Related papers: The Space Complexity of Generating Tent Codes
This work is motivated by a question whether it is possible to calculate a chaotic sequence efficiently, e.g., is it possible to get the $n$-th bit of a bit sequence generated by a chaotic map, such as $\beta$-expansion, tent map and…
Tent map is a discrete-time piecewise-affine I/O characteristic curve, which is used for chaos-based applications, such as true random number generation. However, tent map suffers from the inability to maintain the output state confined to…
Large deviations in chaotic dynamics have potentially significant and dramatic consequences. We study large deviations of series of finite lengths $N$ generated by chaotic maps. The distributions generally display an exponential decay with…
A simple method to produce a random order type is to take the order type of a random point set. We conjecture that many probability distributions on order types defined in this way are heavily concentrated and therefore sample inefficiently…
This paper describes the design of a modified tent map characterized by a uniform probability density function. The use of this map is proposed as an alternative to the tent map and the Bernoulli shift. It is shown that practical circuits…
In the implementation of discrete time chaotic systems, designers have mostly focused on the choice and synthesis of suitable nonlinear blocks, while correct and fast operation cannot neglect analog memory elements. Herein, a realization…
Chaos reveals a fundamental paradox in the scientific understanding of Complex Systems. Although chaotic models may be mathematically deterministic, they are practically non-determinable due to the finite precision, which is inherent in all…
Trees are useful entities allowing to model data structures and hierarchical relationships in networked decision systems ubiquitously. An ordered tree is a rooted tree where the order of the subtrees (children) of a node is significant. In…
Let us call a sequence of numbers heapable if they can be sequentially inserted to form a binary tree with the heap property, where each insertion subsequent to the first occurs at a leaf of the tree, i.e. below a previously placed number.…
In this paper we consider the problem of encoding data into \textit{repeat-free} sequences in which sequences are imposed to contain any $k$-tuple at most once (for predefined $k$). First, the capacity of the repeat-free constraint are…
In this letter, we prove that the perfectly secure One-Time Pad (OTP) encryption can be seen as finding the initial condition on the binary map under a random switch based on the perfectly random pad. This turns out to be a special case of…
An orientable sequence of order $n$ is a cyclic binary sequence such that each length-$n$ substring appears at most once \emph{in either direction}. Maximal length orientable sequences are known only for $n\leq 7$, and a trivial upper bound…
We proposed the deep zoom analysis of the composition of the logistic map and the tent map, which are well-known discrete unimodal chaotic maps. The deep zoom technique transforms each point of a given chaotic orbit by removing its first…
A scheme for pseudo-random binary sequence generation based on the two-dimensional discrete-time Henon map is proposed. Properties of the proposed sequences pertaining to linear complexity, linear complexity profile, correlation and…
The logistic map is one of the simple systems exhibiting order to chaos transition. In this work we have investigated the possibility of using the logistic map in the chaotic regime ({\sc logmap}) for a pseudo random number generator. To…
In this paper, by using Logistic, Sine and Tent systems we define a combination chaotic system. Some properties of the chaotic system are studied by using figures and numerical results. A color image encryption algorithm is introduced based…
In this paper, we approximate the hidden Markov model of chaotic-map truly random number generators (TRNGs) and describe its fundamental limits based on the approximate entropy-rate of the underlying bit-generation process. We demonstrate…
Chaos, a nonlinear dynamical system, favors cryptography due to their inherent sensitive dependence on the initial condition, mixing, and ergodicity property. In recent years, the nonlinear behavior of chaotic maps has been utilized as a…
This paper presents a new generator of chaotic bit sequences with mixed-mode (continuous and discrete) inputs. The generator has an improved level of chaotic properties in comparison with the existing single source (input) digital chaotic…
This paper is a study of the dynamics of a new family of maps from the complex plane to itself, which we call twisted tent maps. A twisted tent map is a complex generalization of a real tent map. The action of this map can be visualized as…