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Old 2015-03-08, 21:52   #1
Sep 2011

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Default 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: and 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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Old 2015-03-09, 01:40   #2
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Oct 2004

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'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.
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Old 2015-03-09, 03:04   #3
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Jun 2011
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How was the existing code written? By the same people who created the algorithm?
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Old 2015-03-09, 13:54   #4
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Feb 2007

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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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