20050127, 16:07  #1 
Nov 2003
1C40_{16} Posts 
Simultaneous Factoring
Just a thought.
I see that NFSNET is now doing 5,307+, having just sieved 5,307. I not that it is possible to do BOTH of them at the same time and save 25% of the run time. For each number, we need to sieve the norms of two polynomials. This is a total of "four sieve procedures" for the two numbers. But one of the sieves is the SAME for both numbers. The linear polynomial is the same for both numbers. At the cost of some additional memory it should be possible to do both numbers at once. You would need to sieve the linear polynomial only once. This would save 25%. Perhaps NFSNET should look into this for their siever. Bob 
20050127, 17:44  #2  
Bamboozled!
"πΊππ·π·π"
May 2003
Down not across
23723_{8} Posts 
Quote:
I'll think about it. Paul 

20050127, 20:38  #3 
"Nancy"
Aug 2002
Alexandria
4640_{8} Posts 
I once mentioned the same idea to Peter Montgomery, he replied that a certain Bob Silverman mentioned it almost ten years earlier. He also told me that this idea is not implemented in the CWI siever, however multiple polynomial NFS for factoring one number is. Maybe the code could be adapted to the manynumbersatonce idea.
He also mentioned another nice trick to use symmetry in the algebraic polynomial: for even polynomials, F(a,b) is smooth iff F(a,b) is, so the algebraic side only needs to sieve nonnegative values. For symmetric polynomials (same coefficients lefttoright as righttoleft), F(a,b) is smooth iff F(b,a) is, though this symmetry seems harder to exploit. He said these tricks are not implemented in the CWI siever, either. Alex 
20050127, 21:15  #4  
Nov 2003
2^{6}·113 Posts 
Quote:
Hi, I was aware of the symmetry tricks as well; I had even suggested one or two to Peter some time ago. I looked into implementing one of the simpler ones (you discussed it above) and concluded that you needed too much memory and saving of state information to be effective. Bob 

20141015, 04:20  #5 
Dec 2012
426_{8} Posts 
I hope it is alright to bump this 9yearold topic. I am wondering if the situation is any different, here in the future. Is it?

20141015, 09:08  #6 
(loop (#_fork))
Feb 2006
Cambridge, England
6,323 Posts 
Yes: manylinearsides factorisation has been implemented by the EPFL group and used to collect half a dozen largestSNFS records in succession.
http://eprint.iacr.org/2014/653.pdf 
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