Information-theoretically secure Symmetric Private Information Retrieval (SPIR) is known to be infeasible over noiseless channels with a single server. Known solutions to overcome this infeasibility involve additional resources such as database replication, shared randomness, or noisy channels. In this paper, we propose an alternative approach for achieving SPIR with information-theoretic security guarantees, without relying on shared randomness, noisy channels, or data replication. Specifically, we demonstrate that it is sufficient to use a noiseless binary adder multiple-access channel, where inputs are controlled by two non-colluding servers and the output is observed by the client, alongside a public noiseless communication channel between the client and the servers. Furthermore, in this setting, we characterize the optimal file rates, i.e., the file lengths normalized by the number of channel uses, that can be transferred.

翻译：信息论安全的对称私有信息检索（SPIR）已知在单服务器无噪声信道上不可行。克服这一不可行性的已知解决方案涉及额外资源，如数据库复制、共享随机性或噪声信道。本文提出一种实现具有信息论安全保证的SPIR的替代方法，该方法不依赖共享随机性、噪声信道或数据复制。具体而言，我们证明仅需使用无噪声二进制加法多址信道（其输入由两个非共谋服务器控制，输出由客户端观测），并辅以客户端与服务器之间的公共无噪声通信信道即可实现。此外，在此设定下，我们刻画了可传输文件速率（即信道使用次数归一化的文件长度）的最优值。