The best size for an RSA modulus depends on one's security needs. The larger the modulus, the greater the security, but also the slower the RSA operations. One should choose a modulus length upon consideration, first, of one's security needs, such as the value of the protected data and how long it needs to be protected, and, second, of how powerful one's potential enemies are.
Odlyzko's paper considers the security of RSA key sizes based on factoring techniques available in 1995 and the ability to tap large computational resources via computer networks. A specific assessment of the security of 512-bit RSA keys shows that one may be factored for less than $1,000,000 in cost and eight months of effort in 1997 [Rob95d]. It is believed that 512-bit keys no longer provide sufficient security with the advent of new factoring algorithms and distributed computing. Such keys should not be used after 1997 or 1998. Recommended key sizes are now 768 bits for personal use, 1024 bits for corporate use, and 2048 bits for extremely valuable keys like the key pair of a certifying authority. A 768-bit key is expected to be secure until at least the year 2004.