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ThinkMind // INTERNET 2012, The Fourth International Conference on Evolving Internet // View article internet_2012_4_10_90007


Maximum Likelihood Decoding Algorithm for Some Goppa and BCH Codes: Application to the Matrix Encoding Method for Steganography

Authors:
Thierry P. Berger
Mohamed Bouye Medeni

Keywords: Steganography; Error-correcting Codes; Complete Decoding; Goppa Codes; Embedding Efficient

Abstract:
The idea of ”Matrix encoding” was introduced in steganography by Crandall in 1998. The implementation was then proposed by Westfeld with steganography algorithm F5. Matrix encoding using linear codes (syndrome coding) is a general approach to improving embedding efficiency of steganographic schemes. The covering radius of the code corresponds to the maximal number of embedding changes needed to embed any message. Steganographers, however, are more interested in the average number of embedding changes rather than the worst case. In fact, the concept of embedding efficiency - the average number of bits embedded per embedding change - has been frequently used in steganography to compare and evaluate performance of steganographic schemes. The aim of this paper is to transform some algebraic decoding algorithms up to the error correcting capacity into a maximum likelihood decoder by the use of a limited exhaustive search. This algorithm is directly inspired from those proposed by N. Courtois, M. Finiasz, and N. Sendrier in the context of electronic signature. It remains exponential, however it becomes practicable for for some small BCH and Goppa codes (typically, with an error correcting capacity until 4).

Pages: 85 to 89

Copyright: Copyright (c) IARIA, 2012

Publication date: June 24, 2012

Published in: conference

ISSN: 2308-443X

ISBN: 978-1-61208-204-2

Location: Venice, Italy

Dates: from June 24, 2012 to June 29, 2012

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