Explain the P vs. NP problem and its implications for information security and optimization problems. What would be the consequences if P were equal to NP?

The P vs. NP problem asks whether every problem whose solution can be quickly verified by a computer can also be quickly solved by a computer. If P equals NP, every hard problem with easy-to-check solutions would also have easy-to-find solutions, revolutionizing fields such as cryptography, scheduling, and logistics. For instance, most modern encryption methods would become obsolete because breaking them would be as easy as verifying a guessed key. However, most experts believe P does not equal NP, implying that there are inherently hard problems that cannot be solved efficiently.