Secure Computation with Shared EPR Pairs (Or: How to Teleport in Zero-Knowledge)
Secure Computation with Shared EPR Pairs (Or: How to Teleport in Zero-Knowledge)
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DOI：
10.48550/arxiv.2304.10480
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发表时间：
2023-04
期刊：
影响因子：
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通讯作者：
James Bartusek;Dakshita Khurana;Akshayaram Srinivasan
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文献类型：
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作者：
James Bartusek;Dakshita Khurana;Akshayaram Srinivasan
发送方能否在不知道接收方接收到哪个字符串的情况下，以非交互方式向接收方发送两个字符串中的一个？是否存在仅（黑箱）使用对称密钥原语的最小交互安全多方计算？我们在各方可以访问共享EPR对的模型中为这些问题提供了肯定的答案，从而展示了该资源的加密能力。首先，我们在共享EPR对模型中，假设LWE的（次指数）硬度，构造了一个随机接收位的单次（即单消息）字符串无关传输（OT）协议。在此基础上，我们证明{\em通过量子通道安全隐形传态}是可能的。具体来说，给定任何量子操作$Q$的描述，具有（量子）输入$\rho$的发送方可以发送一条经典消息，该消息安全地将$Q(\rho)$传输给接收方。也就是说，我们实现了一个理想的量子信道，它从发送方接收输入$\rho$，并可证明地将$Q(\rho)$传递给接收方，而不泄露任何其他信息。这立即给出了共享EPR对模型中的许多应用：(1)单向\emph{经典}随机函数的非交互式安全计算，(2)基于标准（次指数）硬度假设的QMA的NIZK，以及(3)非交互式\emph{零知识}状态合成协议。接下来，我们为共享EPR对模型中的经典功能构建了一个两轮（最优）安全多方计算协议，该协议在（量子可访问）随机oracle模型中是\emph{无条件安全}的。
Can a sender non-interactively transmit one of two strings to a receiver without knowing which string was received? Does there exist minimally-interactive secure multiparty computation that only makes (black-box) use of symmetric-key primitives? We provide affirmative answers to these questions in a model where parties have access to shared EPR pairs, thus demonstrating the cryptographic power of this resource. First, we construct a one-shot (i.e., single message) string oblivious transfer (OT) protocol with random receiver bit in the shared EPR pairs model, assuming the (sub-exponential) hardness of LWE. Building on this, we show that {\em secure teleportation through quantum channels} is possible. Specifically, given the description of any quantum operation $Q$, a sender with (quantum) input $\rho$ can send a single classical message that securely transmits $Q(\rho)$ to a receiver. That is, we realize an ideal quantum channel that takes input $\rho$ from the sender and provably delivers $Q(\rho)$ to the receiver without revealing any other information. This immediately gives a number of applications in the shared EPR pairs model: (1) non-interactive secure computation of unidirectional \emph{classical} randomized functionalities, (2) NIZK for QMA from standard (sub-exponential) hardness assumptions, and (3) a non-interactive \emph{zero-knowledge} state synthesis protocol. Next, we construct a two-round (round-optimal) secure multiparty computation protocol for classical functionalities in the shared EPR pairs model that is \emph{unconditionally-secure} in the (quantum-accessible) random oracle model.