Strong Secrecy for Erasure Wiretap Channels

Abstract

We show that duals of certain low-density parity-check (LDPC) codes, when used in a standard coset coding scheme, provide strong secrecy over the binary erasure wiretap channel (BEWC). This result hinges on a stopping set analysis of ensembles of LDPC codes with block length $n$ and girth $\ge 2k$, for some $k\ge 2$. We show that if the minimum left degree of the ensemble is $l_{\min }$, the expected probability of block error is $\calO(\frac{1}{n^{\lceil l_\mathrm{min} k /2 \rceil - k}})$ when the erasure probability $\epsilon <{\epsilon }_{\mathrm{ef}}$, where ${\epsilon }_{\mathrm{ef}}$ depends on the degree distribution of the ensemble. As long as $l_{\min }>2$ and $k>2$, the dual of this LDPC code provides strong secrecy over a BEWC of erasure probability greater than $1-{\epsilon }_{\mathrm{ef}}$.

Submitted to the Information Theory Workship (ITW) 2010, Dublin

References in corpus (1)

• Secure Nested Codes for Type II Wiretap Channels

Cited by in corpus (14)

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• Semantically Secure Lattice Codes for the Gaussian Wiretap Channel
• Strong Secrecy on the Binary Erasure Wiretap Channel Using Large-Girth LDPC Codes
• Filter Design with Secrecy Constraints: The MIMO Gaussian Wiretap Channel
• Coding for Cryptographic Security Enhancement using Stopping Sets
• Polynomial-Time, Semantically-Secure Encryption Achieving the Secrecy Capacity
• Performance Analysis and Design of Two Edge Type LDPC Codes for the BEC Wiretap Channel
• Physical-Layer Security over Correlated Erasure Channels
• Polar Coding for Secure Transmission in MISO Fading Wiretap Channels
• Multi-message Authentication over Noisy Channel with Secure Channel Codes
• Polar Coding for Achieving the Capacity of Marginal Channels in Nonbinary-Input Setting
• Secure Polar Coding for the Two-Way Wiretap Channel
• Secrecy Transmission on Block Fading Channels: Theoretical Limits and Performance of Practical Codes
• On the Construction of Polar Codes for Achieving the Capacity of Marginal Channels