Improving random number generators by chaotic iterations. Application in data hiding

In this paper, a new pseudo-random number generator (PRNG) based on chaotic iterations is proposed. This method also combines the digits of two XORshifts PRNGs. The statistical properties of this new generator are improved: the generated sequences can pass all the DieHARD statistical test suite. In addition, this generator behaves chaotically, as defined by Devaney. This makes our generator suitable for cryptographic applications. An illustration in the field of data hiding is presented and the robustness of the obtained data hiding algorithm against attacks is evaluated.Comment: 6 pages, 8 figures, In ICCASM 2010, Int. Conf. on Computer Application and System Modeling, Taiyuan, China, pages ***--***, October 201

Curvature singularity and film-skating during drop impact

We study the influence of the surrounding gas in the dynamics of drop impact on a smooth surface. We use an axisymmetric 3D model for which both the gas and the liquid are incompressible; lubrication regime applies for the gas film dynamics and the liquid viscosity is neglected. In the absence of surface tension a finite time singularity whose properties are analysed is formed and the liquid touches the solid on a circle. When surface tension is taken into account, a thin jet emerges from the zone of impact, skating above a thin gas layer. The thickness of the air film underneath this jet is always smaller than the mean free path in the gas suggesting that the liquid film eventually wets the surface. We finally suggest an aerodynamical instability mechanism for the splash.Comment: 5 figure

Localization for a random walk in slowly decreasing random potential

We consider a continuous time random walk $X$ in random environment on $\Z^+$ such that its potential can be approximated by the function $V: \R^+\to \R$ given by V(x)=\sig W(x) -\frac{b}{1-\alf}x^{1-\alf} where \sig W a Brownian motion with diffusion coefficient \sig>0 and parameters $b$, \alf are such that $b>0$ and 0<\alf<1/2. We show that $\P$-a.s.\ (where $\P$ is the averaged law) \lim_{t\to \infty} \frac{X_t}{(C^*(\ln\ln t)^{-1}\ln t)^{\frac{1}{\alf}}}=1 with C^*=\frac{2\alf b}{\sig^2(1-2\alf)}. In fact, we prove that by showing that there is a trap located around (C^*(\ln\ln t)^{-1}\ln t)^{\frac{1}{\alf}} (with corrections of smaller order) where the particle typically stays up to time $t$. This is in sharp contrast to what happens in the "pure" Sinai's regime, where the location of this trap is random on the scale $\ln^2 t$.Comment: 14pages, 7 figure

Chaotic iterations versus Spread-spectrum: chaos and stego security

A new framework for information hiding security, called chaos-security, has been proposed in a previous study. It is based on the evaluation of unpredictability of the scheme, whereas existing notions of security, as stego-security, are more linked to information leaks. It has been proven that spread-spectrum techniques, a well-known stego-secure scheme, are chaos-secure too. In this paper, the links between the two notions of security is deepened and the usability of chaos-security is clarified, by presenting a novel data hiding scheme that is twice stego and chaos-secure. This last scheme has better scores than spread-spectrum when evaluating qualitative and quantitative chaos-security properties. Incidentally, this result shows that the new framework for security tends to improve the ability to compare data hiding scheme

Planar Ising magnetization field I. Uniqueness of the critical scaling limit

The aim of this paper is to prove the following result. Consider the critical Ising model on the rescaled grid $a\mathbb{Z}^2$, then the renormalized magnetization field $$\Phi^a:=a^{15/8}\sum_{x\in a\mathbb{Z}^2}\sigma_x\delta_x,$$ seen as a random distribution (i.e., generalized function) on the plane, has a unique scaling limit as the mesh size $a\searrow0$. The limiting field is conformally covariant.Comment: Published in at http://dx.doi.org/10.1214/13-AOP881 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org