Two tidbits of potential interest

[M.B.Jr.]

Hi Werner,


On Fri, Sep 25, 2009 at 6:19 AM, Werner Koch <wk at gnupg.org> wrote:
> On Thu, 24 Sep 2009 21:13, marcio.barbado at gmail.com said:
>
>> Is this a generic asymmetric premise?
>> I mean: is it valid both to the (computational) Mathematics behind
>> OpenPGP's and X.509's public keys' integers?
>
> Yes.  All real world asymmetric algorithms are build on a hard so solve
> computional problem.  Factoring is such a hard problem and the RSA
> algorithm is based on it.  Another widely used hard problem is solving
> the discrete logarithm, the DSA and Elgamal algorithms are based on it.
>


so, focusing on key pair generation, one could state RSA keys are
built upon the product of large primes, which would put factoring as
the main problem to be solved;

whereas Elgamal keys are more complex than that, once it involves
primes under the discrete logarithms' context.

And as a conclusion, Elgamal problems would be harder to solve. Is it correct?


Regards,





Marcio Barbado, Jr.