Paper 2024/1161

On the Concrete Security of Non-interactive FRI

Abstract

FRI is a cryptographic protocol widely deployed today as a building block of many efficient SNARKs that help secure transactions of hundreds of millions of dollars per day. The Fiat-Shamir security of FRI—vital for understanding the security of FRI-based SNARKs—has only recently been formalized and established by Block et al. (ASIACRYPT ’23). In this work, we complement the result of Block et al. by providing a thorough concrete security analysis of non-interactive FRI under various parameter settings from protocols deploying (or soon to be deploying) FRI today. We find that these parameters nearly achieve their desired security targets (being at most 1-bit less secure than their targets) for non-interactive FRI with respect to a certain security conjecture about the FRI Protocol. However, in all but one set of parameters, we find that the provable security of non-interactive FRI under these parameters is severely lacking, being anywhere between 21- and 63-bits less secure than the conjectured security. The conjectured security of FRI assumes that known attacks are optimal, the security of these systems would be severely compromised should a better attack be discovered. In light of this, we present parameter guidelines for achieving 100-bits of provable security for non-interactive FRI along with a methodology for tuning these parameters to suit the needs of protocol designers.