Approximations to Isentropic Planar Magneto-Hydrodynamics Equations by Relaxed Euler-Type Systems

In this paper, the authors consider an approximation to the isentropic planar Magneto-hydrodynamics (MHD for short) equations by a kind of relaxed Euler-type system. The approximation is based on the generalization of the Maxwell law for nonNewtonian fluids together with the Maxwell correction for the Amp`ere law, hence the approximate system becomes a first-order quasilinear symmetrizable hyperbolic systems with partial dissipation. They establish the global-in-time smooth solutions to the approximate Euler-type equations in a small neighbourhood of constant equilibrium states and obtain the global-in-time convergence towards the isentropic planar MHD equations. In addition, they also establish the global-in-time error estimates of the limit based on stream function techniques and energy estimates for error variables.     

A pair of stream functions for three-dimensional vortex flows

Introducing a vector potential, that is based on a pair of stream functions, and a velocity potential, antisymmetric equations for the stream functions are derived with the help of a variational principle. It is found that the equations are in a suitable form to investigate flows with helical symmetry, and, for example, to connect upstream axisymmetric flows with downstream helical flows. The special case of a transition from an upstream solid-body vortex to a downstream helical flow is investigated in detail. Furthermore, the stream-function equations are particularly useful to investigate general small-amplitude inertia waves on vortex flows. Time-dependent helical flows that are time-independent in a suitably rotating frame of reference can also be discussed with the proposed method.     

An activated fluid stream – New techniques for cold water cleaning

Electrochemical, acoustic and imaging techniques are used to characterise surface cleaning with particular emphasis on the understanding of the key phenomena relevant to surface cleaning. A range of novel techniques designed to enhance and monitor the effective cleaning of a solid/liquid interface is presented. Among the techniques presented, mass transfer of material to a sensor embedded in a surface is demonstrated to be useful in the further exploration of ultrasonic cleaning of high aspect ratio micropores. In addition the effect of micropore size on the cleaning efficacy is demonstrated. The design and performance of a new cleaning system reliant on the activation of bubbles within a free flowing stream is presented. This device utilised acoustic activation of bubbles within the stream and at a variety of substrates. Finally, a controlled bubble swarm is generated in the stream using electrolysis, and its effect on both acoustic output and cleaning performance are compared to the case when no bubbles are added. This will demonstrate the active role that the electrochemically generated bubble swarm can have in extending the spatial zone over which cleaning is achieved.     

Linearization of nonlinear filter generators and its application to cryptanalysis of stream ciphers

Nonlinear filter generators are commonly used as keystream generators in stream ciphers. A nonlinear filter generator utilizes a nonlinear filtering function to combine the outputs of a linear feedback shift register (LFSR) to improve the linear complexity of keystream sequences. However, the LFSR-based stream ciphers are still potentially vulnerable to algebraic attacks that recover the key from some keystream bits. Although the known algebraic attacks only require polynomial time complexity of computations, all have their own constraints. This paper uses the linearization of nonlinear filter generators to cryptanalyze LFSR-based stream ciphers. Such a method works for any nonlinear filter generators. Viewing a nonlinear filter generator as a Boolean network that evolves as an automaton through Boolean functions, we first give its linearization representation. Compared to the linearization representation in Limniotis et al. (2008), this representation requires lower spatial complexity of computations in most cases. Based on the representation, the key recoverability is analyzed via the observability of Boolean networks. An algorithm for key recovery is given as well. Compared to the exhaustive search to recover the key, using this linearization representation requires lower time complexity of computations, though it leads to exponential time complexity.     

不可压磁流体力学方程组的高精度数值解法

为数值求解低雷诺数下不可压流体在电磁场作用下的流动,提出一种四阶紧致差分方法.由二维原始变量的MHD方程组出发,推导出具有较少未知量的电流密度-涡量-流函数形式MHD方程组.建立了求解二维非定常不可压MHD方程组的电流密度-涡量-流函数形式的四阶精度紧致差分格式.为验证本文提出的高精度紧致差分方法的精确性和可靠性,对有...     

