Archive for randomness


Posted in Mountains, pictures, Statistics, Travel, University life with tags , , , , , , , , , , , on October 21, 2020 by xi'an

certified RNGs

Posted in Statistics with tags , , , , , , , on April 27, 2020 by xi'an

A company called Gaming Laboratories International (GLI) is delivering certificates of randomness. Apparently using Marsaglia’s DieHard tests. Here are some unforgettable quotes from their webpage:

“…a Random Number Generator (RNG) is a key component that MUST be adequately and fully tested to ensure non-predictability and no biases exist towards certain game outcomes.”

“GLI has the most experienced and robust RNG testing methodologies in the world. This includes software-based (pseudo-algorithmic) RNG’s, Hardware RNG’s, and hybrid combinations of both.”

“GLI uses custom software written and validated through the collaborative effort of our in-house mathematicians and industry consultants since our inception in 1989. An RNG Test Suite is applied for randomness testing.”

“No lab in the world provides the level of iGaming RNG assurance that GLI does. Don’t take a chance with this most critical portion of your iGaming system.”

really random generators [again!]

Posted in Books, Statistics with tags , , , , , , , , , on March 2, 2020 by xi'an

A pointer sent me to Chemistry World and an article therein about “really random numbers“. Or “truly” random numbers. Or “exactly” random numbers. Not particularly different from the (in)famous lava lamp generator!

“Cronin’s team has developed a robot that can automatically grow crystals in a 10 by 10 array of vials, take photographs of them, and use measurements of their size, orientation, and colour to generate strings of random numbers. The researchers analysed the numbers generated from crystals grown in three solutions – including a solution of copper sulfate – and found that they all passed statistical tests for the quality of their randomness.” Chemistry World, Tom Metcalfe, 18 February 2020

The validation of this truly random generator is thus exactly the same as a (“bad”) pseudo-random generator, namely that in the law of large number sense, it fits the predicted behaviour. And thus the difference between them cannot be statistical, but rather cryptographic:

“…we considered the encryption capability of this random number generator versus that of a frequently used pseudorandom number generator, the Mersenne Twister.” Lee et al., Matter, February 10, 2020

Meaning that the knowledge of the starting point and of the deterministic transform for the Mersenne Twister makes it feasible to decipher, which is not the case for a physical and non-reproducible generator as the one advocated. One unclear aspect of the proposed generator is the time required to produce 10⁶, even though the authors mention that “the bit-generation rate is significantly lower than that in other methods”.

certified randomness, 187m away…

Posted in Statistics with tags , , , , , , , on May 3, 2018 by xi'an

As it rarely happens with Nature, I just read an article that directly relates to my research interests, about a secure physical random number generator (RNG). By Peter Bierhost and co-authors, mostly physicists apparently. Security here means that the outcome of the RNG is unpredictable. This very peculiar RNG is based on two correlated photons sent to two measuring stations, separated by at least 187m, which have to display unpredictable outcomes in order to respect the impossibility of faster-than-light communications, otherwise known as Bell inequalities. This is hardly practical though, especially when mentioning that the authors managed to produce 2¹⁰ random bits over 10 minutes, post processing “the measurement of 55 million photon pairs”. (I however fail to see why the two-arm apparatus would be needed for regular random generation as it seems relevant solely for the demonstration of randomness.) I also checked the associated supplementary material, which is mostly about proving some total variation bound, and constructing a Bell function. What is most puzzling in this paper (and the associated supplementary material) is the (apparent) lack of guarantee of uniformity of the RNG. For instance, a sentence (Supplementary Material, p.11) about  a distribution being “within TV distance of uniform” hints at the method being not provably uniform, which makes the whole exercise incomprehensible…

more random than random!

Posted in Books, Kids, pictures, Statistics with tags , , , , , , on December 8, 2017 by xi'an

A revealing question on X validated the past week was asking for a random generator that is “more random” than the outcome of a specific random generator, à la Oliver Twist:The question is revealing of a quite common misunderstanding of the nature of random variables (as deterministic measurable transforms of a fundamental alea) and of their maybe paradoxical ability to enjoy stability or predictable properties. And much less that it relates to the long-lasting debate about the very [elusive] nature of randomness. The title of the question is equally striking: “Random numbers without pre-specified distribution” which could be given some modicum of meaning in a non-parametric setting, still depending on the choices made at the different levels of the model…