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 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 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 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 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 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...
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