20150308, 21:52  #1 
Sep 2011
39_{16} 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. 
20150309, 01:40  #2 
Tribal Bullet
Oct 2004
2×29×61 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.

20150309, 03:04  #3 
Basketry That Evening!
"Bunslow the Bold"
Jun 2011
40<A<43 89<O<88
3·29·83 Posts 
How was the existing code written? By the same people who created the algorithm?

20150309, 13:54  #4 
"Ben"
Feb 2007
2·3^{2}·191 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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