20220119, 07:08  #1 
Jan 2022
19 Posts 
Independent factorization of large numbers
Dear math gurus, Please tell me why most number factorization programs do not use a GPU?
I need to factorize not a small number (154 characters), tell me is it really possible to do this on a home computer? I'm going to use JAFU or MSiev, I realized from the forum that it is required to use the GNFS algorithm, please tell me  am I in the right direction? Last fiddled with by Lessiv on 20220119 at 08:04 
20220119, 10:30  #2  
Bamboozled!
"๐บ๐๐ท๐ท๐ญ"
May 2003
Down not across
2×3×29×67 Posts 
Quote:
As a matter of interest, what is your number? Post it here and several people will be able to factor it for you within a day or few. Most GPUs do not have enough memory to be effective with the GNFS. 

20220119, 10:47  #3  
Undefined
"The unspeakable one"
Jun 2006
My evil lair
5×7×191 Posts 
Quote:
My calculator says that 154รlogโ10 = 511.5769... so 154 seems right. Quote:
Ability to do so doesn't guarantee an equivalent amount of desire or motivation to do so. I wonder if the OP is willing to offer something in return? 

20220119, 11:24  #4 
Bamboozled!
"๐บ๐๐ท๐ท๐ญ"
May 2003
Down not across
2×3×29×67 Posts 
You are correct. Mea culpa.

20220119, 11:26  #5 
Bamboozled!
"๐บ๐๐ท๐ท๐ญ"
May 2003
Down not across
2·3·29·67 Posts 
If the reason why it is to be factored  for instance, for which specific key it is the public modulus  were offered I may be motivated to perform the factorization.

20220119, 11:29  #6  
Just call me Henry
"David"
Sep 2007
Liverpool (GMT/BST)
13617_{8} Posts 
Quote:
If it is an 512 bit RSA number people may be reluctant to factor it without proof of its source. I believe a decent modern pc(or an AWS instance) can factor this in 2 or 3 weeks. 

20220119, 16:22  #7 
Jan 2022
19_{10} Posts 
Yes, you're right  it's a RSA modulud (N)
There was a "Factoring as a Service" project on GIT, I wanted to use just such a service for factoring numbers, but the project is no longer active, looking for a solution  I found this forum. Regarding the legality, there are no violations, keys of this length are no longer used, as evidenced by the service itself that was used by AMAZON (AWS). For the assistance provided, I am ready to thank the helper. Last fiddled with by Lessiv on 20220119 at 16:23 
20220119, 16:37  #8 
Sep 2009
2·1,213 Posts 
There are several programs you could use to factor it:
ggnfs  this works better if you also have msieve. Search for factMsieve.pl or factmsieve.py for scripts to drive it. yafu  this will need the lattice siever from ggnfs and msieve. cadonfs  this is a complete package that does not need other software. Whatever you use I suggest you start by factoring a 100 digit number as a quick test. Then work up by factoring a 110 digit number, then a 120 digit number, etc until you get up to 140 or 150 digits before tackling your 154 digit number. Since you know it's a RSA key there is no need to run ECM before you start GNFS. ECM is only useful for numbers that might have a small factor. 
20220119, 16:57  #9  
Bamboozled!
"๐บ๐๐ท๐ท๐ญ"
May 2003
Down not across
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Quote:
So which key is it? If there are no violations I can't see that you have any real reason to hide its identity. 

20220119, 16:59  #10 
Jan 2022
19 Posts 
Thanks for the detailed answer, that's exactly what I assumed (according to ECM).
I have a PC with an Intel I9 processor, will use it. Assumed that there is a person or a company on the forum that has a more solid computer package, I thought to use the help, but apparently I'll have to try it myself by trial and error :ัะปัะฑะบะฐ: Or maybe someone understands how to rent AWS on Amazon, for faster factoring? According to the description, this number was factorized in less than 24 hours, and this is about 6 years ago Sorry, but here I do not understand  why should I waste precious time. Of course, I will run a small number, just to check that everything is set up as it should and then skip the factoring of the Real number. Last fiddled with by Lessiv on 20220119 at 17:06 
20220119, 17:02  #11  
Jan 2022
23_{8} Posts 
Quote:
It is just necessary that this number is NOT in the public domain, so that other participants do not use it 

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