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.

翻译：发送方能否非交互地将两个字符串中的一个传输给接收方，且不告知其具体收到哪个字符串？是否存在仅需（黑盒）使用对称密钥原语的最小交互安全多方计算？我们在各方可访问共享EPR对的模型中为这些问题给出了肯定答案，从而证明了该资源的密码学能力。首先，我们假设LWE的（子指数）困难性，在共享EPR对模型中构建了具有随机接收方比特的一次性（即单消息）字符串不经意传输（OT）协议。在此基础上，我们展示了通过量子通道实现安全隐形传态的可能性。具体而言，给定任意量子操作$Q$的描述，持有（量子）输入$\rho$的发送方可通过发送单条经典消息，将$Q(\rho)$安全地传输给接收方。即我们实现了理想量子通道：该通道从发送方接收输入$\rho$，可验证地将$Q(\rho)$交付给接收方，且不泄露任何其他信息。这立即在共享EPR对模型中产生了多项应用：（1）单向经典随机化功能的非交互安全计算；（2）基于标准（子指数）困难性假设的QMA的NIZK；（3）非交互零知识状态合成协议。接下来，我们在共享EPR对模型中构建了两轮（轮数最优）经典功能安全多方计算协议，该协议在（量子可访问）随机谕言模型中具有无条件安全性。