Biblio

Chaotic dynamics is widely used to design pseudo-random number generators and for other applications, such as secure communications and encryption. This paper aims to study the dynamics of the discrete-time chaotic maps in the digital (i.e., finite-precision) domain. Differing from the traditional approaches treating a digital chaotic map as a black box with different explanations according to the test results of the output, the dynamical properties of such chaotic maps are first explored with a fixed-point arithmetic, using the Logistic map and the Tent map as two representative examples, from a new perspective with the corresponding state-mapping networks (SMNs). In an SMN, every possible value in the digital domain is considered as a node and the mapping relationship between any pair of nodes is a directed edge. The scale-free properties of the Logistic map's SMN are proved. The analytic results are further extended to the scenario of floating-point arithmetic and for other chaotic maps. Understanding the network structure of a chaotic map's SMN in digital computers can facilitate counteracting the undesirable degeneration of chaotic dynamics in finite-precision domains, also helping to classify and improve the randomness of pseudo-random number sequences generated by iterating the chaotic maps.

The methods are based on injecting unpredictability into means and objects of protection are called stochastic methods of information security. The effective protection can be done only by using stochastic methods against an active opponent. The effectiveness of stochastic protection methods is defined by the quality of the used pseudo-random number generators and hash functions. The proposed hashing algorithm DOZENHASH is based on the using of 3D stochastic transformations of DOZEN family. The principal feature of the algorithm is that all input and output data blocks as well as intermediate results of calculations are represented as three-dimensional array of bytes with 4 bytes in each dimension. Thus, the resulting transformation has a high degree of parallelism at the level of elementary operations, in other words, it is focused on the implementation using heterogeneous supercomputer technologies.