Random number generation plays an essential role in technology with important applications in areas ranging from cryptography to Monte Carlo methods, and other probabilistic algorithms. All such applications require high-quality sources of random numbers, yet effective methods for assessing whether a source produce truly random sequences are still missing. Current methods either do not rely on a formal description of randomness (NIST test suite) on the one hand, or are inapplicable in principle (the characterization derived from the Algorithmic Theory of Information), on the other, for they require testing all the possible computer programs that could produce the sequence to be analysed. Here we present a rigorous method that overcomes these problems based on Bayesian model selection. We derive analytic expressions for a model's likelihood which is then used to compute its posterior distribution. Our method proves to be more rigorous than NIST's suite and Borel-Normality criterion and its implementation is straightforward. We applied our method to an experimental device based on the process of spontaneous parametric downconversion to confirm it behaves as a genuine quantum random number generator. As our approach relies on Bayesian inference our scheme transcends individual sequence analysis, leading to a characterization of the source itself.

Improving randomness characterization through Bayesian model selection / Díaz Hernández Rojas, Rafael; Solís, Aldo; Angulo Martínez, Alí M; U'Ren, Alfred B; Hirsch, Jorge G; Marsili, Matteo; Pérez Castillo, Isaac. - In: SCIENTIFIC REPORTS. - ISSN 2045-2322. - 7:1(2017), p. 3096. [10.1038/s41598-017-03185-y]

Improving randomness characterization through Bayesian model selection

Díaz Hernández Rojas, Rafael
Primo
;
Pérez Castillo, Isaac
2017

Abstract

Random number generation plays an essential role in technology with important applications in areas ranging from cryptography to Monte Carlo methods, and other probabilistic algorithms. All such applications require high-quality sources of random numbers, yet effective methods for assessing whether a source produce truly random sequences are still missing. Current methods either do not rely on a formal description of randomness (NIST test suite) on the one hand, or are inapplicable in principle (the characterization derived from the Algorithmic Theory of Information), on the other, for they require testing all the possible computer programs that could produce the sequence to be analysed. Here we present a rigorous method that overcomes these problems based on Bayesian model selection. We derive analytic expressions for a model's likelihood which is then used to compute its posterior distribution. Our method proves to be more rigorous than NIST's suite and Borel-Normality criterion and its implementation is straightforward. We applied our method to an experimental device based on the process of spontaneous parametric downconversion to confirm it behaves as a genuine quantum random number generator. As our approach relies on Bayesian inference our scheme transcends individual sequence analysis, leading to a characterization of the source itself.
2017
Bayesian inference; model selection; cryptography; random number generators
01 Pubblicazione su rivista::01a Articolo in rivista
Improving randomness characterization through Bayesian model selection / Díaz Hernández Rojas, Rafael; Solís, Aldo; Angulo Martínez, Alí M; U'Ren, Alfred B; Hirsch, Jorge G; Marsili, Matteo; Pérez Castillo, Isaac. - In: SCIENTIFIC REPORTS. - ISSN 2045-2322. - 7:1(2017), p. 3096. [10.1038/s41598-017-03185-y]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1279644
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