In general, P = NP means that some algorithms will become much faster to solve. We have some algorithms that we depend on being hard. Most notable is encryption. We depend on it being hard for am attacker to crack the encryption (but easy for someone who already knows the answer – eg, your password). P = NP might (but not necessarily) make it easy enough for encryption to therefore be broken.
I say not necessarily because while P = NP does mean certain types of algorithms will become faster (in at least certain cases), it’s still possible for them to be quite slow. P and NP refer to how long algorithms take, based on how they scale with input. P is polynomial and NP is non-polynomial. Polynomial functions scale far better than non-polynomial functions, but that doesn’t mean they necessarily scale well, as there’s plenty of types of polynomial functions, some which scale far, far better than others.
In general, P = NP means that some algorithms will become much faster to solve. We have some algorithms that we depend on being hard. Most notable is encryption. We depend on it being hard for am attacker to crack the encryption (but easy for someone who already knows the answer – eg, your password). P = NP might (but not necessarily) make it easy enough for encryption to therefore be broken.
I say not necessarily because while P = NP does mean certain types of algorithms will become faster (in at least certain cases), it’s still possible for them to be quite slow. P and NP refer to how long algorithms take, based on how they scale with input. P is polynomial and NP is non-polynomial. Polynomial functions scale far better than non-polynomial functions, but that doesn’t mean they necessarily scale well, as there’s plenty of types of polynomial functions, some which scale far, far better than others.