On Jan 8, 8:46 am, mstem...@walkabout.empros.com (Michael Stemper) wrote: > In article <kc6gg1$au...@dont-email.me>, David Bernier <david...@videotron.ca> writes: > >On 01/04/2013 12:01 AM, JT wrote: > >> Does the RSA challenges have a given time complexity of factoring the > >> primeproduct, or did they have one that changed during resent years? > > >The RSA challenge numbers are still available somewhere. > >The contests for prize money has been discontinued. > > >I think many remain unfactored, as far as the general > >public knows, i.e. outside cryptologic agencies and > >government cipher schools. > > >They would deliberately choose n = p*q, p, q odd primes > >with the digit length of p and q being about half that > >of the composite number `n'. >
Not 'about half'. Exactly half.
> I'm surpised. I would have expected them to pick p and q with significantly > different lengths. Doesn't a simplistic attack like Fermat's method get > much easier when p and q are close in magnitude? >
I suggest that you compute the effort needed for a Fermat attack for N = pq, N is 1024 bits, and p and q are identical in (say) the first 3 digits.