392 research outputs found
A Topological Study of Chaotic Iterations. Application to Hash Functions
International audienceChaotic iterations, a tool formerly used in distributed computing, has recently revealed various interesting properties of disorder leading to its use in the computer science security field. In this paper, a comprehensive study of its topological behavior is proposed. It is stated that, in addition to being chaotic as defined in the Devaney's formulation, this tool possesses the property of topological mixing. Additionally, its level of sensibility, expansivity, and topological entropy are evaluated. All of these properties lead to a complete unpredictable behavior for the chaotic iterations. As it only manipulates binary digits or integers, we show that it is possible to use it to produce truly chaotic computer programs. As an application example, a truly chaotic hash function is proposed in two versions. In the second version, an artificial neural network is used, which can be stated as chaotic according to Devaney
The dynamics of the CBC Mode of Operation
In cryptography, the Cipher Block Chaining (CBC), one of the most commonly
used mode in recent years, is a mode of operation that uses a block cipher to
provide confidentiality or authenticity. In our previous research work, we have
shown that this mode of operation exhibits, under some conditions, a chaotic
behaviour. We have studied this behaviour by evaluating both its level of
sensibility and expansivity. In this paper, we intend to deepen the topological
study of the CBC mode of operation and evaluate its property of topological
mixing. Additionally, other quantitative evaluations are performed, and the
level of topological entropy has been evaluated too.Comment: Nonlinearity, IOP Publishing, 2016. arXiv admin note: text overlap
with arXiv:1601.0813
Quantitative Evaluation of Chaotic CBC Mode of Operation
The cipher block chaining (CBC) block cipher mode of operation presents a
very popular way of encrypting which is used in various applications. In
previous research work, we have mathematically proven that, under some
conditions, this mode of operation can admit a chaotic behavior according to
Devaney. Proving that CBC mode is chaotic is only the beginning of the study of
its security. The next step, which is the purpose of this paper, is to develop
the quantitative study of the chaotic CBC mode of operation by evaluating the
level of sensibility and expansivity for this mode.Comment: in International Conference on Advanced Technologies for Signal &
Images Processing ATSIP'2016 , Mar 2016, Monastir, Tunisi
Topological chaos and chaotic iterations, application to Hash functions
International audienceThis paper introduces a new notion of chaotic algorithms. These algorithms are iterative and are based on so-called chaotic iterations. Contrary to all existing studies on chaotic iterations, we are not interested in stable states of such iterations but in their possible unpredictable behaviors. By establishing a link between chaotic iterations and the notion of Devaney's topological chaos, we give conditions ensuring that these kind of algorithms produce topological chaos. This leads to algorithms that are highly unpredictable. After presenting the theoretical foundations of our approach, we are interested in its practical aspects. We show how the theoretical algorithms give rise to computer programs that produce true topological chaos, then we propose applications in the area of information security
Hash Functions Using Chaotic Iterations
International audienceIn this paper, a novel formulation of discrete chaotic iterations in the field of dynamical systems is given. Their topological properties are studied: it is mathematically proven that, under some conditions, these iterations have a chaotic behavior as defined by Devaney. This chaotic behavior allows us to propose a way to generate new hash functions. An illustrative example is detailed in order to show how to use our theoretical study in practice
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