A coding problem in steganography

Authors:
Weiming Zhang;Shiqu Li
Affiliations:
Department of Information Research, Information Engineering University, Zhengzhou, China 450002 and School of Communication and Information Engineering, Shanghai University, Shanghai, China 200076;Department of Information Research, Information Engineering University, Zhengzhou, China 450002
Venue:
Designs, Codes and Cryptography
Year:
2008

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Abstract

To study how to design a steganographic algorithm more efficiently, a new coding problem--steganographic codes (abbreviated stego-codes)--is presented in this paper. The stego-codes are defined over the field with q(q 驴 2) elements. A method of constructing linear stego-codes is proposed by using the direct sum of vector subspaces. And the problem of linear stego-codes is converted to an algebraic problem by introducing the concept of the tth dimension of a vector space. Some bounds on the length of stego-codes are obtained, from which the maximum length embeddable (MLE) code arises. It is shown that there is a corresponding relation between MLE codes and perfect error-correcting codes. Furthermore the classification of all MLE codes and a lower bound on the number of binary MLE codes are obtained based on the corresponding results on perfect codes. Finally hiding redundancy is defined to value the performance of stego-codes.