Muthu Venkitasubramaniam: A Round-Collapse Theorem for Computationally-Sound Protocols; or, TFNP is Hard-on-Average in Pessiland

Friday, December 13, 2019 - 10:30am to 12:00pm
G882, Hewlett
Muthu Venkitasubramaniam
Abstract: Consider the following two fundamental open problems in complexity theory:

* Does a hard-on-average language in NP imply the existence of one-way functions?

* 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 yes. In other words, in Impagliazzo's Pessiland (where NP is hard-on-average, but one-way functions do not exist), TFNP is unconditionally hard (on average).


This result follows from a more general theory of interactive average-case complexity, and in particular, a novel round-collapse theorem for computationally-sound protocols, analogous to Babai-Moran's celebrated round-collapse theorem for information-theoretically sound protocols. As another consequence of this treatment, we show that the existence of O(1)-round public-coin non-trivial arguments (i.e., argument systems that are not proofs) imply the existence of a hard-on-average problem in NP/poly.