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Search: Posts Made By: ThiloHarich
Forum: Factoring 2021-03-05, 09:46
Replies: 13
Views: 3,216
Posted By ThiloHarich
Somebody tried to implement it ...

Somebody tried to implement it

https://github.com/lducas/SchnorrGate
Forum: Factoring 2021-03-04, 15:20
Replies: 13
Views: 3,216
Posted By ThiloHarich
There is a german statement on heise.de ...

There is a german statement on heise.de

https://www.heise.de/news/RSA-zerstoert-Wohl-eher-nicht-5071387.html
Forum: Factoring 2019-10-16, 14:31
Replies: 18
Views: 3,586
Posted By ThiloHarich
I was referring to this hint. Of coarse Fermat...

I was referring to this hint. Of coarse Fermat works only if both factors were really close.

Ahh you check 10^14 a = sqrt(n) + a' in the area sqrt(n) in 1 hour -> quite impressive.
Forum: Factoring 2019-10-16, 11:34
Replies: 18
Views: 3,586
Posted By ThiloHarich
There are some improvements to Fermat's method. ...

There are some improvements to Fermat's method.
See https://en.wikipedia.org/wiki/Fermat%27s_factorization_method -> Sieve improvement.
You can really cut down the candidates to check by applying a...
Forum: Factoring 2019-09-23, 14:16
Replies: 2
Views: 924
Posted By ThiloHarich
RSA Hacking + msieve on heise.de

Here https://www.heise.de/security/meldung/l-f-Crypto-Startup-knackt-angeblich-RSA-und-wird-zur-Lachnummer-4536268.html is an german article on a startup "Crown Sterling" which is cracking 256-Bit...
Forum: Factoring 2019-04-08, 09:27
Replies: 55
Views: 5,661
Posted By ThiloHarich
- Choosing the right m depends on the...

- Choosing the right m depends on the implementation.

Til and me used some adjustments/improvements for odd multipliers m -> in our algorithm the good multipliers are not only even, best...
Forum: Factoring 2019-04-07, 16:35
Replies: 55
Views: 5,661
Posted By ThiloHarich
Sorry. The sum of all divisors - not only...

Sorry.

The sum of all divisors - not only the prime divisors I thought of - can be higher then the number itself. So I misinterpreted your model.

So yes abundant numbers...
Forum: Factoring 2019-04-07, 15:22
Replies: 55
Views: 5,661
Posted By ThiloHarich
You can create the list of good multipliers "k"...

You can create the list of good multipliers "k" on your own easily and check if the numbers fit to your model. I can also send you a txt file with all the k in proper order if you want to.

I try...
Forum: Factoring 2019-04-07, 11:20
Replies: 55
Views: 5,661
Posted By ThiloHarich
Hmm. why should my model be very rough? ...

Hmm.

why should my model be very rough?

I have trained it with 30 million Factorizations on hard numbers (no factor below n^1/3). For different fixed multipliers m and collection good k = k' *...
Forum: Factoring 2019-04-05, 18:36
Replies: 55
Views: 5,661
Posted By ThiloHarich
Correcting b) There are only c*n^1/3...

Correcting
b)
There are only c*n^1/3 multipliers. c=1 for Lehman. c pretty low for Hart.

What I mean is we can find the good multipliers and just store them in an array. - > no complicated...
Forum: Factoring 2019-04-05, 13:57
Replies: 55
Views: 5,661
Posted By ThiloHarich
a) I have also done some investigations in...

a)
I have also done some investigations in optimal multipliers.
One way was just to factor many, many numbers and to record the multipliers which lead to a factorization. It turned out that some...
Forum: Factoring 2019-03-16, 13:23
Replies: 9
Views: 2,493
Posted By ThiloHarich
Hello, welcome to the forum. The pollard rho...

Hello, welcome to the forum.

The pollard rho can be tweaked to work nicely for Fermat numbers.
The Funktion to generate the numbers has to be modified here.
With this modification it was...
Forum: Factoring 2019-02-15, 20:46
Replies: 29
Views: 4,805
Posted By ThiloHarich
brief java implementation

Here is a brief java implementation of our last version.
It works fine for odd numbers up to 40 bits.
For simplicity we have no primes table so it does not works super fast for numbers with factors...
Forum: Factoring 2019-01-21, 08:04
Replies: 29
Views: 4,805
Posted By ThiloHarich
Has anybody tried the Trial Division algorithm :...

