Improving randomness characterization through Bayesian model selection

TL;DR

This paper introduces a Bayesian model selection method for rigorously characterizing the randomness of number generators, surpassing traditional tests and confirming the quantum nature of a physical QRNG device.

Contribution

The paper presents a novel Bayesian approach for randomness characterization that is both rigorous and straightforward to implement, improving upon existing methods like NIST tests and ATI-based criteria.

Findings

The Bayesian method outperforms NIST and Borel-Normality tests in rigor.

Applied to a quantum device, it confirmed genuine quantum randomness.

The approach generalizes beyond individual sequences to source-level characterization.

Abstract

Nowadays random number generation plays an essential role in technology with important applications in areas ranging from cryptography, which lies at the core of current communication protocols, to Monte Carlo methods, and other probabilistic algorithms. In this context, a crucial scientific endeavour is to develop effective methods that allow the characterization of random number generators. However, commonly employed methods either lack formality (e.g. the NIST test suite), or are inapplicable in principle (e.g. the characterization derived from the Algorithmic Theory of Information (ATI)). In this letter we present a novel method based on Bayesian model selection, which is both rigorous and effective, for characterizing randomness in a bit sequence. We derive analytic expressions for a model's likelihood which is then used to compute its posterior probability distribution. Our method proves to be more rigorous than NIST's suite and the Borel-Normality criterion and its implementation is straightforward. We have applied our method to an experimental device based on the process of spontaneous parametric downconversion, implemented in our laboratory, to confirm that it behaves as a genuine quantum random number generator (QRNG). As our approach relies on Bayesian inference, which entails model generalizability, our scheme transcends individual sequence analysis, leading to a characterization of the source of the random sequences itself.