The wiretap channel model, proposed by Wyner, has been studied by various authors from the perspectives of security, reliability and cryptographic protocols. A basic theme of these discussions has been information theoretically secure communication whose degree of secrecy can be theoretically proved. This paper explains a practical implementation of Euclidean Geometry (EG) - Low Density Parity Check (LDPC) codes for wiretap channels of type I and II. The focus has been on efficient encoding and decoding by taking advantage of the cyclic nature of EG codes. The generalized Hamming weights of EG codes can be bounded using those of primitive BCH codes. This provides security guarantees for EG codes in wiretap channels. The asymptotic threshold analysis from the LDPC viewpoint provides added guarantees at long blocklengths. Overall, EGLDPC codes are promising candidates for low-complexity coding over wiretap channels. ©2010 IEEE.

Andrew Edwin Thangaraj

Department of Electrical Engineering

BCH CODE

CRYPTOGRAPHIC PROTOCOLS

EFFICIENT ENCODING

EUCLIDEAN GEOMETRY

Generalized Hamming weight

LDPC CODES

LOW-COMPLEXITY

LOW-DENSITY PARITY-CHECK CODES

PRACTICAL IMPLEMENTATION

SECURE COMMUNICATIONS

THRESHOLD ANALYSIS

WIRETAP CHANNEL

Cryptography

Network protocols

Network security

Asymptotic analysis

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IIT Madras

EG-LDPC codes for the erasure wiretap channel

Proceedings of 16th National Conference on Communications, NCC 2010

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.

Fulltext

IEEE Transactions on Information Theory

Applications of LDPC codes to the wiretap channel

2008 46th Annual Allerton Conference on Communication, Control, and Computing

On the secrecy capacity of arbitrary wiretap channels

Low-density parity-check codes based on finite geometries: a rediscovery and new results

The capacity of low-density parity-check codes under message-passing decoding

On the generalized Hamming weights of cyclic codes

Journal	Proceedings of 16th National Conference on Communications, NCC 2010
Open Access	No