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.
翻译:我们提议在各种预处理模型中为QMA构建三种传统可核查的非互动性证明(CV-NIP)和非互动的零知识证明和参数(CV-NIZK)的构建。 我们建议在秘密参数模型中为QMA构建一种信息在理论上是健全的 CV-NIP 。 在这种模型中,一个受信任的一方生成了一个量子验证关键和经典验证键,并将之交给对应方,同时将之交给对方保密。 或者,我们可以将协议视为一个模式,在模型中,核查者向验证者发送一个以实例为基础的量信息,作为预处理。 - 我们在秘密参数模型中为QMA构建了一个CV-NIZIP, 理论上的CV- NIZK 是一个信息质量, 也就是我们当前在Coladangel、 Viickm-K 和Oudioaldality 的计算方法, 也就是我们当前一个Oudiodrial-Modeal-deal-deal-deal-deal-deal-Oral-deal-Oral-Ial-deal-mo-ILy-ILMK, 和Ory-I-I-I-M-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-