[Cryptography] List of Proven Secure Ciphers / Hashes

[Jerry Leichter]

On Sep 15, 2014, at 5:18 PM, Bear <bear at sonic.net> 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?
Yes, but that's breaking RSA *for the private key*.  Suppose I have a method that decrypts one in 10 messages encrypted with a given private key, but *without* directly revealing the public key.  (No one can even suggest a way one might do this, but imagine such an algorithm exists.)  Can you turn that into a factoring algorithm?
                                                        -- Jerry

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