5 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
On the Collision Property of Chaotic Iterations Based Post-Treatments over Cryptographic Pseudorandom Number Generator
International audienceThere is not a proper mathematical definition of chaos, we have instead a quite big amount of definitions, each of one describes chaos in a more or less general context. Taking in account this, it is clear why it is hard to design an algorithm that produce random numbers, a kind of algorithm that could have plenty of concrete appliceautifat (anul)d bions. However we must use a finite state machine (e.g. a laptop) to produce such a sequence of random numbers, thus it is convenient, for obvious reasons, to redefine those aimed sequences as pseudorandom; also problems arise with floating point arithmetic if one wants to recover some real chaotic property (i.e. properties from functions defined on the real numbers). All this considerations are synthesized in the problem of the Pseudorandom number generators (PRNGs). A solution to these obstacles may be to post-operate on existing PRNGs to improve their performances, using the so-called chaotic iterations, i.e., specific iterations of a boolean function and a shift operator that use the inputted generator. This approach leads to a mathematical description of such PRNGs as discrete dynamical systems, on which chaos properties can be investigated using mathematical topology and measure theory. Such properties are well-formulated, and they allow us to characterize which functions improves the sensitivity to the seed, the expansivity, the ergodicity, or the topological mixing of the generator resulting from such a post-processing. Experience shows that choosing relevant boolean functions in these chaotic iterations improves the randomness of the inputted generator, for instance when considering the number of statistical tests of randomness passed successfully. If we focus on the cryptographical application of PRNGs, there are two main classical notions to be considered, namely collision and avalanche effect. In this article, we recall the chaotic properties of the proposed post-treatment and we study the collision property in families of pseudorandom sequences produced by this process
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
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