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.

Andrew Edwin Thangaraj

Department of Electrical Engineering

Safitha J. Raj

CODING METHODS

Information transfers

PER-SYMBOL

WIRETAP CHANNEL

Data processing

TURBO CODES

IIT Madras is a public technical and research university located in Chennai, Tamil Nadu. Founded in 1959, it is recognised as an Institute of National Importance.

IIT Madras has been ranked as the top engineering institute in India for four years in a row by the National Institutional Ranking Framework of the MHRD

It currently offers undergraduate, postgraduate and research degrees across 16 disciplines in Engineering, Sciences, Humanities and Management. About 596 faculty belonging to science and engineering departments and centres of the Institute are engaged in teaching, research and industrial consultancy.

IIT Madras

Strong and weak secrecy in wiretap channels

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

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.

Fulltext

2010 IEEE Information Theory Workshop, ITW 2010 - Proceedings

Strong secrecy for erasure 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	6th International Symposium on Turbo Codes and Iterative Information Processing, ISTC 2010
Open Access	No