Question

A theoretical question not depending on implementation, how much of a decrease in performance is 1024bit vs 4096bit RSA?

Thanks

Answer 1

According to RSA key lengths:

[…]

With every doubling of the RSA key length, decryption is 6-7 times times slower.

Figure 1 shows how decryption time
increases with modulus length. The
timings were made on a 2GHz Pentium.

The key length also affects the speed
of encryption, but it’s usually the
speed of decryption that we’re more
concerned about because (a) that’s the
part that takes place on the server,
and (b) decryption is much much slower
than encryption, because the
decryption exponent is huge (whereas
the encryption exponent is typically
small).

If we use a 4096-bit modulus, it takes
around a second of CPU time to decrypt
a block of data. Even if you were able
to sacrifice this amount of CPU to
every log on, it leaves us with the
problem that an attacker can
effectively burn a second of CPU time
on our server by firing some random
data at it. With a 1024-bit key
length, decryption takes just 25
milliseconds; with suitable
restrictions on the rate of login
attemps (and thus decryptions) we
allow per remote client, protecting
against a “CPU burn” attack is more
feasible.