certified RNGs

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.”
 

random generators… unfit for ESP testing?!

“The term psi denotes anomalous processes of information or energy transfer that are currently unexplained in terms of known physical or biological mechanisms.”

When re-reading [in the taxi to Birmingham airport] Bem’s piece on “significant” ESP tests, I came upon the following hilarious part that I could not let pass:

“For most psychological experiments, a random number table or the random function built into most programming languages provides an adequate tool for randomly assigning participants to conditions or sequencing stimulus presentations. For both methodological and conceptual reasons, however, psi researchers have paid much closer attention to issues of randomization.

At the methodological level, the problem is that the random functions included in most computer languages are not very good in that they fail one or more of the mathematical tests used to assess the randomness of a sequence of numbers (L’Ecuyer, 2001), such as Marsaglia’s rigorous Diehard Battery of Tests of Randomness (1995). Such random functions are sometimes called pseudo random number generators (PRNGs) because they [are] not random in the sense of being indeterminate because once the initial starting number (the seed) is set, all future numbers in the sequence are fully determined.”

Well, pseudo-random generators included in all modern computer languages that I know have passed tests like diehard. It would be immensely useful to learn of counterexamples as those using the corresponding language should be warned!!!

“In contrast, a hardware-based or “true” RNG is based on a physical process, such as radioactive decay or diode noise, and the sequence of numbers is indeterminate in the quantum mechanical sense. This does not in itself guarantee that the resulting sequence of numbers can pass all the mathematical tests of randomness (…) Both Marsaglia’s own PRNG algorithm and the “true” hardware-based Araneus Alea I RNG used in our experiments pass all his diehard tests (…) At the conceptual level, the choice of a PRNG or a hardware-based RNG bears on the interpretation of positive findings. In the present context, it bears on my claim that the experiments reported in this article provide evidence for precognition or retroactive influence.”

There is no [probabilistic] validity in the claim that hardware random generators are more random than pseudo-random ones. Hardware generators may be unpredictable even by the hardware conceptor, but the only way to check they produce generations from a uniform distribution follows exactly the same pattern as for PRNG. And the lack of reproducibility of the outcome makes it impossible to check the reproducibility of the study. But here comes the best part of the story!

“If an algorithm-based PRNG is used to determine the successive left-right positions of the target pictures, then the computer already “knows” the upcoming random number before the participant makes his or her response; in fact, once the initial seed number is generated, the computer implicitly knows the entire sequence of left/right positions. As a result, this information is potentially available to the participant through real-time clairvoyance, permitting us to reject the more extraordinary claim that the direction of the causal arrow has actually been reversed.”

Extraordinary indeed… But not more extraordinary than conceiving that a [psychic] participant in the experiment may “see” the whole sequence of random numbers!

“In contrast, if a true hardware-based RNG is used to determine the left/right positions, the next number in the sequence is indeterminate until it is actually generated by the quantum physical process embedded in the RNG, thereby ruling out the clairvoyance alternative. This argues for using a true RNG to demonstrate precognition or retroactive influence. But alas, the use of a true RNG opens the door to the psychokinesis interpretation: The participant might be influencing the placement of the upcoming target rather than perceiving it, a possibility supported by a body of empirical evidence testing psychokinesis with true RNGs (Radin, 2006, pp.154–160).”

Good! I was just about to make the very same objection! If someone can predict the whole sequence of [extremely long integer] values of a PRNG, it gets hardly more irrational to imagine that he or she can mentally impact a quantum mechanics event. (And hopefully save Schröninger’s cat in the process.) Obviously, it begets the question as to how a subject could forecast a location of the picture that depends on the random generation but not forecast the result of the random generation.

“Like the clairvoyance interpretation, the psychokinesis interpretation also permits us to reject the claim that the direction of the causal arrow has been reversed. Ironically, the psychokinesis alternative can be ruled out by using a PRNG, which is immune to psychokinesis because the sequence of numbers is fully determined and can even be checked after the fact to confirm that its algorithm has not been perturbed. Over the course of our research program—and within the experiment just reported—we have obtained positive results using both PRNGs and a true RNG, arguably leaving precognition/reversed causality the only nonartifactual interpretation that can account for all the positive results.”

