What's the state of the art in factorization?
thierry.moreau at connotech.com
Thu Apr 22 11:55:02 EDT 2010
Jerry Leichter wrote:
> On Apr 21, 2010, at 7:29 PM, Samuel Neves wrote:
>>> EC definitely has practical merit. Unfortunately the patent issues
>>> protocols using EC public keys are murky.
>>> Neither RSA nor EC come with complexity proofs.
>> While EC (by that I assume you mean ECDSA) does not have a formal
>> security proof, i.e., it is as hard as the EC discrete log, it it much
>> closer to one than RSA is to factoring. In particular, Pointcheval and
>> Stern, and later Brown come close to a formal proof for ECDSA ....
> It's perhaps worth pointing out again how little formal complexity
> proves tell you about security.
> Suppose we could show that RSA was as hard as factoring. So? Nothing
> is really known about how hard factoring is. At worst, it's NP-complete
> (though that's actually considered unlikely). But suppose *that* was in
> fact known to be the case. What would it tell us about the difficulty
> of factoring any particular product of two primes? Absolutely nothing.
> NP-completeness is a worst-case result. In principle, it could be the
> case that factoring is "easy" for numbers less than a billion bits long
> - it just becomes much harder "eventually". (I put "easy" in quotes
> because it's usually taken to mean "there's a poly-time algorithm", and
> that's a meaningless statement for a finite set of problems. *Every*
> finite set of problems has a O(1) time solution - just make a lookup
> There are some concrete complexity results - the kind of stuff Rogoway
> does, for example - but the ones I've seen tend to be in the block
> cipher/cryptographic hash function spaces. Does anyone one know of
> similar kinds of results for systems like RSA?
> -- Jerry
E.g. Koblitz, Neal; Menezes, Alfred, "Another Look at ``Provable
Security''", Cryptology ePrint Archive: Report 2004/152, available at
- Thierry Moreau
The Cryptography Mailing List
Unsubscribe by sending "unsubscribe cryptography" to majordomo at metzdowd.com
More information about the cryptography