An encrypted hard drive is EXACTLY uniformly distributed random bytes if you do not know the encryption key. No one would be able to tell the difference between a drive that is just purely random numbers or is actually filled with content. (Of course excluding the usually intentionally added readable header)
If this was not the case, the encryption would be broken, and most everyone agrees that good encryption does exist.
The "quality of the probability calculations" as you put it is 100% in this case and any less would be a huge deal (as in - breaks all of the internet).
So, now you just take those same random bytes and use them as the seed for your LLM token choices. The output has the _cryptographically_ proven exact same quality as if you were using a true RNG (which you likely weren't using anyways).
You just need to know your LLM distribution and the encryption key, then with each new token you exponentially increase the chance of knowing whether it fits your encryption key. Without actually affecting the token choice in a perceivable manner.
> choosing different words that it otherwise would
The "that is otherwise would" is carrying all the weight here. "Otherwise" is sampling from a distribution. You just sample from the same distribution but with a cryptographically secure, seeded RNG. https://en.wikipedia.org/wiki/Cryptographically_secure_pseud...
"Knowing the LLM distribution" seems to me like the only hard part because you don't know the context of any random snippet.