How quickly can cryptographically secure pseudorandom numbers be generated? Probably something parallel that runs on GPU.

Assume that we are consuming such a large quantity of random numbers that statistical irregularities that show up after 2^64 samples will become visible. This means we cannot just use AES in counter mode to generate a random stream.

This seems useful only as a curiosity: what could need so much cryptographic randomness so quickly? Monte Carlo simulations do not require cryptographic security. What could even consume numbers that quickly?

Maybe high-bandwidth encrypted communications of data at rest. Other than data at rest, it's hard to imagine data being produced so quickly as to require an extremely fast cPRNG to encrypt it. But even data at rest is limited by disk bandwidth.

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