[Cryptography] List of Proven Secure Ciphers / Hashes

[Arnold Reinhold]

On Wed, 3 Sep 2014 12:17 Lodewijk andr? de la porte wrote:

> asserting P!=NP is a prerequisite for all crypto, but it isn't proven.

There is no reason to think P!=NP is a prerequisite for crypto. In fact AES-256 is in complexity class C, as it can be solved in constant time, namely no more than 2^256 steps. The same is true for all block ciphers in use today. Of course, testing 2^256 possibilities not practical to do, but it is still constant time.

> 
> If you do assert P!=NP then you're still stuck without method to determine
> if, for operation F, there exists no method that inverts F that's in P. If
> you'd have the proof for P!=NP you might be able to extend that proof,
> somehow relate to it.

Even if an algorithm is in P, it is not necessarily tractable. A cipher whose difficulty grows as L^100, where L is the key length, could be perfectly suitable. 

Here is a link to a couple of sci.crypt posts on the subject from 1995: http://theworld.com/~reinhold/p=np.txt

Arnold Reinhold