A Round-Collapse Theorem for Computationally-Sound Protocols; or, TFNP is Hard (on Average) in Pessiland

Consider the following two fundamental open problems in complexity theory: 1) Does a hard-on-average language in NP imply the existence of one-way functions? 2) Does a hard-on-average language in NP imply a hard problem in TFNP (i.e., the class of total NP search problem)? We show that the answer to (at least) one of these questions is ...More