Explain the fundamental distinction between P (problems solvable in polynomial time) and NP (problems verifiable in polynomial time). Discuss the theoretical consequences if P were equal to NP, specifically focusing on the collapse of modern cryptographic systems like RSA. Conversely, discuss the implications if P does not equal NP. Provide examples of NP-complete problems (e.g., the traveling salesman problem) and explain why no polynomial-time algorithm has been found for them despite significant effort.