Zero-Knowledge proofs are a staple of cryptography, discovered in a seminal work of Goldwasser, Micali and Rackoff. They are protocols that allow a prover to convince a verifier that a statement is true, essentially without revealing any information about why the statement is true. But unlike traditional proofs, they require interaction between the prover and verifier, and there is always some non-zero probability of the verifier getting convinced of an incorrect statement (imperfect soundness). Known impossibility results show that these drawbacks are unavoidable. Traditional zero-knowledge proofs use cryptographic assumptions such as the existence of one-way functions. In this (hopefully not zero-knowledge) talk, we will see a glimpse of how proof complexity -- using the conjectured absence of optimal proof systems (along the lines of Gödel's incompleteness theorem) -- helps us achieve a relaxation of zero-knowledge proofs with no interaction, no "setup" (a milder form of interaction), and with perfect soundness.

Link to the paper: https://eprint.iacr.org/2025/1296.pdf