Related papers: Logistic Map: A Possible Random Number Generator
Due to the rapid development of the Internet in recent years, the need to find new tools to reinforce trust and security through the Internet has became a major concern. The discovery of new pseudo-random number generators with a strong…
One of the key requirement of many schemes is that of random numbers. Sequence of random numbers are used at several stages of a standard cryptographic protocol. A simple example is of a Vernam cipher, where a string of random numbers is…
Chaotic attractors, chaotic saddles and periodic orbits are examples of chain-recurrent sets. Using arbitrary small controls, a trajectory starting from any point in a chain-recurrent set can be steered to any other in that set. The…
Random graphs have proven to be one of the most important and fruitful concepts in modern Combinatorics and Theoretical Computer Science. Besides being a fascinating study subject for their own sake, they serve as essential instruments in…
The striking fractal geometry of strange attractors underscores the generative nature of chaos: like probability distributions, chaotic systems can be repeatedly measured to produce arbitrarily-detailed information about the underlying…
The quantum baker's map is the quantization of a simple classically chaotic system, and has many generic features that have been studied over the last few years. While there exists a semiclassical theory of this map, a more rigorous study…
This paper reveals a novel numerical method, the sequential test, which approves chaos through sequences of numbers observations. The method alights alongside the Lyapunov exponent and bifurcation diagram test. Explicitly elucidation of the…
Chaotic semiconductor lasers have been widely investigated for generating true random numbers with the merit of unpredictability relative to pseudorandom numbers generated by a computing process, especially for the lasers with external…
We present results of an extensive test program of a group of pseudorandom number generators which are commonly used in the applications of physics, in particular in Monte Carlo simulations. The generators include public domain programs,…
The ultimate random number generators are those certified to be unpredictable -- including to an adversary. The use of simple quantum processes promises to provide numbers that no physical observer could predict but, in practice, unwanted…
Random number generation is a key technology that is useful in a variety of ways. Random numbers are often used to generate keys for data encryption. Random numbers generated at a sufficiently long length can encrypt sensitive data and make…
Periodicity analysis of sequences generated by a deterministic system is a long-standing challenge in both theoretical research and engineering applications. To overcome the inevitable degradation of the Logistic map on a finite-precision…
It is shown that superefficient Monte Carlo computations can be carried out by using chaotic dynamical systems as non-uniform random-number generators. Here superefficiency means that the expectation value of the square of the error…
Many open problems in biology, as in the physical sciences, display nonlinear and 'chaotic' dynamics, which, to the extent possible, cannot be reasonably understood. Moreover, mathematical models which aim to predict/estimate unknown…
The purpose of this letter is to define a distance on the underlying phase space of a chaotic map, based on natural invariant density of the map. It is observed that for logistic map this distance is equivalent to Wootters' statistical…
Networks of chaotic coupled maps are considered as string and language generators. It is shown that such networks can be used as encrypting systems where the ciphertext contains information about the evolution of the network and also about…
$\mathbf F_2$-linear pseudorandom number generators are very popular due to their high speed, to the ease with which generators with a sizable state space can be created, and to their provable theoretical properties. However, they suffer…
Chaotic dynamics can be quite heterogeneous in the sense that in some regions the dynamics are unstable in more directions than in other regions. When trajectories wander between these regions, the dynamics is complicated. We say a chaotic…
A shift-periodic map is a one-dimensional map from the real line to itself which is periodic up to a linear translation and allowed to have singularities. It is shown that iterative sequences $x_{n+1}=F(x_n)$ generated by such maps display…
We develop a method for generating pseudorandom binary sequences using the Bernoulli map on cubic algebraic integers. The distinguishing characteristic of our generator is that it generates chaotic true orbits of the Bernoulli map by exact…