More on Bernstein's Number Field Sieve
Russ Nelson writes "Dan Bernstein has a response to Bernstein's
NFS analyzed by Lenstra and Shamir, entitled Circuits for integer
factorization. He notes that the issue of the cost of
factorization is still open, and that it may in fact be inexpensive to
factor 1024-bit keys. We don't know, and that's what his research is
intended to explore."
A quantum computer could do this in no time. Of course someone would have to build a really big one to do a 1024 bit number.