[QUOTE=jasonp]Version 0.88 is now available.[/QUOTE]
I've had to repost 0.88 to include a fix for a buffer overflow
that I inadvertently introduced at the last minute.

Sorry 'bout that,
jasonp

[QUOTE=jasonp]I've had to repost 0.88 to include a fix for a buffer overflow
that I inadvertently introduced at the last minute.

Sorry 'bout that,
jasonp[/QUOTE]

os 0.88 faster (or equal) in speed than 0.87 for Athlons?

Luigi

[QUOTE=ET_]os 0.88 faster (or equal) in speed than 0.87 for Athlons?
[/QUOTE]
I've added a few optimizations that improve the speed for moderate-
size factorizations; my test c70 is ~10% faster. Otherwise for bigger
jobs the speed on the athlon should be the same (or <1% better).

jasonp

If you are still looking for suggestions, how about this.
Relax the restriction on Quadratic Polynomials and allow Cubic, Quartic, and Quintic polynomials.

[QUOTE=Joe O]If you are still looking for suggestions, how about this.
Relax the restriction on Quadratic Polynomials and allow Cubic, Quartic, and Quintic polynomials.[/QUOTE]
Is that even practical with the quadratic sieve? Yes, the name should change, but I thought the quadratic version has a big advantage because modular square roots are easy compared to higher-order roots.

If a quintic version of QS is feasible, why bother with NFS, which also typically uses 5th-order polynomials?

jasonp

[QUOTE=Joe O]If you are still looking for suggestions, how about this.
Relax the restriction on Quadratic Polynomials and allow Cubic, Quartic, and Quintic polynomials.[/QUOTE]

The suggestion "isn't even nonsense". It is totally devoid of meaning.

It shows a total lack of understanding of the algorithm. The so called
"restriction on Quadratic polynomials" does not exist. There is no restriction,
per se. Please explain how you think relaxing this so-called restriction would
work, or how it would be faster.

(1) Suppose, as per the suggest we were somehow able to use general
cubic or higher degree polynomials. Explain how to construct such polynomials
so that when evaluated, they yield squares modulo the number being factored.
If you argue that instead of finding A^2 = B^2 mod N and computing (A+B,N),
we find A^3 = B^3 mod N, explain how to do so (non-trivially) when one of
the factors of N is -1 mod 6 instead of +1 mod 6.


(2) Suppose we choose a cubic polynomial f(x) with M = floor(N^1/3).
I suggest that you look at the size of f(M). QS produces values that are
about k * N^1/2 where k is the sieve length. This would produce values
that are near k*N^2/3. Higher degrees have similar problems.

QS produces values Q such that Q^2 mod N is *small*. Explain how to do
this with higher degree polynomials. It can be done for cubic polynomials
when N has certain very restricted forms, but the algorithm has turned out to
be totally impractical.


The Number Field Sieve does use higher degree polynomials, but uses TWO
different polynomials (whereas QS uses one) and needs to find TWO smooth
norms per relation (whereas QS only needs one).

SIQS Centennial
 

Jason,

FWIW, this evening, msieve finished factoring its 100th cyclotomic
number which has been submitted to
Factorizations of Cyclotomic Numbers
[url]http://www.asahi-net.or.jp/~KC2H-MSM/cn/index.htm[/url]

Excellent software!!! :bow:

Tom

[QUOTE=error404]Jason,

FWIW, this evening, msieve finished factoring its 100th cyclotomic
number which has been submitted to
Factorizations of Cyclotomic Numbers
[url]http://www.asahi-net.or.jp/~KC2H-MSM/cn/index.htm[/url]

Excellent software!!! :bow:

Tom[/QUOTE]

Probably a few more.

I've been cleaning up all [i]small[/i] composites below 90 digits using msieve.

There are still about 150 composite with less then 100 digits left in this tables, so plenty of [i]easy[/i] work todo.

[QUOTE=smh]Probably a few more.

I've been cleaning up all [i]small[/i] composites below 90 digits using msieve.

There are still about 150 composite with less then 100 digits left in this tables, so plenty of [i]easy[/i] work todo.[/QUOTE]

I myself did five :-)

Luigi

[QUOTE=ET_]I myself did five :-)

Luigi[/QUOTE]
Ehh, weren't that partition numbers?

[QUOTE=error404]
FWIW, this evening, msieve finished factoring its 100th cyclotomic
number which has been submitted to
Factorizations of Cyclotomic Numbers
[url]http://www.asahi-net.or.jp/~KC2H-MSM/cn/index.htm[/url]

Excellent software!!!
[/QUOTE][QUOTE=smh]Probably a few more.

I've been cleaning up all [i]small[/i] composites below 90 digits using msieve.

There are still about 150 composite with less then 100 digits left in this tables, so plenty of [i]easy[/i] work todo.[/QUOTE]
It makes my day to see Real Work getting done!

Are you guys coordinating with each other to avoid duplicate work?

jasonp