[Cryptography] List of Proven Secure Ciphers / Hashes

[Bear]

On Mon, 2014-09-15 at 13:18 -0400, Jerry Leichter wrote:

> No.  RSA is no harder than factoring (we still have no proof that it's *as hard as factoring*).  

Wait.  If I have both members of an RSA key pair, can't I do 
Euclidean reduction (which is only O(logN)) to find the factors
of the key modulus?

And isn't that why RSA systems where a common modulus is shared
among more than one keypair are considered insecure?  

In short, if we can use a solution to RSA to perform factoring, 
then isn't that a proof that factoring is no harder than RSA?

				Bear