We propose three constructions of classically verifiable non-interactive proofs (CV-NIP) and non-interactive zero-knowledge proofs and arguments (CV-NIZK) for QMA in various preprocessing models. - We construct an information theoretically sound CV-NIP for QMA in the secret parameter model where a trusted party generates a quantum proving key and classical verification key and gives them to the corresponding parties while keeping it secret from the other party. Alternatively, we can think of the protocol as one in a model where the verifier sends an instance-independent quantum message to the prover as preprocessing. - We construct a CV-NIZK for QMA in the secret parameter model. It is information theoretically sound and zero-knowledge. - Assuming the quantum hardness of the leaning 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 indistinguishable 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.

中文翻译：

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具有预处理功能的QMA经典可验证（双模式）NIZK

我们提出了在各种预处理模型中针对QMA的经典可验证非交互式证明（CV-NIP）和非交互式零知识证明和参数（CV-NIZK）的三种构造。-我们在秘密参数模型中为QMA构建理论上合理的CV-NIP信息，在该模型中，受信方会生成量子证明密钥和经典验证密钥，并将它们提供给相应的各方，同时又要保持对对方的秘密。另外，我们可以将协议视为模型中的一种协议，其中验证者将与实例无关的量子消息作为预处理发送给证明者。-我们在秘密参数模型中为QMA构建CV-NIZK。从理论上讲，它是可靠且零知识的信息。-假设倾斜误差的量子硬度问题，我们在模型中构造了一个用于QMA的CV-NIZK，其中受信方生成CRS，验证者将与实例无关的量子消息发送给证明者作为预处理。此模型与Coladangelo，Vidick和Zhang（CRYPTO '20）最近的工作中所考虑的模型相同。我们的构造具有所谓的双模性质，这意味着生成CRS有两种计算上无法区分的模式，而我们在一种模式下具有信息理论上的可靠性，而在另一种模式下具有信息理论上的零知识特性。这回答了Coladangelo等人留下的未解决问题，即理论上要获得健全性或零知识信息。据我们所知，我们是任何型号的QMA的首款双模NIZK。