Factoring large N into prime factors

[bert2612]

Hi, I am writing up a project based on an algorithm for factoring large numbers, I have reached seemingly simple point where I am stuck, I wonder if anyone can help me?

I am trying to factor a large N such that N=pq for unknown primes p and q, I have described a method to find a value for (p-1)(q-1) from N and now have the problem of recovering p and q.

So N is given and (p-1)(q-1) is given, how do I carry on? Thanks

 

[dodo]

Hi, Bert,
see this thread:
https://www.physicsforums.com/showthread.php?t=584239

It would be interesting if you can comment on your method, as finding phi(n) for large semiprimes is hard.

 

[bert2612]

thanks, that's perfect.

The way in which i found (p-1)(q-1) is to take a set of sequences of powers of x mod N for x=1,2,...,N-1 and work out their periods, each period turns out to be a divisor of (p-1)(q-1), if a large enough number of divisors is taken, then the value of (p-1)(q-1) can be predicted with high probability. That's basically all I've got, if anyone knows the specific theorem I am exploiting here it would be greatly appreciated as I should include it in my work, I know it's Euler but I'm having trouble finding a specific name so I can reference it and perhaps find a proof.