Honestly, that's probably the least interesting implication of a constructive proof that p=np.
The entire field of cryptography is based around the idea of problems easy to solve with a short piece of information but hard to solve without it. If P=NP (and we have a constructive proof with an algorithm where the constants & degree aren't rediculous), the entire field of cryptography would collapse. Only 1-time pad's would be safe.
Polynomial doesn't mean practical. In practice, O(n^100) is not an improvement over O(2^n).
Also, we could imagine an algorithm that takes O(2^n) operation to verify and O(100^n) to find a solution. Both are exponential time (not NP), but the difference ensures that you can make it both safe and fast enough for use. I don't know if we could build such an algorithm if we had constructive P=NP though.
The entire field of cryptography is based around the idea of problems easy to solve with a short piece of information but hard to solve without it. If P=NP (and we have a constructive proof with an algorithm where the constants & degree aren't rediculous), the entire field of cryptography would collapse. Only 1-time pad's would be safe.