Secure image encryption scheme using 4D-Hyperchaotic systems based reconfigurable pseudo-random number generator and S-Box

This paper introduces the design of a hardware efficient reconfigurable pseudorandom number generator (PRNG) using two different feedback controllers based four-dimensional (4D) hyperchaotic systems i.e. Hyperchaotic-1 and -2 to provide confidentiality for digital images. The parameter's value of these two hyperchaotic systems is set to be a specific value to get the benefits i.e. all the multiplications (except a few multiplications) are performed using hardwired shifting operations rather than the binary multiplications, which doesn't utilize any hardware resource. The ordinary differential equations (ODEs) of these two systems have been exploited to build a generic architecture that fits in a single architecture. The proposed architecture provides an opportunity to switch between two different 4D hyperchaotic systems depending on the required behavior. To ensure the security strength, that can be also used in the encryption process in which encrypt the input data up to two times successively, each time using a different PRNG configuration. The proposed reconfigurable PRNG has been designed using Verilog HDL, synthesized on the Xilinx tool using the Virtex-5 (XC5VLX50T) and Zynq (XC7Z045) FPGA, its analysis has been done using Matlab tool. It has been found that the proposed architecture of PRNG has the best hardware performance and good statistical properties as it passes all fifteen NIST statistical benchmark tests while it can operate at 79.101-MHz or 1898.424-Mbps and utilize only 0.036 %, 0.23 %, and 1.77 % from the Zynq (XC7Z045) FPGA's slice registers, slice LUTs, and DSP blocks respectively. Utilizing these PRNGs, we design two 16 × 16 substitution boxes (S-boxes). The proposed S-boxes fulfill the following criteria: Bijective, Balanced, Non-linearity, Dynamic Distance, Strict Avalanche Criterion (SAC) and BIC non-linearity criterion. To demonstrate these PRNGs and S-boxes, a new three different scheme of image encryption algorithms have been developed: a) Encryption using S-box-1, b) Encryption using S-box-2 and, c) Two times encryption using S-box-1 and S-box-2. To demonstrate that the proposed cryptosystem is highly secure, we perform the security analysis (in terms of the correlation coefficient, key space, NPCR, UACI, information entropy and image encryption quantitatively in terms of (MSE, PSNR and SSIM)).     

Model Misspecification of Generalized Gamma Distribution for Accelerated Lifetime-Censored Data

Abstract

The performance of reliability inference strongly depends on the modeling of the product’s lifetime distribution. Many products have complex lifetime distributions whose optimal settings are not easily found. Practitioners prefer to use simpler lifetime distribution to facilitate the data modeling process while knowing the true distribution. Therefore, the effects of model mis-specification on the product’s lifetime prediction is an interesting research area. This article presents some results on the behavior of the relative bias (RB) and relative variability (RV) of pth quantile of the accelerated lifetime (ALT) experiment when the generalized Gamma (GG₃) distribution is incorrectly specified as Lognormal or Weibull distribution. Both complete and censored ALT models are analyzed. At first, the analytical expressions for the expected log-likelihood function of the misspecified model with respect to the true model is derived. Consequently, the best parameter for the incorrect model is obtained directly via a numerical optimization to achieve a higher accuracy model than the wrong one for the end-goal task. The results demonstrate that the tail quantiles are significantly overestimated (underestimated) when data are wrongly fitted by Lognormal (Weibull) distribution. Moreover, the variability of the tail quantiles is significantly enlarged when the model is incorrectly specified as Lognormal or Weibull distribution. Precisely, the effect on the tail quantiles is more significant when the sample size and censoring ratio are not large enough. Supplementary materials for this article are available online.     

A new MM algorithm for constrained estimation in the proportional hazards model

The constrained estimation in Cox’s model for the right-censored survival data is studied and the asymptotic properties of the constrained estimators are derived by using the Lagrangian method based on Karush–Kuhn–Tucker conditions. A novel minorization–maximization (MM) algorithm is developed for calculating the maximum likelihood estimates of the regression coefficients subject to box or linear inequality restrictions in the proportional hazards model. The first M-step of the proposed MM algorithm is to construct a surrogate function with a diagonal Hessian matrix, which can be reached by utilizing the convexity of the exponential function and the negative logarithm function. The second M-step is to maximize the surrogate function with a diagonal Hessian matrix subject to box constraints, which is equivalent to separately maximizing several one-dimensional concave functions with a lower bound and an upper bound constraint, resulting in an explicit solution via a median function. The ascent property of the proposed MM algorithm under constraints is theoretically justified. Standard error estimation is also presented via a non-parametric bootstrap approach. Simulation studies are performed to compare the estimations with and without constraints. Two real data sets are used to illustrate the proposed methods.     

