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A coding problem in steganography

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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 ≥ 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.

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Authors and Affiliations

  1. Department of Information Research, Information Engineering University, Zhengzhou, 450002, China

    Weiming Zhang & Shiqu Li

  2. School of Communication and Information Engineering, Shanghai University, Shanghai, 200076, China

    Weiming Zhang

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  1. Weiming Zhang
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  2. Shiqu Li
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Correspondence to Weiming Zhang.

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Communicated by P. Wild.

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Zhang, W., Li, S. A coding problem in steganography. Des. Codes Cryptogr. 46, 67–81 (2008). https://doi.org/10.1007/s10623-007-9135-9

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  • DOI: https://doi.org/10.1007/s10623-007-9135-9

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