Quote:
Originally Posted by tetramur
A. Joux created in 2013 a new algorithm (index calculus, JIC) for finding a discrete logarithm with time complexity of L_{Q} (1/4, c) for c > 0. Can we find an algorithm for integer factorization with the same time complexity, using JIC?
If yes, then for RSA1024 it would be several billions times better than GNFS.

Joux's algorithm, as I understand it, is more like an analogue of SNFS than GNFS. Probably there is an associated factorization algorithm but surely it would not apply to RSA1024. My uneducated guess is that it would not apply to any numbers except those specially engineered for it. I'd love to hear from those more familiar with it.