508 research outputs found
A mechanism for randomness
We investigate explicit functions that can produce truly random numbers. We
use the analytical properties of the explicit functions to show that certain
class of autonomous dynamical systems can generate random dynamics. This
dynamics presents fundamental differences with the known chaotic systems. We
present realphysical systems that can produce this kind of random time-series.
We report theresults of real experiments with nonlinear circuits containing
direct evidence for this new phenomenon. In particular, we show that a
Josephson junction coupled to a chaotic circuit can generate unpredictable
dynamics. Some applications are discussed.Comment: Accepted in Physics Letters A (2002). 11 figures (.eps
A Novel Chaotic Image Encryption using Generalized Threshold Function
In this paper, after reviewing the main points of image encryption and
threshold function, we introduce the methods of chaotic image encryption based
on pseudorandom bit padding that the bits be generated by the novel generalized
threshold function (segmentation and self-similarity) methods. These methods
decrease periodic effect of the ergodic dynamical systems in randomness of the
chaotic image encryption. The essential idea of this paper is that given
threshold functions of the ergodic dynamical systems. To evaluate the security
of the cipher image of this scheme, the key space analysis, the correlation of
two adjacent pixels and differential attack were performed. This scheme tries
to improve the problem of failure of encryption such as small key space and
level of security.Comment: 7 pages, 5 figures, Published in international Journal of Computer
Applications (March 2012
On Pseudo-Random Number Generators Using Elliptic Curves and Chaotic Systems
Elliptic Curve Cryptography (ECC) is a relatively recent branch of cryptography which is based on the arithmetic on elliptic curves and security of the hardness of the Elliptic Curve Discrete Logarithm Problem (ECDLP). Elliptic curve cryptographic schemes are public-key mechanisms that provide encryption, digital signature and key exchange capabilities. Elliptic curve algorithms are also applied to generation of sequences of pseudo-random numbers. Another recent branch of cryptography is chaotic dynamical systems where security is based on high sensitivity of iterations of maps to initial conditions and parameters. In the present work, we give a short survey describing state-of-the-art of several suggested constructions for generating sequences of pseudorandom number generators based on elliptic curves (ECPRNG) over finite fields of prime order. In the second part of the paper we propose a method of generating sequences of pseudorandom points on elliptic curves over finite fields which is driven by a chaotic map. Such a construction improves randomness of the sequence generated since it combines good statistical properties of an ECPRNG and a CPRNG (Chaotic Pseudo- Random Number Generator). The algorithm proposed in this work is of interest for both classical and elliptic curve cryptography
Applying dissipative dynamical systems to pseudorandom number generation: Equidistribution property and statistical independence of bits at distances up to logarithm of mesh size
The behavior of a family of dissipative dynamical systems representing
transformations of two-dimensional torus is studied on a discrete lattice and
compared with that of conservative hyperbolic automorphisms of the torus.
Applying dissipative dynamical systems to generation of pseudorandom numbers is
shown to be advantageous and equidistribution of probabilities for the
sequences of bits can be achieved. A new algorithm for generating uniform
pseudorandom numbers is proposed. The theory of the generator, which includes
proofs of periodic properties and of statistical independence of bits at
distances up to logarithm of mesh size, is presented. Extensive statistical
testing using available test packages demonstrates excellent results, while the
speed of the generator is comparable to other modern generators.Comment: 6 pages, 3 figures, 3 table
Exact solutions to chaotic and stochastic systems
We investigate functions that are exact solutions to chaotic dynamical
systems. A generalization of these functions can produce truly random numbers.
For the first time, we present solutions to random maps. This allows us to
check, analytically, some recent results about the complexity of random
dynamical systems. We confirm the result that a negative Lyapunov exponent does
not imply predictability in random systems. We test the effectiveness of
forecasting methods in distinguishing between chaotic and random time-series.
Using the explicit random functions, we can give explicit analytical formulas
for the output signal in some systems with stochastic resonance. We study the
influence of chaos on the stochastic resonance. We show, theoretically, the
existence of a new type of solitonic stochastic resonance, where the shape of
the kink is crucial. Using our models we can predict specific patterns in the
output signal of stochastic resonance systems.Comment: 31 pages, 18 figures (.eps). To appear in Chaos, March 200
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