Fiat-Shamir for Repeated Squaring with Applications to PPAD-Hardness and VDFs

The Fiat-Shamir transform is a methodology for compiling a (public-coin) interactive proof system for a language L into a non-interactive argument system for L. Proving security of the Fiat-Shamir transform in the standard model, especially in the context of succinct arguments, is largely an unsolved problem. The work of Canetti et al. (STOC 2019) proved the security of the Fiat-Shamir transform applied to the Goldwasser-Kalai-Rothblum (STOC 2008) succinct interactive proof system under a very strong “optimal learning with errors” assumption. Achieving a similar result under standard assumptions remains an important open question.