Secure Compute-and-Forward in a Bidirectional Relay

Abstract

We consider the basic bidirectional relaying problem, in which two users in a wireless network wish to exchange messages through an intermediate relay node. In the compute-and-forward strategy, the relay computes a function of the two messages using the naturally-occurring sum of symbols simultaneously transmitted by user nodes in a Gaussian multiple access (MAC) channel, and the computed function value is forwarded to the user nodes in an ensuing broadcast phase. In this paper, we study the problem under an additional security constraint, which requires that each user's message be kept secure from the relay. We consider two types of security constraints: perfect secrecy, in which the MAC channel output seen by the relay is independent of each user's message; and strong secrecy, which is a form of asymptotic independence.We propose a coding scheme based on nested lattices, the main feature of which is that given a pair of nested lattices that satisfy certain "goodness" properties, we can explicitly specify probability distributions for randomization at the encoders to achieve the desired security criteria. In particular, our coding scheme guarantees perfect or strong secrecy even in the absence of channel noise. The noise in the channel only affects reliability of computation at the relay, and for Gaussian noise, we derive achievable rates for reliable and secure computation. We also present an application of our methods to the multi-hop line network in which a source needs to transmit messages to a destination through a series of intermediate relays.

Towards an algebraic network information theory: Simultaneous joint typicality decoding

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Perfect Secrecy in Physical-Layer Network Coding Systems From Structured Interference

“…In essence, the structured interference observed by the relay can be exploited to achieve strong secrecy in the wireless transmissions [25], [26]. In [26]- [29] the role of interference in achieving strong secrecy was demonstrated using lattice encoders; however [27] and [28] rely on the use of random dithering and good nested lattice codes in arbitrarily high dimensions. In the wiretap channel studied in [29] the superposition of the interference to the data was viewed as a modulo addition operation, i.e., the superposition was assumed to take place in the code space and not in the signal space.…”

Lattice Gaussian Sampling by Markov Chain Monte Carlo: Bounded Distance Decoding and Trapdoor Sampling

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