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Authors: Luigi Marangio 1 and Christophe Guyeux 2

Affiliations: 1 Department of Computer Science and Complex Systems, Université Bourgogne Franche-Comté, Femto-St Institute, France, Department of Mathematics, Universitá di Pisa and Italy ; 2 Department of Computer Science and Complex Systems, Université Bourgogne Franche-Comté, Femto-St Institute and France

ISBN: 978-989-758-378-0

Keyword(s): Pseudorandom Number Generators, Dynamical Systems, Security.

Related Ontology Subjects/Areas/Topics: Data and Application Security and Privacy ; Data Protection ; Formal Methods for Security ; Information and Systems Security ; Security and Privacy in Complex Systems

Abstract: In the domain of cryptography, an important role is played by PseudoRandom Number Generators (PRNGs). Designing such generators might be complicated for different reasons: an appropriate formal abstract notion of randomness should be formulated, and after that, it may be hard to design an algorithm that produces such random numbers on a finite state machine. A possible approach to tackle this problem has been proposed and studied in recent works (for instance (Guyeux and Bahi, 2012)), where the authors considered to post-operate on existing PRNGs, using the so-called chaotic iterations, i.e., specific iterations of a boolean function and a shift operator that use the inputted generator. This process has at least two positive aspects : boolean functions avoid the problem of numbers representation (e.g. floating point arithmetic), and it is possible to describe the PRNGs based on chaotic iterations as dynamical systems, with a formal mathematical description. This class of PRNGs has bee n proven to be useful also for cryptographical applications, after a suitable redefinition of the generators in the cryptographical domain. In this article we propose a Markov chain model of the PRNGs based on chaotic iterations and we will use it to compute the entropy of the proposed generators. Moreover we will prove that the security property is preserved when a cryptographic PRNG is post processed with iterations of a suitable boolean functions. (More)

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Paper citation in several formats:
Marangio, L. and Guyeux, C. (2019). Entropy and Security of Pseudorandom Number Generators based on Chaotic Iterations.In Proceedings of the 16th International Joint Conference on e-Business and Telecommunications - Volume 2: SECRYPT, ISBN 978-989-758-378-0, pages 402-407. DOI: 10.5220/0007839304020407

@conference{secrypt19,
author={Luigi Marangio. and Christophe Guyeux.},
title={Entropy and Security of Pseudorandom Number Generators based on Chaotic Iterations},
booktitle={Proceedings of the 16th International Joint Conference on e-Business and Telecommunications - Volume 2: SECRYPT,},
year={2019},
pages={402-407},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0007839304020407},
isbn={978-989-758-378-0},
}

TY - CONF

JO - Proceedings of the 16th International Joint Conference on e-Business and Telecommunications - Volume 2: SECRYPT,
TI - Entropy and Security of Pseudorandom Number Generators based on Chaotic Iterations
SN - 978-989-758-378-0
AU - Marangio, L.
AU - Guyeux, C.
PY - 2019
SP - 402
EP - 407
DO - 10.5220/0007839304020407

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