20151117, 22:06  #1 
Sep 2011
3×19 Posts 
Lattice Sieving Parameters
Now that I can generate a sublattice basis and reduce it, I think I'm ready to write a lattice siever. However, there seems to be more parameters I don't know how to set:
1) the sieving region and 2) the threshold for sieving point values before checking it for smoothness 3) how do I choose special q's? outside the factor base? 4) (I'll probably think of more as I go along) How do I set these parameters? Last fiddled with by paul0 on 20151117 at 22:09 
20151117, 22:50  #2  
Nov 2003
16444_{8} Posts 
Quote:
These depend on the size of the composite, the size of the factor base, and the number of large primes. Quote:
Quote:


20151118, 14:00  #3 
Sep 2011
3×19 Posts 
I was reading Franke's siever's readme, it uses this as bound: log(abs(polynomial value))lambda*log(factor base bound)
As for and , I think I have to experiment to find good values, as I doubt anyone has data for small composites. Last fiddled with by paul0 on 20151118 at 14:12 
20151118, 15:09  #4 
Just call me Henry
"David"
Sep 2007
Cambridge (GMT/BST)
2·2,909 Posts 
For I and J powers of 2 are often convenient.
Ideally you would select special qs from within and outside the factorbase. Yield decreases as the special q gets larger. Composite special qs have been experimented with. 
20151118, 20:43  #5 
Sep 2011
3×19 Posts 
EDIT: btw, my lattice siever is operational. I'll upload it to github when I'm satisfied with it :) Last fiddled with by paul0 on 20151118 at 21:31 
20151118, 23:17  #6  
Nov 2003
2^{2}·5·373 Posts 
Quote:
Are you handling skew? What method do you use to split the large primes? Last fiddled with by R.D. Silverman on 20151118 at 23:18 

20151120, 21:12  #7  
Sep 2011
71_{8} Posts 
Quote:
But for now, I'm trying to finish my undergraduate degree, I'm swamped. 

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