Non-interactive classical verification of quantum computation
Non-interactive classical verification of quantum computation
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DOI：
10.1007/978-3-030-64381-2_6
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发表时间：
2019-11
期刊：
影响因子：
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通讯作者：
G. Alagic;Andrew M. Childs;A. Grilo;S. Hung
中科院分区：
文献类型：
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作者：
G. Alagic;Andrew M. Childs;A. Grilo;S. Hung
在最近的一项突破中，Mahadev构建了一个交互式协议，使纯粹的经典方能够将任何量子计算委托给不可信的量子证明者。我们表明，这同样的任务，实际上可以performednon-interactive（与设置）和inzero-knowledge.Our协议的结果从一系列显着的改进，原来的四个消息协议的Mahadev。我们开始首先使第一个消息独立于实例，并将其移动到离线设置阶段。然后，我们建立了一个平行的重复定理所产生的三个消息协议，具有渐近最优的速率。这反过来又支持Fiat-Shamir启发式算法的应用，消除了第二条消息并给出了非交互式协议。最后，我们采用经典的非交互式零知识（NIZK）参数和经典的全同态加密（FHE），给出了这种结构的零知识变体。这产生了第一个纯经典的NIZK参数系统，量子模拟。我们建立我们的协议的安全性在量子安全密码学的标准假设下。具体来说，我们的协议在量子随机预言模型中是安全的，假设带错误的学习是量子困难的。NIZK结构还需要电路专用FHE。
In a recent breakthrough, Mahadev constructed an interactive protocol that enables a purely classical party to delegate any quantum computation to an untrusted quantum prover. We show that this same task can in fact be performednon-interactively(with setup) and inzero-knowledge.Our protocols result from a sequence of significant improvements to the original four-message protocol of Mahadev. We begin by making the first message instance-independent and moving it to an offline setup phase. We then establish a parallel repetition theorem for the resulting three-message protocol, with an asymptotically optimal rate. This, in turn, enables an application of the Fiat-Shamir heuristic, eliminating the second message and giving a non-interactive protocol. Finally, we employ classical non-interactive zero-knowledge (NIZK) arguments and classical fully homomorphic encryption (FHE) to give a zero-knowledge variant of this construction. This yields the first purely classical NIZK argument system for, a quantum analogue of.We establish the security of our protocols under standard assumptions in quantum-secure cryptography. Specifically, our protocols are secure in the Quantum Random Oracle Model, under the assumption that Learning with Errors is quantumly hard. The NIZK construction also requires circuit-private FHE.