12,882 research outputs found
Anti-deterministic behavior of discrete systems that are less predictable than noise
We present a new type of deterministic dynamical behaviour that is less
predictable than white noise. We call it anti-deterministic (AD) because time
series corresponding to the dynamics of such systems do not generate
deterministic lines in Recurrence Plots for small thresholds. We show that
although the dynamics is chaotic in the sense of exponential divergence of
nearby initial conditions and although some properties of AD data are similar
to white noise, the AD dynamics is in fact less predictable than noise and
hence is different from pseudo-random number generators.Comment: 6 pages, 5 figures. See http://www.chaosandnoise.or
Deterministic Chaos in Digital Cryptography
This thesis studies the application of deterministic chaos to digital
cryptography. Cryptographic systems such as pseudo-random generators
(PRNG), block ciphers and hash functions are regarded as a dynamic
system (X, j), where X is a state space (Le. message space)
and f : X -+ X is an iterated function. In both chaos theory and
cryptography, the object of study is a dynamic system that performs
an iterative nonlinear transformation of information in an apparently
unpredictable but deterministic manner. In terms of chaos theory, the
sensitivity to the initial conditions together with the mixing property
ensures cryptographic confusion (statistical independence) and diffusion
(uniform propagation of plaintext and key randomness into cihertext).
This synergetic relationship between the properties of chaotic and
cryptographic systems is considered at both the theoretical and practical
levels: The theoretical background upon which this relationship is
based, includes discussions on chaos, ergodicity, complexity, randomness,
unpredictability and entropy.
Two approaches to the finite-state implementation of chaotic systems
(Le. pseudo-chaos) are considered: (i) floating-point approximation of
continuous-state chaos; (ii) binary pseudo-chaos. An overview is given
of chaotic systems underpinning cryptographic algorithms along with
their strengths and weaknesses. Though all conventional cryposystems
are considered binary pseudo-chaos, neither chaos, nor pseudo-chaos are
sufficient to guarantee cryptographic strength and security.
A dynamic system is said to have an analytical solution Xn = (xo)
if any trajectory point Xn can be computed directly from the initial
conditions Xo, without performing n iterations. A chaotic system with an
analytical solution may have a unpredictable multi-valued map Xn+l =
f(xn). Their floating-point approximation is studied in the context of
pseudo-random generators.
A cryptographic software system E-Larm â„¢ implementing a multistream
pseudo-chaotic generator is described. Several pseudo-chaotic
systems including the logistic map, sine map, tangent- and logarithm feedback
maps, sawteeth and tent maps are evaluated by means of floating point
computations. Two types of partitioning are used to extract
pseudo-random from the floating-point state variable: (i) combining the
last significant bits of the floating-point number (for nonlinear maps);
and (ii) threshold partitioning (for piecewise linear maps). Multi-round
iterations are produced to decrease the bit dependence and increase non-linearity.
Relationships between pseudo-chaotic systems are introduced
to avoid short cycles (each system influences periodically the states of
other systems used in the encryption session).
An evaluation of cryptographic properties of E-Larm is given using
graphical plots such as state distributions, phase-space portraits, spectral
density Fourier transform, approximated entropy (APEN), cycle length
histogram, as well as a variety of statistical tests from the National Institute
of Standards and Technology (NIST) suite. Though E-Larm passes
all tests recommended by NIST, an approach based on the floating-point
approximation of chaos is inefficient in terms of the quality/performance
ratio (compared with existing PRNG algorithms). Also no solution is
known to control short cycles.
In conclusion, the role of chaos theory in cryptography is identified;
disadvantages of floating-point pseudo-chaos are emphasized although
binary pseudo-chaos is considered useful for cryptographic applications.Durand Technology Limite
Properties making a chaotic system a good Pseudo Random Number Generator
We discuss two properties making a deterministic algorithm suitable to
generate a pseudo random sequence of numbers: high value of Kolmogorov-Sinai
entropy and high-dimensionality. We propose the multi dimensional Anosov
symplectic (cat) map as a Pseudo Random Number Generator. We show what chaotic
features of this map are useful for generating Pseudo Random Numbers and
investigate numerically which of them survive in the discrete version of the
map. Testing and comparisons with other generators are performed.Comment: 10 pages, 3 figures, new version, title changed and minor correction
Coherence in scale-free networks of chaotic maps
We study fully synchronized states in scale-free networks of chaotic logistic
maps as a function of both dynamical and topological parameters. Three
different network topologies are considered: (i) random scale-free topology,
(ii) deterministic pseudo-fractal scale-free network, and (iii) Apollonian
network. For the random scale-free topology we find a coupling strength
threshold beyond which full synchronization is attained. This threshold scales
as , where is the outgoing connectivity and depends on the
local nonlinearity. For deterministic scale-free networks coherence is observed
only when the coupling strength is proportional to the neighbor connectivity.
