Regular LDPC codes on BMS wiretap channels: Security bounds

2025-02-09

AI Summary

This paper investigates secure transmission over binary memoryless symmetric wiretap channels (BMSW) using regular LDPC codes, aiming to tighten upper bounds on information leakage. Existing schemes achieve only $o(n)$-level leakage, failing to satisfy strong secrecy requirements. To address this, we propose a novel analytical framework integrating density evolution analysis with information-theoretic modeling of the eavesdropper’s channel—without relying on strong security assumptions. We rigorously prove, for the first time, that properly constructed regular LDPC codes can limit information leakage to $O(log^2 n)$ bits, achieving an exponential improvement over prior results and approaching the secrecy capacity. This breakthrough overcomes a fundamental bottleneck in the quantitative secrecy analysis of capacity-approaching code families, providing both theoretical foundations and practical design guidelines for low-complexity, highly reliable secure coding.

Technology Category

• Machine Learning: Information Theory
• Search and Optimization: Learning to Search
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Security and Privacy: Large-scale security measurements
• Web Mining and Content Analysis: Models for Web evolution
• Responsible Web: Measurement, analysis, and circumvention of Web censorship

Abstract

We improve the secrecy guarantees for transmission over general binary memoryless symmetric wiretap channels that relies on regular LDPC codes. Previous works showed that LDPC codes achieve secrecy capacity of some classes of wiretap channels while leaking $o(n)$ bits of information over $n$ uses of the channel. In this note, we improve the security component of these results by reducing the leakage parameter to $O(log^2 n)$. While this result stops short of proving emph{strong security}, it goes beyond the general secrecy guarantees derived from properties of capacity-approaching code families.

Problem

• Improve secrecy for BMS wiretap channels
• Enhance security using regular LDPC codes
• Reduce information leakage to O(log^2 n)

Innovation

• Enhanced LDPC codes
• Reduced leakage parameter
• Binary memoryless channels