Well, it would be a very well guarded secret. But even then the question is how public key crypto is broken. If they can easily generate exploits for implementations, because they know a essential implementation detail everybody else is missing, then it would be fundamentally different from being able to break RSA directly, or if they have a constructive prove of P=NP.
Remember that factoring primes isn't know to be NP Hard. There is no complexity breakthrough required, we just don't know how to do it quickly. So we don't get P=NP from any factoring breakthrough.
Depends on the breakthrough, we know that multiplication is in P and therefore factorization in NP. So a P?=NP breakthrough may or may not have consequences for integer factorization. ( Actually since I did write that, I wonder if P=NP would invalidate any public key crypto, since efficient encryption should be in P.)
Comments
Well, it would be a very well guarded secret. But even then the question is how public key crypto is broken. If they can easily generate exploits for implementations, because they know a essential implementation detail everybody else is missing, then it would be fundamentally different from being able to break RSA directly, or if they have a constructive prove of P=NP.
Remember that factoring primes isn't know to be NP Hard. There is no complexity breakthrough required, we just don't know how to do it quickly. So we don't get P=NP from any factoring breakthrough.
Depends on the breakthrough, we know that multiplication is in P and therefore factorization in NP. So a P?=NP breakthrough may or may not have consequences for integer factorization. ( Actually since I did write that, I wonder if P=NP would invalidate any public key crypto, since efficient encryption should be in P.)