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Old 2019-01-22, 01:38   #4
CRGreathouse's Avatar
Aug 2006

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Originally Posted by tetramur View Post
A. Joux created in 2013 a new algorithm (index calculus, JIC) for finding a discrete logarithm with time complexity of LQ (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 RSA-1024 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 RSA-1024. 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.
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