Random Walk in a N-Cube Without Hamiltonian Cycle to Chaotic Pseudorandom Number Generation: Theoretical and Practical Considerations

Contassot-Vivier, Sylvain; Couchot, Jean-François; Guyeux, Christophe; Héam, Pierre-Cyrille

doi:10.1142/s0218127417500146

Cited by 10 publications

(19 citation statements)

References 16 publications

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“…The asynchronous iteration graph associated with f is the directed graph Γ( f ) defined by: the set of vertices is B N ; for all x ∈ B N and i ⊂ 1; N , the graph Γ( f ) contains an arc from x to F f (i, x) labeled by subset i. We have previously established that [52], [53]:…”

Section: Chaotic Iterations: the Theorymentioning

confidence: 99%

CIPRNG: A VLSI Family of Chaotic Iterations Post-Processings for $\mathbb {F}_{2}$ -Linear Pseudorandom Number Generation Based on Zynq MPSoC

Bakiri

Couchot

Guyeux

2018

IEEE Trans. Circuits Syst. I

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Hardware pseudorandom number generators are continuously improved to satisfy both physical and ubiquitous computing security system challenges. The main contribution of this work is to propose two post-processing modules in hardware, to improve the randomness of linear PRNGs while succeeding in passing the TestU01 statistical battery of tests. They are based on chaotic iterations and are denoted by CIPRNG-MC and CIPRNG-XOR. They have various interesting properties, encompassing the ability to improve the statistical profile of the generators on which they iterate. Such post-processing have been implemented on FPGA and ASIC without inferring any blocs (RAM or DSP). A comparison in terms of area, throughput, and statistical tests, is performed. The hardware pseudorandom number generation can reach a throughput/latency ratio equal to 8.5 Gbps for Zynq-FPGA and 10.9 Gbps for ASIC, being thus the fastest FPGA generators based on chaos that can pass TestU01. In particular, it is established that CIPRNG-XOR is 2.5 times faster and 5 times more efficient that almost all linear PRNGs who pass TestU01.

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Section: Chaotic Iterations: the Theorymentioning

confidence: 99%

CIPRNG: A VLSI Family of Chaotic Iterations Post-Processings for $\mathbb {F}_{2}$ -Linear Pseudorandom Number Generation Based on Zynq MPSoC

Bakiri

Couchot

Guyeux

2018

IEEE Trans. Circuits Syst. I

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“…Full details on the use of Gray codes to build chaotic PRNGs can be found in [6,10]. For the sake of clarity, we briefly recall the main principles in this section.…”

Section: Using Gray Codes In Chaotic Prngsmentioning

confidence: 99%

“…This theoretical subject has received a lot of attention in recent years [1][2][3][4][5]. The article [6] is situated in this thematic field. Indeed, it focuses on a Random Walk in a N-cube where a balanced Hamiltonian cycle has been removed.…”

Section: Introductionmentioning

confidence: 99%

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Gray Codes Generation Algorithm and Theoretical Evaluation of Random Walks in N-Cubes

2018

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In previous works, some of the authors have proposed a canonical form of Gray Codes (GCs) in N-cubes (hypercubes of dimension N). This form allowed them to draw an algorithm that theoretically provides exactly all the GCs for a given dimension N. In another work, we first have shown that any of these GC can be used to build the transition function of a Pseudorandom Number Generator (PRNG). Also, we have found a theoretical quadratic upper bound of the mixing time, i.e., the number of iterations that are required to provide a PRNG whose output is uniform. This article, extends these two previous works both practically and theoretically. On the one hand, another algorithm for generating GCs is proposed that provides an efficient generation of subsets of the entire set of GCs related to a given dimension N. This offers a large choice of GC to be used in the construction of Choatic Iterations based PRNGs (CI-PRNGs), leading to a large class of possible PRNGs. On the other hand, the mixing time has been theoretically shown to be in N log(N), which was anticipated in the previous article, but not proven.

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“…It is worth mentioning that the study of dynamics over finite graphs has been recently considered by Bahi et al by setting links between Devaney chaos and strong connectivity in order to provide an algorithm for the generation of strongly connected graphs and to construct Pseudo Random Number Generators (PRNGs) [6]. This approach has also allowed for the obtainment of PRNGs based on the construction of Hamiltonian cycles over an N-cube [7,8]. It is also worth mentioning that such results can also be considered in connection with finite state machines [9] and explained using Turing machines [10].…”

Section: Introductionmentioning

confidence: 99%

Dynamics on Binary Relations over Topological Spaces

et al. 2018

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Abstract:The existence of chaos and the quest of dense orbits have been recently considered for dynamical systems given by multivalued linear operators. We consider the notions of topological transitivity, topologically mixing property, hypercyclicity, periodic points, and Devaney chaos in the general case of binary relations on topological spaces, and we analyze how they can be particularized when they are represented with graphs and digraphs. The relations of these notions with different types of connectivity and with the existence of Hamiltonian paths are also exposed. Special attention is given to the study of dynamics over tournaments. Finally, we also show how disjointness can be introduced in this setting.

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Random Walk in a N-Cube Without Hamiltonian Cycle to Chaotic Pseudorandom Number Generation: Theoretical and Practical Considerations

Abstract: International audienc

Cited by 10 publications

References 16 publications

CIPRNG: A VLSI Family of Chaotic Iterations Post-Processings for $\mathbb {F}_{2}$ -Linear Pseudorandom Number Generation Based on Zynq MPSoC

CIPRNG: A VLSI Family of Chaotic Iterations Post-Processings for $\mathbb {F}_{2}$ -Linear Pseudorandom Number Generation Based on Zynq MPSoC

Gray Codes Generation Algorithm and Theoretical Evaluation of Random Walks in N-Cubes

Dynamics on Binary Relations over Topological Spaces

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