Implementation of Oblivious Transfer over Binary-Input AWGN Channels by Polar Codes

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.