a good random number generator.

scholarly journals A Lightweight BCH Code Corrector of TRNG with Measurable Dependence

2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
Hojoong Park ◽  
Yongjin Yeom ◽  
Ju-Sung Kang
Keyword(s):  
Linear Code ◽  
Random Number ◽  
Random Number Generator ◽  
The Other ◽  
Bch Code ◽  
Compression Rate ◽  
Number Generator ◽  
Von Neumann ◽  
Other Hand ◽  
Cryptographic Algorithms

We propose a new lightweight BCH code corrector of the random number generator such that the bitwise dependence of the output value is controllable. The proposed corrector is applicable to a lightweight environment and the degree of dependence among the output bits of the corrector is adjustable depending on the bias of the input bits. Hitherto, most correctors using a linear code are studied on the direction of reducing the bias among the output bits, where the biased input bits are independent. On the other hand, the output bits of a linear code corrector are inherently not independent even though the input bits are independent. However, there are no results dealing with the independence of the output bits. The well-known von Neumann corrector has an inefficient compression rate and the length of output bits is nondeterministic. Since the heavy cryptographic algorithms are used in the NIST’s conditioning component to reduce the bias of input bits, it is not appropriate in a lightweight environment. Thus we have concentrated on the linear code corrector and obtained the lightweight BCH code corrector with measurable dependence among the output bits as well as the bias. Moreover, we provide some simulations to examine our results.

scholarly journals Deep Learning-Based Security Verification for a Random Number Generator Using White Chaos

Entropy ◽  
2020 ◽  
Vol 22 (10) ◽  
pp. 1134
Author(s):  
Cai Li ◽  
Jianguo Zhang ◽  
Luxiao Sang ◽  
Lishuang Gong ◽  
Longsheng Wang ◽  
...  
Keyword(s):  
Deep Learning ◽  
Predictive Model ◽  
Random Number ◽  
Random Number Generator ◽  
External Cavity ◽  
Number Generator ◽  
Output Data ◽  
Final Output ◽  
Linear Congruential

In this paper, a deep learning (DL)-based predictive analysis is proposed to analyze the security of a non-deterministic random number generator (NRNG) using white chaos. In particular, the temporal pattern attention (TPA)-based DL model is employed to learn and analyze the data from both stages of the NRNG: the output data of a chaotic external-cavity semiconductor laser (ECL) and the final output data of the NRNG. For the ECL stage, the results show that the model successfully detects inherent correlations caused by the time-delay signature. After optical heterodyning of two chaotic ECLs and minimal post-processing are introduced, the model detects no patterns among corresponding data. It demonstrates that the NRNG has the strong resistance against the predictive model. Prior to these works, the powerful predictive capability of the model is investigated and demonstrated by applying it to a random number generator (RNG) using linear congruential algorithm. Our research shows that the DL-based predictive model is expected to provide an efficient supplement for evaluating the security and quality of RNGs.

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

2020 ◽  
Vol 31 (03) ◽  
pp. 2050037
Author(s):  
Sumit Adak ◽  
Kamalika Bhattacharjee ◽  
Sukanta Das
Keyword(s):  
Cellular Automata ◽  
Random Number ◽  
Random Number Generator ◽  
Random Number Generation ◽  
Maximal Length ◽  
Number Generator ◽  
Greedy Strategy ◽  
Pseudo Random Number ◽  
Pseudo Random Number Generator

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.

scholarly journals Hybrid Clayton-Frank Convolution-Based Bivariate Archimedean Copula

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Maxwell Akwasi Boateng ◽  
Akoto Yaw Omari-Sasu ◽  
Richard Kodzo Avuglah ◽  
Nana Kena Frempong
Keyword(s):  
Convolution Operator ◽  
Cumulative Distribution Function ◽  
Random Variables ◽  
Archimedean Copula ◽  
The Other ◽  
Cumulative Distribution ◽  
Entire Real Line ◽  
Proposed Model ◽  
To Come ◽  
The Right

This study exploits the closure property of the converse convolution operator to come up with a hybrid Clayton-Frank Archimedean copula for two random variables. Pairs of random variables were generated and the upper tail observation of the cumulative distribution function (CDF) was used to assess the right skew behavior of the proposed model. Various values of the converse convolution operator were used to see their effect on the proposed model. The simulation covered lengths n=10i,  i=2,3,4,5, and 6. The proposed model was compared with about 40 other bivariate copulas (both Archimedean and elliptical). The proposed model had parameters that spanned the entire real line, thus removing restrictions on the parameters. The parameters theta and omega were varied for a selected interval and the hybrid Clayton-Frank model was, in most cases, found to outperform the other copulas under consideration.

