"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?

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lilyball an hour ago | parent [-]

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.

	▲	gzread 44 minutes ago \| parent [-]
		If you have 300 bits of shuffling entropy, you have a lot of potential assignments that can never happen because you won't test them before the universe runs out. No matter how you pick them. Of course a PRNG generates the same sequence every time with the same seed, but that's true of every RNG, even a TRNG where the "seed" is the current space and time coordinates. To get more results from the distribution you have to use more seeds. You can't just run an RNG once, get some value, and then declare the RNG is biased towards the value you got. That's not a useful definition of bias.