# Entropy and Security of Pseudorandom Number Generators based on Chaotic Iterations

### Luigi Marangio, Christophe Guyeux

#### 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 been 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.

Download#### Paper Citation

#### in Harvard Style

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

#### in Bibtex Style

@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},

}

#### in EndNote Style

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