Polar Coding for Secret-Key Generation

TL;DR

This paper introduces polar coding schemes that jointly optimize reliability and secrecy for secret-key generation across various models, achieving capacity with low complexity and broad applicability.

Contribution

It proposes the first low-complexity, secret-key capacity-achieving polar coding schemes for multiple models, including vector quantization and multiterminal communication.

Findings

Achieves secret-key capacity for several models.

Works with non-degraded sources without secret seeds.

Applies to biometric system secrecy and privacy.

Abstract

Practical implementations of secret-key generation are often based on sequential strategies, which handle reliability and secrecy in two successive steps, called reconciliation and privacy amplification. In this paper, we propose an alternative approach based on polar codes that jointly deals with reliability and secrecy. Specifically, we propose secret-key capacity-achieving polar coding schemes for the following models: (i) the degraded binary memoryless source (DBMS) model with rate-unlimited public communication, (ii) the DBMS model with one-way rate-limited public communication, (iii) the 1-to-m broadcast model and (iv) the Markov tree model with uniform marginals. For models (i) and (ii) our coding schemes remain valid for non-degraded sources, although they may not achieve the secret-key capacity. For models (i), (ii) and (iii), our schemes rely on pre-shared secret seed of negligible rate; however, we provide special cases of these models for which no seed is required. Finally, we show an application of our results to secrecy and privacy for biometric systems. We thus provide the first examples of low-complexity secret-key capacity-achieving schemes that are able to handle vector quantization for model (ii), or multiterminal communication for models (iii) and (iv).