On Sep 3, 2013, at 3:16 PM, Faré <fah...@gmail.com> wrote: > Can't you trivially transform a hash into a PRNG, a PRNG into a > cypher, and vice versa? No.

> hash->PRNG: append blocks that are digest (seed ++ counter ++ seed) Let H(X) = SHA-512(X) || SHA-512(X) where '||' is concatenation. Assuming SHA-512 is a cryptographically secure hash H trivially is as well. (Nothing in the definition of a cryptographic hash function says anything about minimality.) But H(X) is clearly not useful for producing a PRNG. If you think this is "obviously" wrong, consider instead: H1(X) = SHA-512(X) || SHA-512(SHA-512(X)) Could you determine, just from black-box access to H1, that it's equally bad as a PRNG? (You could certainly do it with about 2^256 calls to H1 with distinct inputs - by then you have a .5 chance of a duplicated top half of the output, almost certainly with a distinct bottom half. But that's a pretty serious bit of testing....) I don't actually know if there exists a construction of a PRNG from a cryptographically secure hash function. (You can build a MAC, but even that's not trivial; people tried all kinds of things that failed until the HMAC construction was proven correct.) -- Jerry _______________________________________________ The cryptography mailing list cryptography@metzdowd.com http://www.metzdowd.com/mailman/listinfo/cryptography