We show that duals of certain low-density paritycheck (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 ≥ 2k, for some k ≥ 2. We show that if the minimum left degree of the ensemble is lmin, the expected probability of block error is O(1/n[lmink/2]-k) when the erasure probability ε &lt; εef, where εef depends on the degree distribution of the ensemble. As long as lmin &gt; 2 and k &gt; 2, the dual of this LDPC code provides strong secrecy over a BEWC of erasure probability greater than 1-εef. © 2010 IEEE.

Andrew Edwin Thangaraj

Department of Electrical Engineering

BLOCK ERRORS

BLOCK LENGTHS

Coding scheme

DEGREE DISTRIBUTIONS

LDPC CODES

STOPPING SET

WIRETAP CHANNEL

Codes (symbols)

Coding errors

Error correction

Probability

Channel coding

Fulltext

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IIT Madras

2010 IEEE Information Theory Workshop, ITW 2010 - Proceedings

The renewed interest for physical-layer security techniques has put forward a new role for error-control codes. In addition to ensuring reliability, carefully designed codes have been shown to provide a level of information-theoretic secrecy, by which the amount of information leaked to an adversary may be controlled. The ability to achieve information-theoretic secrecy relies on the study of alternative coding mechanisms, such as channel resolvability and privacy amplification, in which error-control codes are exploited as a means to shape the distribution of stochastic processes. This use of error-control codes, which goes much beyond that of correcting errors, creates numerous new design challenges. The objective of this paper is threefold. First, the paper aims at providing system engineers with explicit tools to build simple secrecy codes in order to stimulate interest and foster their integration in communication system prototypes. Second, it aims at providing coding and information theorists with a synthetic overview of the theoretical concepts and techniques for secrecy. Finally, it aims at highlighting the open challenges and opportunities faced for the integration of these codes in practical systems. © 2015 IEEE.

Proceedings of the IEEE

Error-Control Coding for Physical-Layer Secrecy

For an arbitrary degree distribution pair (DDP), we construct a sequence of low-density parity-check (LDPC) code ensembles with girth growing logarithmically in block-length using Ramanujan graphs. When the DDP has minimum left degree at least three, we show using density evolution analysis that the expected bit-error probability of these ensembles, when passed through a binary erasure channel with erasure probability ε , decays as O(exp (-c 1nc2)) with the block-length n for positive constants c1 and c2 , as long as ε is less than the erasure threshold εth of the DDP. This guarantees that the coset coding scheme using the dual sequence provides strong secrecy over the binary erasure wiretap channel for erasure probabilities greater than 1-εth. © 2011 IEEE.

IEEE Transactions on Information Forensics and Security

Strong secrecy on the binary erasure wiretap channel using large-girth LDPC codes

In the wiretap channel model, symbols transmitted through a main channel to a legitimate receiver are observed by an eavesdropper across a wiretapper's channel. The goal of coding for wiretap channels is to facilitate error-free decoding across the main channel, while ensuring zero information transfer across the wiretapper's channel. Strong secrecy requires the total information transfer to the eavesdropper to tend to zero, while weak secrecy requires the per-symbol information transfer to go to zero. In this paper, we will consider coding methods for binary wiretap channels with a noiseless main channel and a BEC or a BSC wiretapper's channel. We will provide conditions and codes that achieve strong and weak secrecy for the BEC case. For the BSC case, we will discuss some existing coding methods and develop additional criteria for secrecy. © 2010 IEEE.

6th International Symposium on Turbo Codes and Iterative Information Processing, ISTC 2010

Strong and weak secrecy in wiretap channels

With the advent of quantum key distribution (QKD) systems, perfect (i.e., information-theoretic) security can now be achieved for distribution of a cryptographic key. QKD systems and similar protocols use classical error-correcting codes for both error correction (for the honest parties to correct errors) and privacy amplification (to make an eavesdropper fully ignorant). From a coding perspective, a good model that corresponds to such a setting is the wire tap channel introduced by Wyner in 1975. In this correspondence, we study fundamental limits and coding methods for wire tap channels. We provide an alternative view of the proof for secrecy capacity of wire tap channels and show how capacity achieving codes can be used to achieve the secrecy capacity for any wiretap channel. We also consider binary erasure channel and binary symmetric channel special cases for the wiretap channel and propose specific practical codes. In some cases our designs achieve the secrecy capacity and in others the codes provide security at rates below secrecy capacity. For the special case of a noiseless main channel and binary erasure channel, we consider encoder and decoder design for codes achieving secrecy on the wiretap channel; we show that it is possible to construct linear-time decodable secrecy codes based on low-density parity-check (LDPC) codes that achieve secrecy. © 2007 IEEE.

Journal	2010 IEEE Information Theory Workshop, ITW 2010 - Proceedings
Open Access	Yes