Network Oblivious Transfer via Noisy Broadcast Channels

TL;DR

This paper explores how noisy broadcast channels can be used to implement oblivious transfer securely, providing capacity bounds and explicit protocols for both colluding and non-colluding receivers, bridging information theory and cryptography.

Contribution

It introduces new capacity bounds and two explicit oblivious transfer protocols tailored for noisy broadcast channels, including collusion-resistant mechanisms.

Findings

Capacity bounds are tight for non-colluding receivers.

Protocols achieve privacy and correctness under different collusion scenarios.

The framework unifies network information theory with cryptographic security.

Abstract

This paper investigates information-theoretic oblivious transfer via a discrete memoryless broadcast channel with one sender and two receivers. We analyze both non-colluding and colluding honest-but-curious user models and establish general upper bounds on the achievable oblivious transfer capacity region for each case. Two explicit oblivious transfer protocols are proposed. The first ensures correctness and privacy for independent, non-colluding receivers by leveraging the structure of binary erasure broadcast channels. The second protocol, secure even under receiver collusion, introduces additional entropy-sharing and privacy amplification mechanisms to preserve secrecy despite information leakage between users. Our results show that for the non-colluding case, the upper and lower bounds on oblivious transfer capacity coincide, providing a complete characterization of the achievable region. The work provides a unified theoretical framework bridging network information theory and cryptographic security, highlighting the potential of noisy broadcast channels as powerful primitives for multi-user privacy-preserving communication.