The Tau One-Way Functions Class : P != NP

We prove the existence of a class of functions we call T (Greek Tau), each of whose members satisfies the conditions of one-way functions. Each member of T is a function computable in polynomial time, with negligible probability of finding its inverse by any polynomial probabilistic algorithm. This is accomplished by constructing each member in T with a collection of independent universal hash functions that produce a starting coordinate and a path within a sequence of unique random bit matrices. The existence of one-way functions implies that P != NP.