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 R.D. Silverman 2005-01-27 16:07

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

 xilman 2005-01-27 17:44

[QUOTE=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[/QUOTE]A nice idea!

Paul

 akruppa 2005-01-27 20:38

I once mentioned the same idea to Peter Montgomery, he replied that a certain Bob Silverman :wink: 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 [I]one[/I] 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

 R.D. Silverman 2005-01-27 21:15

[QUOTE=akruppa]I once mentioned the same idea to Peter Montgomery, he replied that a certain Bob Silverman :wink: 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 [I]one[/I] 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[/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

 Jayder 2014-10-15 04:20

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?

 fivemack 2014-10-15 09:08

Yes: many-linear-sides factorisation has been implemented by the EPFL group and used to collect half a dozen largest-SNFS records in succession.

[url]http://eprint.iacr.org/2014/653.pdf[/url]

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