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Title:
Classically Verifiable NIZK for QMA with Preprocessing
Authors: Tomoyuki Morimae, Takashi Yamakawa
Abstract:We propose three constructions of classically verifiable noninteractive zeroknowledge proofs and arguments (CVNIZK) for QMA in various preprocessing models.

We construct a CVNIZK 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 zeroknowledge.

Assuming the quantum hardness of the learning with errors problem, we construct a CVNIZK for QMA in a model where a trusted party generates a CRS and the verifier sends an instanceindependent 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 socalled dualmode property, which means that there are two computationally indistinguishable modes of generating CRS, and we have information theoretical soundness in one mode and information theoretical zeroknowledge property in the other. This answers an open problem left by Coladangelo et al, which is to achieve either of soundness or zeroknowledge information theoretically. To the best of our knowledge, ours is the first dualmode NIZK for QMA in any kind of model.

We construct a CVNIZK for QMA with quantum preprocessing in the quantum random oracle model. This quantum preprocessing is the one where the verifier sends a random Paulibasis states to the prover. Our construction uses the FiatShamir 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 FiatShamir transformation.
ePrint: https://eprint.iacr.org/2022/1157
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