We will discuss recent progress on instantiating the Fiat-Shamir heuristic using explicit hash functions. Over the last few years, a sequence of works has obtained positive results in this setting by either making strong (but simple and meaningful) cryptographic assumptions or by focusing on round-compressing restricted classes of public-coin interactive proofs. Among other consequences, this has led to a construction of non-interactive zero knowledge (NIZK) proofs in the CRS model under the LWE assumption.

Over the course of two talks, we will discuss many of the ideas and techniques in this line of work, with an emphasis on the notion of correlation intractable hash functions as an organizing principle and useful cryptographic tool.