A new direct version of the Cook-Mayne method for wind pressure probabilities in temperate storms

The original Cook-Mayne (CM) method for obtaining a wind pressure or load of a prescribed probability is reviewed. A new direct calculation method is introduced. This does not require either Monte Carlo simulations or the assumption that extreme pressures conform to the ultimate Fisher-Tippett Type I asymptote. The required value is calculated directly with no intermediate stages. The new method still relies on the original assumptions that both the pressure coefficient and the wind dynamic head have extremes which conform to the ultimate FT1 asymptote.Violation of these two assumptions is studied in some cases where calculations based on these assumptions are compared with exact results. The direct CM method is found to retain accuracy in spite of departures from the assumptions and therefore can provide a robust design tool.     

交通流的有序运动与混沌运动相互转化现象的仿真研究

用Matlab软件编制皮埃莱(Bieriey)模型来产生仿真交通流。在一定的参数组合下,仿真研究了交通流车队中前后车辆之间的车头间距的变化过程。分析了这种车头间距变化过程的曲线。给出该曲线的二维(间距差与速度差)和三维(间距差、速度差、时间)相图。从相图上可以明显地看出存在奇怪吸引子,这说明基于跟驰模型产生的交通流存在着混沌现象。从相图还可以清楚地看出交通流混沌运动与有序运动之间的转化过程。联系交通流的实际情况,对仿真结果做了分析。     

混沌理论对建筑与城市设计领域的启示

混沌理论给人类思维方式带来了深刻的变革。本文简要介绍了混沌理论的五个要点及其适用对象,针对每个要点探讨了对建筑与城市设计领域的启示,指出复杂性是城市的本质属性,要实现城市与建筑的可持续发展应该将它们视为有生命的存在。     

Asymptotic Properties of a Probabilistic‐Statistical Model of Particle Classification in Hydrocyclones

The peculiarities of practical implementation of a probabilistic‐statistical model for a hydrodynamic stage of particle classification process of liquid‐solid polydisperse systems in cylinder‐conic hydrocyclones of small size have been investigated. Within reasonable assumptions, stationary solutions of the Fokker‐Planck‐Kolmogorov kinetic equation were obtained for the considered separation process. In order to describe changes in characteristics of suspension separation in hydrocyclones it was proposed to use stationary distributions, which parameters depend not only on hydraulic and dynamic features of flows inside an apparatus, but also are determined by relative magnitudes of the impact of particle classification and centrifugal forces in comparison with the intensity of random perturbations.     

Unsteady micropolar fluid flow in a thin domain with Tresca fluid–solid interface law

We consider a micropolar fluid flow in a two-dimensional domain. We assume that the velocity field satisfies a non-linear slip boundary condition of friction type on a part of the boundary while the micro-rotation field satisfies non-homogeneous Dirichlet boundary conditions. We prove the existence and uniqueness of a solution. Then motivated by lubrication problems we assume that the thickness and the roughness of the domain are of order $0<\epsilon <<1$ and we study the asymptotic behaviour of the flow as $\epsilon$ tends to zero. By using the two-scale convergence technique we derive the limit problem which is totally decoupled for the limit velocity and pressure $(v^0,p^0)$ on one hand and the limit micro-rotation $Z^0$ on the other hand. Moreover we prove that $v^0$, $p^0$ and $Z^0$ are uniquely determined via auxiliary well-posed problems.     

A thermoelastic diffusion theory with microtemperatures and microconcentrations

This article is concerned with a nonlinear theory of thermodynamics for elastic materials in which the particles are subjected to classical displacement, temperature, and mass diffusion fields and whose microelements possess microtemperatures and microconcentrations. The equations of the linear theory are also obtained. It is shown that there exists coupling between temperature, chemical potential, microtemperatures, and microconcentrations even for isotropic bodies. With the help of the semigroup theory of linear operators, we prove the well-posedness of the linear anisotropic problem and we study the asymptotic behavior of the solutions.     

Distribution of Quasimidranges and Associated Mixtures

In this paper are presented and discussed tabulations of the cumulative distribution functions of quasimidranges and mixtures of quasimidranges of samples from a normal distribution. The tabulations extend up to samples of size 21. For quasimidranges not involving the extreme values of the sample, the departure from normality is very small. The physical problem giving rise to the mixtures is discussed.