[Cryptography] Why is ECC secure?

[Viktor Dukhovni]

On Thu, Aug 13, 2015 at 07:57:32PM -0700, Ray Dillinger wrote:

> > When it comes to cryptanalysis, the real question is the amount of work
> > that has gone into breaking things like the RSA trapdoor function as
> > opposed to just "prime numbers" or factoring. Both ECC and RSA use prime
> > numbers, and the discrete logarithm problem has probably received a similar
> > amount of study to factoring (and indeed there are spooky similarities
> > between these problems too).
> 
> One thing to point out is that RSA is at least as hard as factoring
> because if you can solve RSA, you can use the solution to factor its
> modulus.  IOW, there can be no shortcut that makes it easier than
> factoring.

That's backwards, factoring trivially solves RSA.  I'm not aware
of any proof that solving RSA necessarily factors the modulus.
However, there are partial results in that direction:

    https://www.iacr.org/archive/eurocrypt2009/54790037/54790037.pdf

-- 
	Viktor.