mersenneforum.org  

Go Back   mersenneforum.org > Search Forums

Showing results 1 to 15 of 15
Search took 0.01 seconds.
Search: Posts Made By: Ilya Gazman
Forum: Factoring 2020-09-15, 03:11
Replies: 17
Views: 5,546
Posted By Ilya Gazman
This is how I see it. [$]Q(x)[/$] is smooth iff...

This is how I see it. [$]Q(x)[/$] is smooth iff [$]b+dx^2[/$] is smooth, [$]ex-c[/$] is smooth and [$]ex+c[/$] is smooth. Because if just two or one of them is smooth, it cannot be used for...
Forum: Factoring 2020-09-09, 02:35
Replies: 17
Views: 5,546
Posted By Ilya Gazman
Looks like those methods didn't work well. ...

Looks like those methods didn't work well.

What gave me the best results so far is a brute force with primes starting at [$]c\approx \root 6\of{N}[/$]. I pick a prime of that size, then calculate...
Forum: Factoring 2020-09-07, 23:44
Replies: 17
Views: 5,546
Posted By Ilya Gazman
Oops looks like I got it a bit wrong. This is...

Oops looks like I got it a bit wrong. This is what I meant.

Let [$]f(c) = 2N-c^2[/$]
Let [$]g(x)=f(\sqrt{2N-pg}+px)[/$]

[$$]g(x)=2N-(\sqrt{2N-pg}+px)^2=p(g-2x\sqrt{2N-pg} - px^2)[/$$]
Forum: Factoring 2020-09-07, 17:50
Replies: 17
Views: 5,546
Posted By Ilya Gazman
Yes, fixing is the way to go ;) Cross my...

Yes, fixing is the way to go ;)

Cross my previous suggestion, I got a better idea.

Let's say our sieving bound is $m$, then we can pick primes near [$]\frac{n^{\frac{1}{3}}}{m}[/$], let say...
Forum: Factoring 2020-09-07, 14:38
Replies: 17
Views: 5,546
Posted By Ilya Gazman
Nice!!! I made some progress as well....

Nice!!!

I made some progress as well. [$]f[/$], 200 bits in 88 milliseconds, but there is a catch ;)
[$]c[/$] comes to be of the same size as [$]f[/$]

Here is the idea:

Pick two big primes...
Forum: Factoring 2020-09-06, 18:08
Replies: 17
Views: 5,546
Posted By Ilya Gazman
lol, didn't realize you would like to run it. It...

lol, didn't realize you would like to run it. It was more like a reference to show you the idea.

Here is the full source code: https://github.com/gazman-sdk/quadratic-sieve-Java/tree/just_for_fun
Forum: Factoring 2020-09-06, 13:08
Replies: 17
Views: 5,546
Posted By Ilya Gazman
Actually, I want [$]a*b[/$] to be near [$]2N[/$]....

Actually, I want [$]a*b[/$] to be near [$]2N[/$]. Because then [$]c[/$] becomes neglectable, since [$]ab-2N = -c^2[/$].

Maybe the definition of [$]ad=e^2[/$] is a bit confusing. It implies that...
Forum: Factoring 2020-09-04, 15:41
Replies: 17
Views: 5,546
Posted By Ilya Gazman
Smile QS in sub-quadratic space

LaurV, there is more to it. Actually I just got an idea of how to make it sub-quadratic, of the size of [$] N^{\frac{1}{3}} [/$].

Let me start fresh, I try to add some more deatails.
...
Forum: Factoring 2020-09-03, 03:11
Replies: 17
Views: 5,546
Posted By Ilya Gazman
Talking Quadratic Sieve improvement idea

Hey, I got an idea for improving QS, please tell me if you already heard it and what do you think about it.

Let [$]N[/$] be the number we wish to factor.

We can look at the congruence of...
Forum: Factoring 2020-08-26, 21:41
Replies: 6
Views: 3,933
Posted By Ilya Gazman
Nice! This actually helped a bit. I rewrote the...

Nice! This actually helped a bit. I rewrote the update function to only use local variables.

public void update(byte[] logs) {
int length = logs.length;
int currentPosition =...
Forum: Factoring 2020-08-26, 21:36
Replies: 6
Views: 3,933
Posted By Ilya Gazman
Yeah it is maintained by the Wheel class, each...

Yeah it is maintained by the Wheel class, each prime has two Wheel instances that track the current position in the logs array.

My sieving bound M is represented by an array of the size S where...
Forum: Factoring 2020-08-26, 19:30
Replies: 6
Views: 3,933
Posted By Ilya Gazman
Cool How to optimize the sieving stage of QS?

My latest version (https://github.com/gazman-sdk/quadratic-sieve-Java) of QS is moving in fifth of the speed of light as it only 5 times slower than Tills version now, lol.

40% of my sieving code...
Forum: Factoring 2020-08-22, 17:14
Replies: 3
Views: 3,873
Posted By Ilya Gazman
Those are excellent points! I also sow your Java...

Those are excellent points! I also sow your Java implementation, it's about 15 times faster then what I got so far ;)

Here are a few other ideas:

1. Select the the sieving bound `m` to be the...
Forum: Factoring 2020-08-20, 18:08
Replies: 3
Views: 3,873
Posted By Ilya Gazman
Quadratic Sieve optimizations

Please share the quadratic sieve optimizations you know, and remember, there is no optimization to small if it makes the code run faster ;)

Here are some examples to get you started:

1. Big...
Forum: Factoring 2016-02-15, 09:11
Replies: 3
Views: 3,083
Posted By Ilya Gazman
Smile Java Quadratic Sieve

Hi,

I am developer and I got pure math knowledge, but I heard about the Integer Factorization problem and got interested.
I spent the last few months trying to understand it and implemented the...
Showing results 1 to 15 of 15

 
All times are UTC. The time now is 02:52.

Mon Apr 12 02:52:55 UTC 2021 up 3 days, 21:33, 1 user, load averages: 1.80, 1.87, 1.87

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2021, Jelsoft Enterprises Ltd.

This forum has received and complied with 0 (zero) government requests for information.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation.
A copy of the license is included in the FAQ.