RSA-1024 has 309 decimal digits, or 1024 bits.[1]
So the relative increase in size in bits is 1024/762, roughly a 34% increase, a factor of about 1.34.
Currently the complexity of the NFS is thought to be:
exp( c (ln n)^(1/3) (ln ln n)^(2/3) ) [2]
where c is about 2. That means that RSA-1024 (1024 bits) will take about 18% to 19% longer than RSA-230 (762 bits).[3]
[0] https://en.wikipedia.org/wiki/RSA_numbers#RSA-230
[1] https://en.wikipedia.org/wiki/RSA_numbers#RSA-1024
[2] https://en.wikipedia.org/wiki/General_number_field_sieve
[3] Program:
#!/usr/bin/python
from math import *
ln = log
def complexity( n ):
return exp( \
(64./9)**(1./3) * \
(ln(n)**(1./3)) * \
(ln(ln(n))**(2./3)) \
)
print complexity(762)
print complexity(1024)
print complexity(1024)/complexity(762)