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August 19th, 2018, 02:25 AM  #1 
Newbie Joined: Aug 2018 From: Sydney Posts: 6 Thanks: 1  Thoughts about factorising an RSA modulus
As I've pondered my likely inability to factorise a 2048 bit RSA modulus that would give me control of some equipment that I own, I've wondered whether anything can be made of the public exponent. No doubt I'm traversing a well worn path to failure, but anyway. I've reduced(?) the problem to finding pairs of n1, n2 that satisfy N = E(n1^2  n2^2)  2(n1 * k1  n2 * k2) where N, E (prime), k1, and k2 are known. In this particular instance N is composite (it isn't always), but unlike the original public modulus, was not created with the intention that it be the product of large primes, so there is at least the possibility that it has a factor that is of a tractable size. So far an elliptic curve factorisation program hasn't found it, but it's only been a few hours. But I'm wondering whether knowing the factor is going to help anyway. Is there a way to leverage knowledge of a factor of N to get n1 and n2 more quickly? 
August 19th, 2018, 03:23 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 19,879 Thanks: 1835 
What is the equipment you referred to?

August 19th, 2018, 04:56 AM  #3 
Newbie Joined: Aug 2018 From: Sydney Posts: 6 Thanks: 1  I'd rather not say at this stage. However, if you're concerned about legal issues, I'm in Australia. The Australian equivalent of the DCMA clearly allows me to break any protection scheme for the purpose of achieving interoperability, or where the protection scheme limits my use of the device in which the protected software is embedded.

August 19th, 2018, 04:58 AM  #4 
Newbie Joined: Aug 2018 From: Sydney Posts: 6 Thanks: 1  
August 21st, 2018, 08:07 PM  #5 
Newbie Joined: Aug 2018 From: Sydney Posts: 6 Thanks: 1  I'll take that as a "no". Anyway, the factorisation program made no headway in factorising N over several days, and I gave up.


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factorising, modulus, rsa, thoughts 
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