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if it's not an easy factorization => it will be hard. According to recent results we believe state-sized adversary should be able to do it. If you're threat model is against criminals, then you might be OK.

EDIT: if 1024bits factorization is easy in general, you can say goodbye to every 1024bits RSA modulus. My first statement doesn't mean it can never be easy, it means that if you try and factor it the easy way and it doesn't work... you are in for a lot of work and research.




Well, it isn't known who provided the number in the first place. Whoever that unknown party is presumably knows the factorization they used to construct p. This could be a state, or could be a criminal enterprise. Better not to trust it!


Oh right. I guess I forgot this part 8)


Testing for 2 seconds already found the prime factors 271 and 13597. It will probably not be hard.

Edit: To add some more information, p / (271 * 13597) is still not prime, however, the library I was using didn't find any new factors in 30 minutes.


There are no other factors less than 2^32. You can see my other comment for details on verifying this.




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