Guest Column

Abstract

We review a study of average-case complexity through the lens of interactive puzzles- interactive games between a computationally bounded Challenger and computationally-bounded Solver/Attacker. Most notably, we use this treatment to review a recent result showing that if NP is hard-on-the-average, then there exists a sampleable distribution over only true statements of an NP language, for which no probabilistic polynomial time algorithm can find witnesses. We also discuss connections to the problem of whether average-case hardness in NP implies averagecase hardness in TFNP, or the existence of cryptographic one-way functions.