Secret Sharing LDPC Codes for the BPSK-constrained Gaussian Wiretap Channel

TL;DR

This paper proposes a secret sharing scheme over a BPSK-constrained Gaussian wiretap channel using LDPC codes, achieving asymptotic key capacity and practical finite-length code designs.

Contribution

It introduces a novel secret sharing scheme employing LDPC codes tailored for BPSK-constrained Gaussian channels, including both regular and irregular code designs.

Findings

Regular LDPC codes achieve asymptotic key capacity.

Irregular LDPC codes are designed for finite block lengths.

The scheme ensures secure key sharing despite public channel observations.

Abstract

The problem of secret sharing over the Gaussian wiretap channel is considered. A source and a destination intend to share secret information over a Gaussian channel in the presence of a wiretapper who observes the transmission through another Gaussian channel. Two constraints are imposed on the source-to-destination channel; namely, the source can transmit only binary phase shift keyed (BPSK) symbols, and symbol-by-symbol hard-decision quantization is applied to the received symbols of the destination. An error-free public channel is also available for the source and destination to exchange messages in order to help the secret sharing process. The wiretapper can perfectly observe all messages in the public channel. It is shown that a secret sharing scheme that employs a random ensemble of regular low density parity check (LDPC) codes can achieve the key capacity of the BPSK-constrained Gaussian wiretap channel asymptotically with increasing block length. To accommodate practical constraints of finite block length and limited decoding complexity, fixed irregular LDPC codes are also designed to replace the regular LDPC code ensemble in the proposed secret sharing scheme.