Secure Computation in a Bidirectional Relay

TL;DR

This paper introduces a secure bidirectional relaying scheme using lattice coding in Gaussian MACs, ensuring the relay decodes only the XOR of messages while remaining ignorant of individual messages, with optimal rate-power trade-offs.

Contribution

It proposes a novel lattice coding strategy for secure bidirectional relaying that guarantees message secrecy against an honest but curious relay.

Findings

Achieves perfect independence between relay observations and individual messages.

Extends to general finite Abelian group message scenarios.

Provides optimal rate versus power trade-offs for large dimensions.

Abstract

Bidirectional relaying, where a relay helps two user nodes to exchange equal length binary messages, has been an active area of recent research. A popular strategy involves a modified Gaussian MAC, where the relay decodes the XOR of the two messages using the naturally-occurring sum of symbols simultaneously transmitted by user nodes. In this work, we consider the Gaussian MAC in bidirectional relaying with an additional secrecy constraint for protection against a honest but curious relay. The constraint is that, while the relay should decode the XOR, it should be fully ignorant of the individual messages of the users. We exploit the symbol addition that occurs in a Gaussian MAC to design explicit strategies that achieve perfect independence between the received symbols and individual transmitted messages. Our results actually hold for a more general scenario where the messages at the two user nodes come from a finite Abelian group, and the relay must decode the sum within the group of the two messages. We provide a lattice coding strategy and study optimal rate versus average power trade-offs for asymptotically large dimensions.