The systems and methods described herein can be used for enhancing the security of computer passwords by electronically receiving a password, the password comprising a plurality of components, each of the components being of a type of component, storing the received password in an electronic data store, converting the stored password to a topological representation of the password by which each of the plurality of components is represented and stored as its type of component, and storing the topological representation of the password in an electronic data store.