scholarly journals ABOUT RANDOM NUMERIC GENERATOR

2020 ◽  
pp. 023-030
Author(s):  
M. A. BAEVA ◽  
Keyword(s):  
Random Number ◽  
Random Sequence ◽  
Random Number Generator ◽  
Number Generator ◽  
Random Sequences ◽  
Pseudo Random Number ◽  
Pseudo Random Number Generator

In this article, the author considers various types of pseudo-random sequence generators, their distinctive properties. The article provides formulas for calculating the next member of the sequence, knowing the previous ones. The main functions and properties are considered that make it possible to evaluate the quality of the generation of pseudo-random sequences, and based on the analysis performed, the most successful variant of the pseudo-random number generator is selected taking into account the requirements.

scholarly journals The RANLUX Generator: Resonances in a Random Walk Test

1998 ◽  
Vol 09 (04) ◽  
pp. 607-624 ◽  
Author(s):  
Lev N. Shchur ◽  
Paolo Butera
Keyword(s):  
Random Walk ◽  
Dynamical Systems ◽  
Random Number ◽  
Jacobi Matrix ◽  
Random Number Generator ◽  
Number Generator ◽  
Walk Test

Using a recently proposed directed random walk test, we systematically investigate the popular random number generator RANLUX developed by Lüscher and implemented by James. We confirm the good quality of this generator with the recommended luxury level. At a smaller luxury level (for instance equal to 1) resonances are observed in the random walk test. We also find that the lagged Fibonacci and Subtract-with-Carry recipes exhibit similar failures in the random walk test. A revised analysis of the corresponding dynamical systems leads to the observation of resonances in the eigenvalues of Jacobi matrix.

scholarly journals Low power pseudo-random number generator based on lemniscate chaotic map

2021 ◽  
Vol 11 (1) ◽  
pp. 863
Author(s):  
Mohamed Saber ◽  
Marwa M. Eid
Keyword(s):  
Low Power ◽  
Random Number ◽  
Chaotic Map ◽  
Random Number Generator ◽  
Number Generator ◽  
Pseudo Random Number ◽  
Proposed Model ◽  
Wide Range ◽  
Field Programmable ◽  
Pseudo Random Number Generator

Lemniscate chaotic map (LCM) provides a wide range of control parameters, canceling the need for several rounds of substitutions, and excellent performance in the confusion process. Unfortunately, the hardware model of LCM is complex and consumes high power. This paper presents a proposed low power hardware model of LCM called practical lemniscate chaotic map (P-LCM) depending on trigonometric identities to reduce the complexity of the conventional model. The hardware model designed and implement into the field programmable gate array (FPGA) board, Spartan-6 SLX45FGG484-3. The proposed model achieves a 48.3 % reduction in used resources and a 34.6 % reduction in power consumption compared to the conventional LCM. We also introduce a new pseudo-random number generator based on a proposed low power P-LCM model and perform the randomization tests for the proposed encryption system.

scholarly journals On the skewed sinh-normal distribution

2015 ◽  
Vol 3 (1) ◽  
pp. 83
Author(s):  
S. K. Ashour ◽  
Ahmed Saad
Keyword(s):  
Normal Distribution ◽  
Goodness Of Fit ◽  
Random Number ◽  
Random Number Generator ◽  
Likelihood Estimation ◽  
Cumulative Distribution ◽  
Numerical Comparison ◽  
Number Generator ◽  
Goodness Of Fit Test ◽  
Numerical Illustration

<p>Leiva et al. [10] introduce the skewed sinh-normal distribution, which is a skewed version of the sinh-normal distribution, discussed some of its properties and characterized an extension of the Birnbaum–Saunders distribution associated with this distribution. In this paper, we will introduce further properties of the skewed sinh-normal distribution, and introduce a new approximate form of its probability density function and cumulative distribution function (cdf), along with numerical comparison between the exact and approximate values of its cdf. Moreover, a random number generator for the distribution will be suggested and a goodness of fit test will be carried out to examine the effectiveness of the proposed random number generator. Finally, maximum likelihood estimation for the unknown parameter of the skewed sinh-normal distribution will be investigated, and numerical illustration for the new results will be discussed.</p>

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