5,725 research outputs found
A Pseudo Random Numbers Generator Based on Chaotic Iterations. Application to Watermarking
In this paper, a new chaotic pseudo-random number generator (PRNG) is
proposed. It combines the well-known ISAAC and XORshift generators with chaotic
iterations. This PRNG possesses important properties of topological chaos and
can successfully pass NIST and TestU01 batteries of tests. This makes our
generator suitable for information security applications like cryptography. As
an illustrative example, an application in the field of watermarking is
presented.Comment: 11 pages, 7 figures, In WISM 2010, Int. Conf. on Web Information
Systems and Mining, volume 6318 of LNCS, Sanya, China, pages 202--211,
October 201
Global Orbit Patterns for One Dimensional Dynamical Systems
In this article, we study the behaviour of discrete one-dimensional dynamical
systems associated to functions on finite sets. We formalise the global orbit
pattern formed by all the periodic orbits (gop) as the ordered set of periods
when the initial value thumbs the finite set in the increasing order. We are
able to predict, using closed formulas, the number of gop for the set
of all the functions on . We also explore by computer
experiments special subsets of in which interesting patterns of
gop are found.Comment: 33 pages, 1 figur
Improving random number generators by chaotic iterations. Application in data hiding
In this paper, a new pseudo-random number generator (PRNG) based on chaotic
iterations is proposed. This method also combines the digits of two XORshifts
PRNGs. The statistical properties of this new generator are improved: the
generated sequences can pass all the DieHARD statistical test suite. In
addition, this generator behaves chaotically, as defined by Devaney. This makes
our generator suitable for cryptographic applications. An illustration in the
field of data hiding is presented and the robustness of the obtained data
hiding algorithm against attacks is evaluated.Comment: 6 pages, 8 figures, In ICCASM 2010, Int. Conf. on Computer
Application and System Modeling, Taiyuan, China, pages ***--***, October 201
Periodic orbits of the ensemble of Sinai-Arnold cat maps and pseudorandom number generation
We propose methods for constructing high-quality pseudorandom number
generators (RNGs) based on an ensemble of hyperbolic automorphisms of the unit
two-dimensional torus (Sinai-Arnold map or cat map) while keeping a part of the
information hidden. The single cat map provides the random properties expected
from a good RNG and is hence an appropriate building block for an RNG, although
unnecessary correlations are always present in practice. We show that
introducing hidden variables and introducing rotation in the RNG output,
accompanied with the proper initialization, dramatically suppress these
correlations. We analyze the mechanisms of the single-cat-map correlations
analytically and show how to diminish them. We generalize the Percival-Vivaldi
theory in the case of the ensemble of maps, find the period of the proposed RNG
analytically, and also analyze its properties. We present efficient practical
realizations for the RNGs and check our predictions numerically. We also test
our RNGs using the known stringent batteries of statistical tests and find that
the statistical properties of our best generators are not worse than those of
other best modern generators.Comment: 18 pages, 3 figures, 9 table
Randomness Quality of CI Chaotic Generators: Applications to Internet Security
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 level of security is thus becoming a hot topic, because numerous
cryptosystems and data hiding schemes are directly dependent on the quality of
these generators. At the conference Internet`09, we have described a generator
based on chaotic iterations, which behaves chaotically as defined by Devaney.
In this paper, the proposal is to improve the speed and the security of this
generator, to make its use more relevant in the Internet security context. To
do so, a comparative study between various generators is carried out and
statistical results are given. Finally, an application in the information
hiding framework is presented, to give an illustrative example of the use of
such a generator in the Internet security field.Comment: 6 pages,6 figures, In INTERNET'2010. The 2nd Int. Conf. on Evolving
Internet, Valencia, Spain, pages 125-130, September 2010. IEEE Computer
Society Press Note: Best Paper awar
Computational Complexity of Iterated Maps on the Interval (Extended Abstract)
The exact computation of orbits of discrete dynamical systems on the interval
is considered. Therefore, a multiple-precision floating point approach based on
error analysis is chosen and a general algorithm is presented. The correctness
of the algorithm is shown and the computational complexity is analyzed. As a
main result, the computational complexity measure considered here is related to
the Ljapunow exponent of the dynamical system under consideration
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