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Network Oblivious Transfer via Noisy Broadcast Channels

Hadi Aghaee, Christian Deppe, Holger Boche

TL;DR

The paper investigates information-theoretic oblivious transfer over a DM-BC with two receivers under honest-but-curious models. It develops general outer bounds on OT capacity for both non-colluding and colluding scenarios and proposes two OT protocols tailored to noisy broadcast channels: a non-colluding protocol achieving the full region and a collusion-resistant protocol with complementary inner and outer bounds. For the special case of two independent sub-BECs, the non-colluding capacity region is fully characterized, while the colluding case exhibits gaps between bounds. Overall, the work provides a unified information-theoretic framework linking network information theory and cryptographic security, highlighting noisy broadcast channels as powerful primitives for privacy-preserving multi-user communication.

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.

Network Oblivious Transfer via Noisy Broadcast Channels

TL;DR

The paper investigates information-theoretic oblivious transfer over a DM-BC with two receivers under honest-but-curious models. It develops general outer bounds on OT capacity for both non-colluding and colluding scenarios and proposes two OT protocols tailored to noisy broadcast channels: a non-colluding protocol achieving the full region and a collusion-resistant protocol with complementary inner and outer bounds. For the special case of two independent sub-BECs, the non-colluding capacity region is fully characterized, while the colluding case exhibits gaps between bounds. Overall, the work provides a unified information-theoretic framework linking network information theory and cryptographic security, highlighting noisy broadcast channels as powerful primitives for privacy-preserving multi-user communication.

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.

Paper Structure

This paper contains 17 sections, 16 theorems, 91 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Motivation
  3. Related Works
  4. Preliminaries
  5. System model
  6. OT over a Discrete Memoryless Broadcast Channel (DM-BC)
  7. Noiseless Protocol
  8. Noisy Protocol
  9. Collusion scenarios
  10. Main results
  11. Conclusion
  12. Proof of Corollary \ref{['cor']}
  13. Proof of Theorem \ref{['thm:BC-coll']}
  14. Proof of Lemma \ref{['lem: cri. nColl-BC']}
  15. Proof of Theorem \ref{['thm: OT capacity-non-col']}
  16. ...and 2 more sections

Key Result

Lemma 1

Hadi1 For any random variable such $U$ and $V$, we have:

Figures (1)

  • Figure 1: $(a)$-OT over a general BC. $(b)$- OT over a DM-BC made up of two independent BECs.

Theorems & Definitions (29)

  • Lemma 1
  • Definition 1
  • Lemma 2
  • Lemma 3
  • Definition 2
  • Lemma 4
  • Lemma 5
  • Definition 3
  • Remark 1
  • Corollary 6
  • ...and 19 more