"If N = 300, even a 256-bit seed arbitrarily precludes all but an unknown, haphazardly selected, non-random, and infinitesimally small fraction of permissible assignments. This introduces enormous bias into the assignment process and makes total nonsense of the p-value computed by a randomization test."
The first sentence is obviously true, but I'm going to need to see some evidence for "enormous bias" and "total nonsense". Let's leave aside lousy/little/badly-seeded PRNGs. Are there any non-cryptographic examples in which a well-designed PRNG with 256 bits of well-seeded random state produces results different enough from a TRNG to be visible to a user?
The argument against PRNGs this paper makes isn't that the PRNG produces results that can be distinguished from TRNG, but that the 256-bit seed deterministically chooses a single shuffling. If you need 300 bits to truly shuffle the assignment but you only have 256 bits, then that's a lot of potential assignments that can never actually happen. With this argument it doesn't matter what the PRNG is, the fact that it's deterministic is all that matters. And this invalidates the p-value because the p-value assumes that all possible assignments are equiprobable, when in fact a lot of possible assignments have a probability of zero.
I imagine you could change the p-value test to randomly sample assignments generated via the exact same process that was used to generate the assignment used by the experiment, and as you run more and more iterations of this the calculated p-value should converge to the correct value, but then the question becomes is the p-value calculated this way the same as the p-value you'd get if you actually went ahead and used equiprobable assignment to begin with?
Ultimately, this all comes down to the fact that it's not hard to use true randomness for the whole thing, and true randomness produces statistically valid results, if you use true randomness for assignment then you can't screw up the p-value test, and so there's no reason at all to even consider how to safely use a PRNG here, all that does is open the door to messing up.
The only known explanation of what's going on in quantum mechanics is a multiversal one^[1]. Using radioactive decay of an atom as an example: there are an uncountably infinite number of universes that are initially "fungible" (identical in every way), and over time the universes gradually differentiate themselves with the atom going from a non-decayed to decayed state, at different times in each universe. But you will be in all of those universes. So if you thought the atom would decay in, let's say 5 seconds, there would be some universes where you were right and some where you were wrong. That makes it impossible to ever make reliable specific predictions about when the atom will decay. So, in practice that just looks like perfect randomness.
^[1]: There are other interpretations, of course. And those other interpretations are equally explanatory. But they do not claim to be explanations of what is actually happening to unobserved quantum particles. There is also Bohmian mechanics, but I don't know how many people take it seriously.
What's bullshit about it? This is how TRNGs in security enclaves work. They collect entropy from the environment, and use that to continuously reseed a PRNG, which generates bits.
If you're talking "true" in the philosophical sense, that doesn't exist -- the whole concept of randomness relies on an oracle.
What PRNGs lack compared to TRNGs is security (i.e. preventing someone from being able to use past values to predict future values). It's not that they somehow produce statistically invalid results (e.g. they generate 3s more often than 2s or something). Unless they're very poorly constructed.
I don't think hardware random number generators are bullshit, but it's easy to overstate their importance. Outside of cryptography, there aren't a whole lot of cases that truly require that much care in how random numbers are generated. For the kind of examples the article opens with (web page A/B testing, clinical trials, etc.) you'll never have sample sizes large enough to justify worrying about the difference between a half-decent PRNG and a "true" random number generator.
"If N = 300, even a 256-bit seed arbitrarily precludes all but an unknown, haphazardly selected, non-random, and infinitesimally small fraction of permissible assignments. This introduces enormous bias into the assignment process and makes total nonsense of the p-value computed by a randomization test."
The first sentence is obviously true, but I'm going to need to see some evidence for "enormous bias" and "total nonsense". Let's leave aside lousy/little/badly-seeded PRNGs. Are there any non-cryptographic examples in which a well-designed PRNG with 256 bits of well-seeded random state produces results different enough from a TRNG to be visible to a user?
The argument against PRNGs this paper makes isn't that the PRNG produces results that can be distinguished from TRNG, but that the 256-bit seed deterministically chooses a single shuffling. If you need 300 bits to truly shuffle the assignment but you only have 256 bits, then that's a lot of potential assignments that can never actually happen. With this argument it doesn't matter what the PRNG is, the fact that it's deterministic is all that matters. And this invalidates the p-value because the p-value assumes that all possible assignments are equiprobable, when in fact a lot of possible assignments have a probability of zero.
I imagine you could change the p-value test to randomly sample assignments generated via the exact same process that was used to generate the assignment used by the experiment, and as you run more and more iterations of this the calculated p-value should converge to the correct value, but then the question becomes is the p-value calculated this way the same as the p-value you'd get if you actually went ahead and used equiprobable assignment to begin with?
Ultimately, this all comes down to the fact that it's not hard to use true randomness for the whole thing, and true randomness produces statistically valid results, if you use true randomness for assignment then you can't screw up the p-value test, and so there's no reason at all to even consider how to safely use a PRNG here, all that does is open the door to messing up.
Starts interesting, then veers into the usual "true random number" bullshit. Use radioactive decay as source of your random numbers!
How do we know it's truly random?
The only known explanation of what's going on in quantum mechanics is a multiversal one^[1]. Using radioactive decay of an atom as an example: there are an uncountably infinite number of universes that are initially "fungible" (identical in every way), and over time the universes gradually differentiate themselves with the atom going from a non-decayed to decayed state, at different times in each universe. But you will be in all of those universes. So if you thought the atom would decay in, let's say 5 seconds, there would be some universes where you were right and some where you were wrong. That makes it impossible to ever make reliable specific predictions about when the atom will decay. So, in practice that just looks like perfect randomness.
^[1]: There are other interpretations, of course. And those other interpretations are equally explanatory. But they do not claim to be explanations of what is actually happening to unobserved quantum particles. There is also Bohmian mechanics, but I don't know how many people take it seriously.
> usual "true random number" bullshit
What's bullshit about it? This is how TRNGs in security enclaves work. They collect entropy from the environment, and use that to continuously reseed a PRNG, which generates bits.
If you're talking "true" in the philosophical sense, that doesn't exist -- the whole concept of randomness relies on an oracle.
What PRNGs lack compared to TRNGs is security (i.e. preventing someone from being able to use past values to predict future values). It's not that they somehow produce statistically invalid results (e.g. they generate 3s more often than 2s or something). Unless they're very poorly constructed.
Maybe people have bad memories from linear congruential generators, these could go really bad (https://en.wikipedia.org/wiki/Marsaglia%27s_theorem)
I don't think hardware random number generators are bullshit, but it's easy to overstate their importance. Outside of cryptography, there aren't a whole lot of cases that truly require that much care in how random numbers are generated. For the kind of examples the article opens with (web page A/B testing, clinical trials, etc.) you'll never have sample sizes large enough to justify worrying about the difference between a half-decent PRNG and a "true" random number generator.