We prove that every dynamical system $X$ with a free action of countable amenable group $G$ by homeomorphisms has zero-dimensional extension $Y$ which is faithful and principal, i.e. $G$-invariant measure $\mu $ on exactly one preimage

In this article we describe the SHA-3 algorithm and its internal permutation in which potential weaknesses are hidden.  The hash can be used for different purposes, such as pseudo-random bit sequences generator, key wrapping or one pass authentication, especially weak devices (WSN, IoT, etc.). Analysis of function showed that successful preimage attacks possible low round hashes, protection fro...

We prove that the derivative of a non-linear entire function is unbounded on the preimage of an unbounded set. MSC 2010: 30D30.

Double block length hashing covers the idea of constructing a compression function on 2n bits using an n-bit block cipher. In this work, we present a comprehensive indifferentiability analysis of all relevant double length compression functions. Indifferentiability is a stronger security notion than collision and preimage resistance and ensures that a design has no structural flaws. It is very ...

In this paper we investigate the security of the compression function of HAS-160 in encryption mode. The structure of HAS-160 is similar to SHA-1 besides some modifications.This is the first cryptographic attack that breaks the encryption mode of the full 80-round HAS-160. We apply a key recovery attack that requires 2 chosen plaintexts and 2 80-round HAS-160 encryptions. The attack does not ai...

X : f (x) = g(x)} is a compact subset of X\∂X. In case of codimension 0, the Nielsen number is the lower estimate of the number of points in this set. We suggest a generalization of the classical Nielsen theory for the coincidence and as well as the preimage problems in order to provide a framework for some recent Wecken type results for codimension 1. The Nielsen equivalence on the set of coin...

In this paper we propose the Grindahl family of hash functions, which is based on components of the Rijndael algorithm. To make collision search sufficiently difficult, this design has the important feature that no low-weight characteristics form collisions, and at the same time it limits access to the state. We also propose two instances of the Grindahl hash family, Grindahl-256 and Grindahl-5...

Regularities are searched for in the sequences of numbers of preimages for elementary cellular automata (CA). For 46 out of 88 “minimal” rules, recognizable patterns are found, usually in the form of second order recurrence equations with constant coefficients. After introducing the concept of asymptotic emulation of CA rules, it is shown how the regularities in the sequences of preimage number...