Hardware improvement will continue inexorably, but it is important to
realize that hardware improvements make RSA more secure, not less. This
is because a hardware improvement that allows an attacker to factor a
number two digits longer than before will at the same time allow a
legitimate RSA user to use a key dozens of digits longer than before; a
user can choose a new key a dozen digits longer than the old one
without any performance slowdown, yet a factoring attack will become
much more difficult. Thus although the hardware improvement does help
the attacker, it helps the legitimate user much more. This general rule
may fail in the sense that factoring may take place using fast machines
of the future, attacking RSA keys of the past; in this scenario, only
the attacker gets the advantage of the hardware improvement. This
consideration argues for using a larger key size today than one might
otherwise consider warranted. It also argues for replacing one's RSA
key with a longer key every few years, in order to take advantage of
the extra security offered by hardware improvements. This point holds
for other public-key systems as well.

Better factoring algorithms have been more help to the RSA attacker
than have hardware improvements. As the RSA system, and cryptography in
general, have attracted much attention, so has the factoring problem,
and many researchers have found new factoring methods or improved upon
others. This has made factoring easier, for numbers of any size and
irrespective of the speed of the hardware. However, factoring is still
a very difficult problem.

Overall, any recent decrease in security due to algorithm improvement can be offset by increasing the key size. In fact, between general computer hardware improvements and special-purpose RSA hardware improvements, increases in key size (maintaining a constant speed of RSA operations) have kept pace or exceeded increases in algorithm efficiency, resulting in no net loss of security. As long as hardware continues to improve at a faster rate than that at which the complexity of factoring algorithms decreases, the security of RSA will increase, assuming RSA users regularly increase their key size by appropriate amounts. The open question is how much faster factoring algorithms can get; there must be some intrinsic limit to factoring speed, but this limit remains unknown.