We develop a one-out-of-two-oblivious transfer protocol over the binary-input additive white Gaussian noise channel using polar codes. The scheme uses two decoder views linked by automorphisms of the polar transform and publicly draws the encoder at random from the corresponding automorphism group. This yields perfect receiver privacy at any finite blocklength, since the public encoder distribution is independent of the receiver's choice bit. Sender privacy is obtained asymptotically via channel polarization combined with privacy amplification. Because the construction deliberately injects randomness on selected bad bit-channels, we derive a relaxed reliability criterion and evaluate finite-blocklength performance. Finally, we characterize the polar-transform automorphisms as bit-level permutations of bit-channel indices, and exploit this structure to derive and optimize an achievable finite-blocklength OT rate.

翻译：本文提出了一种利用极化码在二进制输入加性高斯白噪声信道上实现二选一不经意传输的协议。该方案通过极化变换的自同构关联两个译码器视角，并公开从对应的自同构群中随机选取编码器。由于公开的编码器分布与接收方的选择比特无关，该设计可在任意有限码长下实现完美的接收方隐私性。通过信道极化与隐私放大技术的结合，发送方隐私性可渐近达成。由于该构造刻意在选定的劣质比特信道上注入随机性，我们推导出了一种松弛的可靠性准则，并评估了有限码长性能。最后，我们将极化变换的自同构特征描述为比特信道索引的比特级置换，并利用此结构推导和优化了可达的有限码长不经意传输速率。