Jerzy A. Gawinecki

On Bad Randomness and Cloning of Contactless Payment and Building Smart Cards

In this paper we study the randomness of some random numbers found in real-life smart card products. We have studied a number of symmetric keys, codes and random nonces in the most prominent contactless smart cards used in buildings, small payments and public transportation used by hundreds of millions of people every day. Furthermore we investigate a number of technical questions in order to see to what extent the vulnerabilities we have discovered could be exploited by criminals. In particular we look at the case MiFare Classic cards, of which some two hundred million are still in use worldwide. We have examined some 50 real-life cards from different countries to discover that it is not entirely clear if what was previously written about this topic is entirely correct. These facts are highly relevant to the practical feasibility of card cloning in order to enter some buildings, make small purchases or in public transportation in many countries. We also show examples of serious security issues due to poor entropy with another very popular contactless smart card used in many buildings worldwide.

Contradiction Immunity and Guess-Then-Determine Attacks on Gost

ABSTRACT GOST is a well-known government standard cipher. Since 2011 several academic attacks on GOST have been found. Most of these attacks start by a so called “Complexity Reduction” step [Courtois Cryptologia 2012] the purpose of which is to reduce the problem of breaking the full 32-round GOST to a low-data complexity attack on a reduced-round GOST. These reductions can be viewed as optimisation problems which seek to maximize the number of values inside the cipher determined at given “cost” in terms of guessing other values. In this paper we look at similar combinatorial optimisation questions BUT at the lower level, inside reduced round versions of GOST. We introduce a key fundamental notion of Contradiction Immunity of a block cipher. A low value translates to working software attacks on GOST with a SAT solver. A high value will be mandatory for any block cipher to be secure. We provide some upper bounds for the Contradiction Immunity of GOST.

Global Non-Small Data Existence of Spherically Symmetric Solutions to Nonlinear Viscoelasticity in a Ball

Abstract. We consider some initial-boundary value problems for non-linear equations of the three dimensional viscoelasticity. We examine the Dirichlet and the Neumann boundary conditions. We assume that the stress tensor is a nonlinear tensor valued function depending on the strain tensor fulfilling the rules of the continuum mechanics. We consider the initial-boundary value problems in a ball BR with radius R. Since, we are interested in proving global existence the spherically symmetric solutions are considered. Therefore we have to examine the spherically symmetric viscoelasticity system in spherical coordinates. Applying the energy method implies estimates in weighted anisotropic Sobolev spaces, where the weight is a power function of radius. Hence the origin of coordinates becomes a singular point. First the existence of weak solutions is proved. Next having appropriate estimates the weak solutions appear bounded and continuous. We have to emphasize that non-small data problem is considered.

Local Existence of the Solution to the Initial-Boundary Value Problem in Nonlinear Thermodiffusion in Micropolar Medium

We prove a theorem about local existence (in time) of the solution to the first initial-boundary value problem for a nonlinear hyperbolic-parabolic system of eight coupled partial differential equations of second order describing the process of thermodiffusion in a three-dimensional micropolar medium. At first, we prove existence, uniqueness and regularity of the solution to this problem for the associated linearized system by using the Faedo-Galerkin method and semi-group theory. Next, we prove (basing on this theorem) an energy estimate for the solution to the linearized system by applying the method of Sobolev spaces. At last, by using the Banach fixed point theorem we prove that the solution of our nonlinear problem exists and is unique.

On the Fundamental Solution of the Operator of Dynamic Linear Thermodiffusion

The fundamental matrix of the 5-by-5 system of partial differential operators describing linear thermodiffusion inside elastic media is by a standard procedure expressible through the fundamental solution of its determinant. This determinant is equal to the square of a wave operator multiplied by the so-called operator of dynamic linear thermodiffusion, which is of the fourth order with respect to the time variable. In this paper, we deduce, by means of a variant of Cagniard-de hoops method, a representation of the fundamental solution of this operator by simple definite integrals. This formula allows the explicit computation of thermal and diffusion effects which result from instantaneous point forces or heat sources.

On Global Existence of Solutions of the Neumann Problem for Spherically Symmetric Nonlinear Viscoelasticity in a Ball

We examine spherically symmetric solutions to the viscoelasticity system in a ball with the Neumann boundary conditions. Imposing some growth restrictions on the nonlinear part of the stress tensor, we prove the existence of global regular solutions for large data in the weighted Sobolev spaces, where the weight is a power function of the distance to the centre of the ball. First, we prove a global a priori estimate. Then existence is proved by the method of successive approximations and appropriate time extension.

K-dron, jego matematyczne modelowanie i zastosowanie

Streszczenie W pracy przedstawiono pojęcie K-dronu, nowego kształtu geometrycznego odkrytego w 1985 roku w Nowym Jorku przez dr. Janusza Kapustę, historię jego odkrycia, związki z geometrią, symetrią sześcianu. Należy podkreślić, że autorzy wyprowadzili nowy wzór∗) na powierzchnie K-dronu, stosując metodę transformacji Laplace’a do wyznaczenia rozwiązania zagadnienia brzegowo-początkowego do równania drgań struny. Wyprowadzony wzór w swojej naturze jest bardziej czytelny ze wzlgędu na swoją strukturę. Otrzymane przez autorów w pracy rozwiązanie opisuje w sposób najbardziej ogólny powierzchnie K-dronu oraz bardziej ogólne powierzchnie nazwane przez autorów n-K-dronem. Wzór na powierzchnie K-dronu uzyskany metodą transformaty Laplace’a posiada przejrzystą interpretację geometryczną, ponieważ jest przedstawiony w postaci kombinacji liniowej równań płaszczyzn o współczynnikach kierunkowych określonych przez odpowiednie kombinacje funkcje Heaviside’a. Szeroko także przedstawiono różnorodne i wielorakie zastosowanie K-dronu.

The Fundamental Matrix of the System of Linear Micropolar Elasticity

We construct the fundamental matrix of the system of partial differential operators governing the motion of linear micropolar elastic media in terms of derivatives of distributions which are convolutions of the fundamental solutions to the wave operator, the Klein-Gordon operator and the micropolar operator.