mersenneforum.org Lattice Sieving - where do I start?
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 2015-03-08, 21:52 #1 paul0   Sep 2011 3916 Posts Lattice Sieving - where do I start? My python NFS implementation is now up and working, and mostly cleaned. I currently use line sieving, now I want to take it up a notch with lattice sieving. But where do I start? Is there an explicit example (like Briggs') I can work with? The papers about lattice sieving are not accessible to me as I do not have a good understanding of lattices. There seems to be two definitions of lattices in wikipedia: http://en.wikipedia.org/wiki/Lattice_(group) and http://en.wikipedia.org/wiki/Lattice_(order). Which one is applicable? Also, please recommend books regarding lattices relevant to NFS. I've gotten this far, lattices should be doable, eventually.
 2015-03-09, 01:40 #2 jasonp Tribal Bullet     Oct 2004 5×23×31 Posts 'The Development of the Number Field Sieve' contains a paper that gives a few details of lattice sieving, but it's not enough to implement the algorithm. I think you're going to have to look at existing code to get all the details you need.
 2015-03-09, 03:04 #3 Dubslow Basketry That Evening!     "Bunslow the Bold" Jun 2011 40
 2015-03-09, 13:54 #4 bsquared     "Ben" Feb 2007 22·941 Posts There is the paper by Franke and Kleinjung: "Continued Fractions and Lattice Sieving". Probably also not enough detail to complete an implementation but it is the best (only?) reference out there for their algorithm that I know of, aside from their code.

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