Has anybody tried the Trial Division algorithm : https://github.com/TilmanNeumann/java-math-library/blob/master/src/de/tilman_neumann/jml/factor/tdiv/TDiv63Inverse.java ?

The idea is pretty...
Forum: Factoring 2019-01-19, 14:58
Replies: 29
Views: 4,805
Posted By ThiloHarich
Lehman suggest to use multipliers for k. His...

Lehman suggest to use multipliers for k.
His argument was that if a/b is closest to the ratio of the divisors of n then using k = a*b*k' is looking in the area.

But there is an other reason. If...
Forum: Factoring 2019-01-18, 23:13
Replies: 29
Views: 4,805
Posted By ThiloHarich
I tried to give the mod 255 Mersenne argument in...

I tried to give the mod 255 Mersenne argument in the link a try in java.
since 255 = 3 * 5 * 17 this should at least check if the number is a square mod 5*17, since in the Lehman_Fast code we use a...
Forum: Factoring 2019-01-18, 09:20
Replies: 29
Views: 4,805
Posted By ThiloHarich
Great that we have similar performance results...

Great that we have similar performance results also in C.

Since there are still many things I have not understood I think the Lehman algorithm has even more potential.

We have discovered some...
Forum: Factoring 2019-01-15, 23:17
Replies: 29
Views: 4,805
Posted By ThiloHarich
@bsquared We did several approaches to get around...

@bsquared We did several approaches to get around always calculating the square root.

We had several checks for certain mods in the code, but they slowed down the whole algorithm.

We only...
Forum: Factoring 2017-02-28, 12:33
Replies: 15
Views: 3,273
Posted By ThiloHarich
Yes my method is not intended to be fast for...

Yes my method is not intended to be fast for bigger Inputs.

It can also be used with multipliers, like the Lehman method.
I have also implemented this.
Unfortunately if the multipliers are...
Forum: Factoring 2017-02-26, 20:16
Replies: 15
Views: 3,273
Posted By ThiloHarich
A simple idea for factoring numbers

While palying with the fremat equation i had an idea which might be used for finding integer factors of a product. The idea is to write the fermat equation in a different way. Instead of having a sum...
Forum: Factoring 2014-11-21, 21:23
Replies: 87
Views: 11,858
Posted By ThiloHarich
Can I use your ECM code

Hello,

can I use the ECM part of your code in my factoring application?
How can i call the ecm.java Class to get a factizization?

To give some Background:
I'm trying a variant of the SIQS...
Forum: Factoring 2010-09-05, 17:05
Replies: 87
Views: 11,858
Posted By ThiloHarich
I did some timings for different JDK or Java...

I did some timings for different JDK or Java compilers.
Times in sec.

jdk 6_21 .588 -> 100%
jdk 7b108 .591 -> 100%
jdk 6_16 .61 -> 104%
jrokit4.0.1 .974 -> 166%
jet7.2 .455 -> 77%...
Forum: Factoring 2010-04-08, 14:23
Replies: 87
Views: 11,858
Posted By ThiloHarich
@ bsquared so you are using JDK 1.4? Switching...

@ bsquared so you are using JDK 1.4?
Switching to JDK 1.6 gives a big performance increase, since the -server Option is not on for a Standard Applet. See...
Forum: Factoring 2010-04-06, 11:15
Replies: 87
Views: 11,858
Posted By ThiloHarich
@ alpertron I made the experience for my java...

@ alpertron I made the experience for my java SIQS that the code produced by gjc is not faster then executing it in the JVM 1.6 (even with no bouns check) see...
Forum: Factoring 2010-01-08, 17:01
Replies: 8
Views: 2,261
Posted By ThiloHarich
I found the reason why I was getting greater and...

I found the reason why I was getting greater and better multipliers.

I took for the factor k a term - log (k), but since q(x) = (sqrt(n) + x)^2 - kn grows with O(sqrt(k*n)*x), a factor - log(k)/2...
Showing results 1 to 25 of 101

 
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