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 2005-01-27, 16:07 #1 R.D. Silverman     Nov 2003 22×5×373 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
2005-01-27, 17:44   #2
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May 2003
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Quote:
 Originally Posted by R.D. Silverman 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
A nice idea!

I'll think about it.

Paul

 2005-01-27, 20:38 #3 akruppa     "Nancy" Aug 2002 Alexandria 1001101000112 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 many-numbers-at-once 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 left-to-right as right-to-left), 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
2005-01-27, 21:15   #4
R.D. Silverman

Nov 2003

22·5·373 Posts

Quote:
 Originally Posted by akruppa 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 many-numbers-at-once 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 left-to-right as right-to-left), 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

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

 2014-10-15, 04:20 #5 Jayder     Dec 2012 1000101102 Posts I hope it is alright to bump this 9-year-old topic. I am wondering if the situation is any different, here in the future. Is it?
 2014-10-15, 09:08 #6 fivemack (loop (#_fork))     Feb 2006 Cambridge, England 13·491 Posts Yes: many-linear-sides factorisation has been implemented by the EPFL group and used to collect half a dozen largest-SNFS records in succession. http://eprint.iacr.org/2014/653.pdf

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