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
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