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

TL;DR

This paper presents a novel polar code-based protocol for oblivious transfer over BI-AWGN channels, achieving perfect secrecy for one party and asymptotic secrecy for the other, with finite-blocklength performance analysis.

Contribution

It introduces a new polar code scheme for oblivious transfer over noisy channels, leveraging automorphisms for secrecy and optimizing finite-blocklength rates.

Findings

Achieves perfect secrecy for Bob at any blocklength.

Provides asymptotic secrecy for Alice via channel polarization.

Empirically verifies reliability and secrecy through simulations.

Abstract

We develop a one-out-of-two oblivious transfer protocol over the binary-input additive white Gaussian noise (BI-AWGN) 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 secrecy for Bob at any blocklength. Secrecy for Alice is obtained asymptotically via channel polarization combined with privacy amplification. Because the construction deliberately injects randomness into selected bad bit-channels, we derive a relaxed reliability criterion, which is empirically certified via Monte-Carlo simulations. We also 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 rate.