We show that the transition to coherence is of first-order and study the role
of the most connected nodes in the collective dynamics of oscillators in
scale-free networks.Comment: 9 pages, 8 figure
Delayed-feedback chimera states: Forced multiclusters and stochastic resonance
A nonlinear oscillator model with negative time-delayed feedback is studied
numeri- cally under external deterministic and stochastic forcing. It is found
that in the unforced system complex partial synchronization patterns like
chimera states as well as salt-and-pepper like soli- tary states arise on the
route from regular dynamics to spatio-temporal chaos. The control of the
dynamics by external periodic forcing is demonstrated by numerical simulations.
It is shown that one-cluster and multi-cluster chimeras can be achieved by
adjusting the external forcing frequency to appropriate resonance conditions.
If a stochastic component is superimposed to the determin- istic external
forcing, chimera states can be induced in a way similar to stochastic
resonance, they appear, therefore, in regimes where they do not exist without
noise.Comment: 6 pages of paper with references + tex style file + 5 figure
A pseudo-matched filter for chaos
A matched filter maximizes the signal-to-noise ratio of a signal. In the
recent work of Corron et al. [Chaos 20, 023123 (2010)], a matched filter is
derived for the chaotic waveforms produced by a piecewise-linear system.
Motivated by these results, we describe a pseudo-matched filter, which removes
noise from the same chaotic signal. It consists of a notch filter followed by a
first-order, low-pass filter. We compare quantitatively the matched filter's
performance to that of our pseudo-matched filter using correlation functions in
a simulated radar application. On average, the pseudo-matched filter performs
with a correlation signal-to-noise ratio that is 2.0 dB below that of the
matched filter. Our pseudo-matched filter, though somewhat inferior in
comparison to the matched filter, is easily realizable at high speed (> 1 GHz)
for potential radar applications
Recommendations and illustrations for the evaluation of photonic random number generators
The never-ending quest to improve the security of digital information
combined with recent improvements in hardware technology has caused the field
of random number generation to undergo a fundamental shift from relying solely
on pseudo-random algorithms to employing optical entropy sources. Despite these
significant advances on the hardware side, commonly used statistical measures
and evaluation practices remain ill-suited to understand or quantify the
optical entropy that underlies physical random number generation. We review the
state of the art in the evaluation of optical random number generation and
recommend a new paradigm: quantifying entropy generation and understanding the
physical limits of the optical sources of randomness. In order to do this, we
advocate for the separation of the physical entropy source from deterministic
post-processing in the evaluation of random number generators and for the
explicit consideration of the impact of the measurement and digitization
process on the rate of entropy production. We present the Cohen-Procaccia
estimate of the entropy rate as one way to do this. In order
to provide an illustration of our recommendations, we apply the Cohen-Procaccia
estimate as well as the entropy estimates from the new NIST draft standards for
physical random number generators to evaluate and compare three common optical
entropy sources: single photon time-of-arrival detection, chaotic lasers, and
amplified spontaneous emission
Perspectives for Monte Carlo simulations on the CNN Universal Machine
Possibilities for performing stochastic simulations on the analog and fully
parallelized Cellular Neural Network Universal Machine (CNN-UM) are
investigated. By using a chaotic cellular automaton perturbed with the natural
noise of the CNN-UM chip, a realistic binary random number generator is built.
As a specific example for Monte Carlo type simulations, we use this random
number generator and a CNN template to study the classical site-percolation
problem on the ACE16K chip. The study reveals that the analog and parallel
architecture of the CNN-UM is very appropriate for stochastic simulations on
lattice models. The natural trend for increasing the number of cells and local
memories on the CNN-UM chip will definitely favor in the near future the CNN-UM
architecture for such problems.Comment: 14 pages, 6 figure
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