A New Simple Technique to Bootstrap Various Lattice Zero-Knowledge Proofs to QROM Secure NIZKs

Abstract

Many of the recent advanced lattice-based \(\varSigma \)-/public-coin honest verifier (HVZK) interactive protocols based on the techniques developed by Lyubashevsky (Asiacrypt’09, Eurocrypt’12) can be transformed into a non-interactive zero-knowledge (NIZK) proof in the random oracle model (ROM) using the Fiat-Shamir transform. Unfortunately, although they are known to be secure in the classical ROM, existing proof techniques are incapable of proving them secure in the quantum ROM (QROM). Alternatively, while we could instead rely on the Unruh transform (Eurocrypt’15), the resulting QROM secure NIZK will incur a large overhead compared to the underlying interactive protocol.