Lattice Sieving - where do I start?

paul0 · 2015-03-08, 21:52

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.

jasonp · 2015-03-09, 01:40

'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.

Dubslow · 2015-03-09, 03:04

How was the existing code written? By the same people who created the algorithm?

bsquared · 2015-03-09, 13:54

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.

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.

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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<A<43 -89<O<-88 7221₁₀ Posts	How was the existing code written? By the same people who created the algorithm?

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.