48,801 research outputs found
Some hints for the design of digital chaos-based cryptosystems: lessons learned from cryptanalysis
In this work we comment some conclusions derived from the analysis of recent
proposals on the field of chaos-based cryptography. These observations remark
the main problems detected in some of those schemes under examination.
Therefore, this paper is a list of what to avoid when considering chaos as
source of new strategies to conceal and protect information
Time lagged ordinal partition networks for capturing dynamics of continuous dynamical systems
We investigate a generalised version of the recently proposed ordinal
partition time series to network transformation algorithm. Firstly we introduce
a fixed time lag for the elements of each partition that is selected using
techniques from traditional time delay embedding. The resulting partitions
define regions in the embedding phase space that are mapped to nodes in the
network space. Edges are allocated between nodes based on temporal succession
thus creating a Markov chain representation of the time series. We then apply
this new transformation algorithm to time series generated by the R\"ossler
system and find that periodic dynamics translate to ring structures whereas
chaotic time series translate to band or tube-like structures -- thereby
indicating that our algorithm generates networks whose structure is sensitive
to system dynamics. Furthermore we demonstrate that simple network measures
including the mean out degree and variance of out degrees can track changes in
the dynamical behaviour in a manner comparable to the largest Lyapunov
exponent. We also apply the same analysis to experimental time series generated
by a diode resonator circuit and show that the network size, mean shortest path
length and network diameter are highly sensitive to the interior crisis
captured in this particular data set
Modelling and control of chaotic processes through their Bifurcation Diagrams generated with the help of Recurrent Neural Network models: Part 1—simulation studies
Many real-world processes tend to be chaotic and also do not lead to satisfactory analytical modelling. It has been shown here that for such chaotic processes represented through short chaotic noisy time-series, a multi-input and multi-output recurrent neural networks model can be built which is capable of capturing the process trends and predicting the future values from any given starting condition. It is further shown that this capability can be achieved by the Recurrent Neural Network model when it is trained to very low value of mean squared error. Such a model can then be used for constructing the Bifurcation Diagram of the process leading to determination of desirable operating conditions. Further, this multi-input and multi-output model makes the process accessible for control using open-loop/closed-loop approaches or bifurcation control etc. All these studies have been carried out using a low dimensional discrete chaotic system of Hénon Map as a representative of some real-world processes
Cryptanalysis of a new chaotic cryptosystem based on ergodicity
This paper analyzes the security of a recent cryptosystem based on the
ergodicity property of chaotic maps. It is shown how to obtain the secret key
using a chosen-ciphertext attack. Some other design weaknesses are also shown.Comment: 10 pages, 5 figure
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