Re: Prime magnitude and keys...a ?

["Perry E. Metzger" <perry@imsi.com>]

Jim choate says:
> > I hope not.  If such a thing existed (if I understand your description
> > correctly) RSA could be cracked by a binary search of keyspace.  The
> > search would be O(log(n)), meaning it would be directly linear with
> > the number of bits in the key.
> > 
> Exactly.
> 
> If you (or anyone else comes across anything that even looks remotely 
> interesting would appreciate knowing about it).

I could believe some sort of amazing mathematical breakthrough that
produced a factoring algorithm that was polynomial in N. The notion
that one will show up thats not merely polynomial but actually
logarithmic in N is, I would say, in the "beyond pipe dream" state. I
might believe something like that showing up someday -- stranger
things have happened -- but I have an incredible amount of trouble
believing that one exists now and has merely been overlooked by people
smart enough to find an amazing result and too stupid to know what
their result implied.

Perry