Computing Jacobi Symbols modulo Sparse Integers and Polynomials and Some Applications

We describe a polynomial time algorithm to compute Jacobi symbols of exponentially large integers of special form, including so-called sparse integers which are exponentially large integers with only polynomially many nonzero binary digits. In a number of papers sequences of Jacobi symbols have been proposed as generators of cryptographically secure pseudorandom bits. Our algorithm allows us to use much larger moduli in such constructions. We also use our algorithm to design a probabilistic polynomial time test which decides if a given integer of the aforementioned type is a perfect square (assuming the Extended Riemann Hypothesis). We also obtain analogues of these results for polynomials over finite fields. Moreover, in this case the perfect square testing algorithm is unconditional. These results can be compared with many known NP-hardness results for some natural problems on sparse integers and polynomials.     

On complexity of round transformations

A modern block cipher consists of round transformations, which are obtained by alternatively applying permutations (P-boxes) and substitutions (S-boxes). Clearly, the most important attribute of a block cipher is its security. However, with respect to the hardware implementation, a good block cipher has to have a reasonable complexity as well. In this paper, we study complexity of round transformations satisfying some basic security criteria. There are several ways to define the complexity of a round transformation, and to choose “necessary” security criteria. It turns out, that for our purpose, it is suitable to view a round transformation as a single Boolean function, not separating it into S-boxes and P-boxes. We require that the Boolean function F possesses some fundamental properties imposed on each block cipher for security reasons; namely, we require that the function is a strictly non-linear bijection and that it has a good diffusion. The total number of variables in the normal algebraic form of the component functions of F is taken as its complexity. We find the minimum complexity of such functions, and this way we establish a lower bound on complexity of all round transformations. To show that the lower bound is the best possible, we construct a round transformation F^′ attaining the bound. We stress that it is not an aspiration of this paper to construct a round transformation which would be of practical use; F^′ is useful only from the theoretical point of view.     

Provable security of block ciphers against linear cryptanalysis: a mission impossible?

In this paper, we are concerned with the security of block ciphers against linear cryptanalysis and discuss the distance between the so-called practical security approach and the actual theoretical security provided by a given cipher. For this purpose, we present a number of illustrative experiments performed against small (i.e. computationally tractable) ciphers. We compare the linear probability of the best linear characteristic and the actual best linear probability (averaged over all keys). We also test the key equivalence hypothesis. Our experiments illustrate both that provable security against linear cryptanalysis is not achieved by present design strategies and the relevance of the practical security approach. Finally, we discuss the (im)possibility to derive actual design criteria from the intuitions underlined in these experiments. F.-X. Standaert is a Postdoctoral researcher of the Belgian Fund for Scientific Research (FNRS).     

Modified Alternating $$\vec{k}$$–generators

This paper deals with a class of pseudorandom bit generators – modified alternating –generators. This class is constructed similarly to the class of alternating step generators. Three subclasses of are distinguished, namely linear, mixed and nonlinear generators. The main attention is devoted to the subclass of linear and mixed generators generating periodic sequences with maximal period lengths. A necessary and sufficient condition for all sequences generated by the linear generators of to be with maximal period lengths is formulated. Such sequences have good statistical properties, such as distribution of zeroes and ones, and large linear complexity. Two methods of cryptanalysis of the proposed generators are given. Finally, three new classes of modified alternating –generators, designed especially to be more secure, are presented.     

Concatenating Indicators of Flats for Designing Cryptographic Functions

Boolean functions with good cryptographic characteristics are needed for the design of robust pseudo-random generators for stream ciphers and of S-boxes for block ciphers. Very few general constructions of such cryptographic Boolean functions are known. The main ones correspond to concatenating affine or quadratic functions. We introduce a general construction corresponding to the concatenation of indicators of flats. We show that the functions it permits to design can present very good cryptographic characteristics.