This is getting rather confusing. Avoid using a PRNG for fear the subject infers about the sequence and avoid using a RNG for fear of the subject tempering with the physical generator. An omniscient psychic would be able to hand both types of generators, wouldn’t he or she!?!

“This still leaves open the artifactual alternative that the output from the RNG is producing inadequately randomized sequences containing patterns that fortuitously match participants’ response biases.”

This objection shows how little confidence the author has in the randomness tests he previously mentioned: a proper random generator is not inadequately randomized. And if chance only rather than psychic powers is involved, there is no explanation for the match with the participants’ response. Unless those participants are so clever as to detect the flaws in the generator…

“In the present experiment, this possibility is ruled out by the twin findings that erotic targets were detected significantly more frequently than randomly interspersed nonerotic targets and that the nonerotic targets themselves were not detected significantly more frequently than chance. Nevertheless, for some of the other experiments reported in this article, it would be useful to have more general assurance that there are not patterns in the left/right placements of the targets that might correlate with response biases of participants. For this purpose, Lise Wallach, Professor of Psychology at Duke University, suggested that I run a virtual control experiment using random inputs in place of human participants.”

Absolutely brilliant! This test replacing the participants with random generators has shown that the subjects’ answers do not correspond to an iid sequence from a uniform distribution. It would indeed require great psychic powers to reproduce a perfectly iid U(0,1) sequence! And the participants were warned about the experiment so naturally expected to see patterns in the sequence of placements.

 

Le Monde sans puzzle

This week, Le Monde mathematical puzzle: is purely geometric, hence inappropriate for an R resolution. In the Science & Médecine leaflet, there is however an interesting central page about random generators, from the multiple usages of those in daily life to the consequences of poor generators on cryptography and data safety. The article is compiling an interview of Jean-Paul Delahaye on the topic with recent illustrations from cybersecurity. One final section gets rather incomprehensible: when discussing the dangers of seed generation, it states that “a poor management of the entropy means that an hacker can saturate the seed and take over the original randomness, weakening the whole system”. I am sure there is something real behind the imagery, but this does not make sense… Another insert mentions a possible random generator built out of the light detectors on a smartphone. And quantum physics. The society IDQ can indeed produce ultra-rapid random generators that way. And it also ran randomness tests summarised here. Using in particular George Marsaglia’s diehard battery.

Another column report that a robot passed the Turing test last week, on Turing‘s death anniversary. Meaning that 33% of the jury was convinced the robot’s answers were given by a human. This reminded me of the Most Human Human book sent to me by my friends from BYU. (A marginalia found in Le Monde is that the test was organised by Kevin Warwick…from the University of Coventry, a funny reversal of the University of Warwick sitting in Coventry! However, checking on his website showed that he has and had no affiliation with this university, being at the University of Reading instead.)

 

Truly random?!

Having purchased the September edition of La Recherche because of its (disappointing!) coverage on black matter, I came by a short coverage on an Intel circuit producing “truly random” numbers… I already discussed this issue in an earlier post, namely that there is no reason physical generators are “more” random than congruential pseudo-random generators, but this short paper repeats the same misunderstanding on the role of “random” generators. The paper mentions dangers of pseudo-random generators for cryptography (but this is only when you know the deterministic function and the sequence of seeds used so far), while it misses the essential aspect of valid generators, namely that their distribution is exactly known (e.g., uniform) and, in the case of parallel generations, which seems to be the case for this circuit, that the generators are completely independent. La Recherche mentions that the entropy of the generator is really high, but this is more worrying than reassuring, as the Intel engineers do not have a more elaborate way to prove uniformity than a Monte Carlo experiment…

There is actually a deeper entry found on Technology Review. (Which may have been the source for the paper in the technology tribune of La Recherche.) The article mentions that the generator satisfied all benchmarks of “randomness” maintained by NIST. Those statistical tests sound much more reassuring than the entropy check mentioned by La Recherche, as they essentially reproduce Marsaglia’s DieHard benchmark… I remain rather skeptical about physical devices, as compared with mathematical functions, because of (a) non-reproducibility which is a negative feature despite what the paper says and of (b) instability of the device, which means that proven uniformity at time t does not induce uniformity at time t+1. Nonetheless, if the gains in execution are gigantic, it may be worth the approximation for most applications. But please stop using “true” in conjunction with randomness!!!