scholarly journals Pattern Occurrence in the Dyadic Expansion of Square Root of Two and an Analysis of Pseudorandom Number Generators

Integers ◽  
2010 ◽  
Vol 10 (1) ◽  
Author(s):  
Koji Nuida
Keyword(s):  
Pseudorandom Number ◽  
Occurrence Rate ◽  
Square Root ◽  
Pseudorandom Number Generators ◽  
Asymptotic Rate ◽  
Binary Word ◽  
Dyadic Expansion ◽  
And Performance

AbstractRecently, designs of pseudorandom number generators (PRNGs) using integer-valued variants of logistic maps and their applications to certain cryptographic schemes have been studied, due mostly to their ease of implementation and performance. However, it has been noted that this ease is reduced for some choices of the PRNGs accuracy parameters. In this article, we show that the distribution of such undesirable accuracy parameters is closely related to the occurrence of some patterns in the dyadic expansion of the square root of 2. We prove that for an arbitrary infinite binary word, the asymptotic occurrence rate of these patterns is bounded in terms of the asymptotic occurrence rate of zeroes. As a consequence, a classical conjecture on asymptotic evenness of occurrence of zeroes and ones in the dyadic expansion of the square root of 2 implies that the asymptotic rate of the undesirable accuracy parameters for the PRNGs is at least 1/6.

scholarly journals Bounds of asymptotic occurrence rates of some patterns in binary words related to integer-valued logistic maps

2009 ◽  
Vol DMTCS Proceedings vol. AK,... (Proceedings) ◽  
Author(s):  
Koji Nuida
Keyword(s):  
Pseudorandom Number ◽  
Occurrence Rate ◽  
Pseudorandom Number Generators ◽  
Binary Word ◽  
Nous Montrons ◽  
International Audience

International audience In this article, we investigate the asymptotic occurrence rates of specific subwords in any infinite binary word. We prove that the asymptotic occurrence rate for the subwords is upper- and lower-bounded in the same way for every infinite binary word, in terms of the asymptotic occurrence rate of the zeros. We also show that both of the bounds are best-possible by constructing, for each bound, a concrete infinite binary word such that the bound is reached. Moreover, we apply the result to analyses of recently-proposed pseudorandom number generators that are based on integer-valued variants of logistic maps. Dans cet article, nous étudions les fréquences asymptotiques d’occurrence de suites spécifiques dans tout mot binaire infini. Nous prouvons que la fréquence asymptotique d’occurrence pour ces suites est borné supérieurement et inférieurement de la même façon pour chaque mot binaire infini, en termes des fréquences asymptotiques d’occurrence de zéros. Nous montrons aussi que les deux limites sont les meilleures possibles en construisant concrètement, pour chaque limite, un mot binaire infini tel que la borne est atteinte à la limite. De plus, nous appliquons ce résultat à des analyses de générateurs de nombres pseudo-aléatoires proposés récemment qui sont basés sur des variantes des fonctions logistiques à valeurs entières.

Unreliability of Available Pseudorandom Number Generators

2020 ◽  
Vol 60 (11) ◽  
pp. 1747-1753
Author(s):  
A. A. Belov ◽  
N. N. Kalitkin ◽  
M. A. Tintul
Keyword(s):  
Pseudorandom Number ◽  
Pseudorandom Number Generators

Uniformity tests on the GPSS-Fortran pseudorandom number generators

1988 ◽  
Vol 19 (3) ◽  
pp. 20-26
Author(s):  
Gerritt K. Janssens
Keyword(s):  
Pseudorandom Number ◽  
Pseudorandom Number Generators

Pseudorandom Number Generators Based on Chaotic Dynamical Systems

2001 ◽  
Vol 08 (02) ◽  
pp. 137-146 ◽  
Author(s):  
Janusz Szczepański ◽  
Zbigniew Kotulski
Keyword(s):  
Dynamical Systems ◽  
Communication Systems ◽  
Initial Conditions ◽  
Pseudorandom Number ◽  
New Approach ◽  
Chaotic Dynamical Systems ◽  
Pseudorandom Number Generators ◽  
Transmission Of Information ◽  
Extreme Sensitivity ◽  
Contemporary Technology

Pseudorandom number generators are used in many areas of contemporary technology such as modern communication systems and engineering applications. In recent years a new approach to secure transmission of information based on the application of the theory of chaotic dynamical systems has been developed. In this paper we present a method of generating pseudorandom numbers applying discrete chaotic dynamical systems. The idea of construction of chaotic pseudorandom number generators (CPRNG) intrinsically exploits the property of extreme sensitivity of trajectories to small changes of initial conditions, since the generated bits are associated with trajectories in an appropriate way. To ensure good statistical properties of the CPRBG (which determine its quality) we assume that the dynamical systems used are also ergodic or preferably mixing. Finally, since chaotic systems often appear in realistic physical situations, we suggest a physical model of CPRNG.

Method of Combining Cryptography and LDPC Coding for Enhanced Privacy

2021 ◽  
Vol 13 (4) ◽  
pp. 51-70
Author(s):  
Bradley Comar
Keyword(s):  
Error Correction ◽  
Pseudorandom Number ◽  
Low Density ◽  
Parity Check ◽  
Pseudorandom Number Generators ◽  
Low Density Parity Check

This paper describes a method of combining cryptographic encoding and low density parity check (LDPC) encoding for the purpose of enhancing privacy. This method uses pseudorandom number generators (PRNGs) to create parity check matrices that are constantly updated. The generated cyphertext is at least as private as a standard additive (XORing) cryptosystem, and also has error correcting capability. The eavesdropper, Eve, has the expanded burden of having to perform cryptanalysis and error correction simultaneously.

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