Steganographic Codes -- a New Problem of Coding Theory

TL;DR

This paper introduces steganographic codes, a new coding problem for efficient data hiding, and explores their algebraic structure, bounds, and relation to error-correcting codes, providing a foundation for future steganography research.

Contribution

It defines steganographic codes over finite fields, proposes a construction method, and establishes bounds and classifications linking them to perfect error-correcting codes.

Findings

Maximum length embeddable (MLE) codes are identified.

A relation between MLE codes and perfect error-correcting codes is established.

Lower bounds on the number of binary MLE codes are derived.

Abstract

To study how to design 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 $q(q\ge2)$ elements. Firstly a method of constructing linear stego-codes is proposed by using the direct sum of vector subspaces. And then the problem of linear stego-codes is converted to an algebraic problem by introducing the concept of $t$th dimension of vector space. And some bounds on the length of stego-codes are obtained, from which the maximum length embeddable (MLE) code is brought up. 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.