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 2016-12-19, 06:29 #1 rxz7545   Dec 2016 28 Posts RSA Key Factoring using Yafu I am trying to use Yafu to factorize RSA Keys. One thing that surprises me is Yafu shows more than 2 factors even though RSA keys should have only 2 factors. Why is this so? For example, when I factor the following no: factor(1522605027922533360535618378132637429718068114961380688657908494580122963258952897654000350692006139) I get these as factors: P2 = 11 P7 = 6698689 P8 = 18633149 P12 = 407893628797 P22 = 4702659209804290841741 P50 = 57813341690015577934703993485336625998708275892717
2016-12-19, 07:07   #2
retina
Undefined

"The unspeakable one"
Jun 2006
My evil lair

3×23×83 Posts

Quote:
 Originally Posted by rxz7545 One thing that surprises me is Yafu shows more than 2 factors even though RSA keys should have only 2 factors. Why is this so?
RSA keys can have as many factors as the creator wants, but they won't be secure of course if they have many small factors. As to why you have so many factors in your number there could be many reasons. But most likely is perhaps it was created by bad software or a copy/paste error.

2016-12-19, 07:44   #3
rxz7545

Dec 2016

2 Posts

Quote:
 Originally Posted by retina RSA keys can have as many factors as the creator wants, but they won't be secure of course if they have many small factors. As to why you have so many factors in your number there could be many reasons. But most likely is perhaps it was created by bad software or a copy/paste error.
But this key is from RSA Factoring Challenge: https://en.wikipedia.org/wiki/RSA_numbers#RSA-155

2016-12-19, 07:54   #4
retina
Undefined

"The unspeakable one"
Jun 2006
My evil lair

3×23×83 Posts

Quote:
 Originally Posted by rxz7545 But this key is from RSA Factoring Challenge: https://en.wikipedia.org/wiki/RSA_numbers#RSA-155
Okay, it is RSA 100. And like I mentioned earlier, copy/paste error, because the factors are:
p=37975227936943673922808872755445627854565536638199
q=40094690950920881030683735292761468389214899724061

2016-12-19, 07:54   #5
Batalov

"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

53×73 Posts

Quote:
 Originally Posted by rxz7545 P2 = 11 P7 = 6698689 P8 = 18633149 P12 = 407893628797 P22 = 4702659209804290841741 P50 = 57813341690015577934703993485336625998708275892717
Compare to the original number...

...and you will find a copy-paste error (you lost one digit)
Code:
152260502792253336053561837813263742971806811496138068865790849458012296325892897654000350692006139
1522605027922533360535618378132637429718068114961380688657908494580122963258952897654000350692006139

Last fiddled with by Batalov on 2016-12-19 at 08:02

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