Narrow Results

In this paper, we propose an algorithm for one-way hash function construction based on the chaotic look-up table with changeable parameter. First, the original message with padding is divided into block messages as groups and then further broken into sub-block messages, which are translated into corresponding ASCII codes by groups. Then the group ASCII codes are successively inputted into the chaotic look-up table updated by changeable parameter to permute corresponding values. Finally, based on the calculation of the values, 128-bit hash value is generated. Performance analysis indicates that our proposed algorithm satisfies sensitive requirements and can resist all kinds of attacks.

The invariant Cantor sets of the logistic map g_μ(x) = μx(1 - x) for μ > 4 are hyperbolic and form a continuous family. We show that this family can be obtained explicitly through solutions of initial value problems for a system of infinitely coupled differential equations due to the hyperbolicity. The same result also applies to the tent map T_a(x) = a(1/2 - |1/2 - x|) for a > 2.

We study analytically and numerically the reinjection probability density for type-II intermittency. We find a new one-parameter class of reinjection probability density where the classical uniform reinjection is a particular case. We derive a new duration probability density of the laminar phase. New characteristic relations e^β(-1 < β < 0) appear where the exponet β deepens on the reinjection probability distributions. Analytical results are in agreement with the numerical simulations.

In this article, we have studied a $1$D map, which is formed by combining the two well-known maps, i.e. the tent and the logistic maps in the unit interval, i.e. $[0,1]$. The point of discontinuity of the map (known as border) denotes the transition from tent map to logistic map. The proposed map can behave as the piecewise smooth or nonsmooth map or both (depending on the behavior of the map just before and after the border) and the dynamics of the map has been studied using analytical tools and numerical simulations. Characterization has been done by primarily studying the Lyapunov exponents and the corresponding bifurcation diagrams. Some peculiar dynamics of this map have been shown numerically. Finally, a Simulink implementation of the proposed map has been demonstrated.

By a fixed continuous map from a 3-space to itself, a knot in the 3-space may be mapped to another knot in the 3-space. We analyze possible knot types of them. Then we map a knot repeatedly by a fixed continuous map and analyze possible infinite sequences of knot types.