I'll take a crack at answering this one; perhaps others will also chime in. "Anyone who considers arithmetical methods of producing random digits is, of course, in a state of sin." -- von Neumann You & von Neumann are right, in theory. However, all "true"/"hardware" random number generators ("TRNG"'s) are subject to measurable biases & other measurement errors, which produce various measurable correlations in their outputs. Even TRNG's need to be "whitened up a bit" by using various crypto functions -- e.g., crypto hash functions, AES boxes, etc. -- which clean up the statistics of their outputs. There have been a few recent talks about this very subject, and -- at least for the case of initializing the crypto packages of networked computers -- a TRNG is useful for producing the initial "seed", but from then on, a PRNG is a lot faster, and nowadays more reliable & trustworthy than a TRNG. And *trust* is the hardest thing to accept in a TRNG, because there's essentially no way to test it! Since you can store >500 GBytes in a chip the size of your pinky fingernail, and since such a chip could easily fit into the enclosure of most TRNG's, I know of no "black box" test to validate your TRNG. I purchased a $35 USB TRNG which utilizes electronic noise to produce a few bits, but can't produce bits fast enough for anything other than seeding a PRNG every once in a while. At 12:48 PM 3/19/2016, Eugene Salamin via math-fun wrote:
For cryptosecure, I don't see how you can do better than a physical noise or quantum source.
Why do computer science people so disdain physical RNG's; it is because they don't involve fun things like algorithm analysis?
This annoys me so much that I've made it into a litmus test.
When I pick up a book that discusses random number generation, I immediately look to see if physical RNG's are discussed, not necessarily praised, and if not, I ignore the entire book.
Now, there is a place for pseudo-RNG's, and that is if the same sequence of random numbers must be generated again since then the initial seed can represent the entire lengthy sequence.