I'd be careful if I were you. Cryptography and cryptographers are an odd bunch. "Never" literally means never, while in your comment "never" means not in our life times, or a thousand, or billions of years. In case of infinite time, 512-bit RNG'ed numbers have to repeat at some point in time.
You may consider this pedantism, but it's this pedantism and conservativeness that calls AES broken today.
I think, from a practical standpoint, if "never" means "never before the heat death of the universe" then I'd be pretty satisfied. Pure math is truly wonderful (I love theoretical stuff) but at some point it does have to shift back to the practical realm.
I agree with you. I was just informing the parent poster how differently cryptographers see the world as compared to us normal people.
Although, in some respects, I do get where they're coming from. New algorithms and computing paradigms develop that make the previous one broken. I'm just guessing here, but it maybe possible that probabilistic computers and awesome algorithms a few decades down the line are able to recover states of a CSPRNG by applying statistical techniques. Obviously, I'm way over my head here but this is a possibility.
If you say that the OP was talking about TRNGs then all bets are off. It could so happen that two consecutive 512-bits are exactly the same. The probability is extremely low (birthday low) but since it's a TRNG there's still a chance that it will happen.
There is one thing that could never happen. Something that's mathematically perfect fits that criteria - the One Time Pad. Even at actual infinite available time frames i.e. you travelling at the speed of light, with quantum computer on board your ship powered by the unobtainium drive, even with that sort of time frame, you shall never be able to decrypt the correct message.
> Something that's mathematically perfect fits that criteria.
No, it doesn't. A one-time pad still needs a source of randomness, and a guarantee no reuse. How certain are you that you don't have a backdoored RNG, or initialization vector reuse?
Or, for a fully general argument, how certain are you that we're not living in a computer simulation, where the Dark Lords of the Matrix can just lookup their logs to see what random values were generated for your one-time pad? Or if we go to that extreme, how can you be absolutely certain of the truth of anything - including mathematics - if said Dark Lords could be messing with our brain and memories?
Or more mundanely, how about this: a flurry of cosmic rays strike the RAM containing the message and by random chance flip the same bits that were set in the on-time pad. Tada, message decrypted.
I'm pretty damn certain none of those hypotheticals are the are even remotely worth worrying about. I may even be more than P(1 - 2^-512) certain that they are false. But it's still merely a very high, finite probability. P(0) or P(1) don't exist - you can approach them, but you can't ever reach them.
Any idea, no matter how crazy or out of place with our understanding of the universe could happen, at least in principle. Therefore if we want “never” have a meaning at all, we need to set an cutoff point where we stop caring. Obviously an appropriate value depends on the situation, but in this case I'm pretty sure that an appropriate cutoff is somewhere up of P(2^-512).
You may consider this pedantism, but it's this pedantism and conservativeness that calls AES broken today.