## CryptoDB

### Paper: Classically Veriﬁable NIZK for QMA with Preprocessing

Authors: Tomoyuki Morimae , Kyoto University Takashi Yamakawa , NTT Search ePrint Search Google Slides ASIACRYPT 2022 We propose three constructions of classically veriﬁable non-interactive zero-knowledge proofs and arguments (CV-NIZK) for QMA in various preprocessing models. 1. We construct a CV-NIZK for QMA in the quantum secret parameter model where a trusted setup sends a quantum proving key to the prover and a classical veriﬁcation key to the veriﬁer. It is information theoretically sound and zero-knowledge. 2. Assuming the quantum hardness of the learning with errors problem, we construct a CV-NIZK for QMA in a model where a trusted party generates a CRS and the veriﬁer sends an instance-independent quantum message to the prover as preprocessing. This model is the same as one considered in the recent work by Coladangelo, Vidick, and Zhang (CRYPTO ’20). Our construction has the so-called dual-mode property, which means that there are two computationally in-distinguishable modes of generating CRS, and we have information theoretical soundness in one mode and information theoretical zero-knowledge property in the other. This answers an open problem left by Coladangelo et al, which is to achieve either of soundness or zero-knowledge information theoretically. To the best of our knowledge, ours is the ﬁrst dual-mode NIZK for QMA in any kind of model. 3. We construct a CV-NIZK for QMA with quantum preprocessing in the quantum random oracle model. This quantum preprocessing is the one where the veriﬁer sends a random Pauli-basis states to the prover. Our construction uses the Fiat-Shamir transformation. The quantum preprocessing can be replaced with the setup that distributes Bell pairs among the prover and the veriﬁer, and therefore we solve the open problem by Broadbent and Grilo (FOCS ’20) about the possibility of NIZK for QMA in the shared Bell pair model via the Fiat-Shamir transformation.
##### BibTeX
@inproceedings{asiacrypt-2022-32352,
title={Classically Veriﬁable NIZK for QMA with Preprocessing},
publisher={Springer-Verlag},
author={Tomoyuki Morimae and Takashi Yamakawa},
year=2022
}