The math behind the security gain by increasing the key length of an RSA key seems slighly more complicated then one might expect. Here is a (short) introductio

The math behind the security gain by increasing the key length of an RSA key seems slighly more complicated then one might expect. Here is a (short) introduction by the GnuPG folks: https://www.gnupg.org/faq/gnupg-faq.html#no_default_of_rsa4096 https://www.gnupg.org/faq/gnupg-faq.html#no_default_of_rsa40... Shorter version: RSA-4096 is roughly 28bits over RSA-2048 (112 vs 140 bits).