Fermi Ma: Post-Quantum Succinct Arguments

Abstract: We prove that Kilian’s four-message succinct argument system
is post-quantum secure in the standard model when instantiated with
any probabilistically checkable proof and any collapsing hash function
(which in turn exist based on the post-quantum hardness of Learning
with Errors).

At the heart of our proof is a general-purpose quantum rewinding
procedure that enables a reduction to repeatedly query a quantum
adversary for accepting transcripts as many times as desired.

Based on joint work with Alessandro Chiesa, Nicholas Spooner, and Mark Zhandry.
https://eprint.iacr.org/2021/334.pdf