Wet paper codes and the dual distance in steganography

TL;DR

This paper analyzes the success conditions of wet paper codes in steganography using coding theory, specifically focusing on the dual distance of codes, and extends the results to systematic codes and orthogonal arrays.

Contribution

It provides necessary and sufficient conditions for successful embedding in wet paper codes based on dual distance, generalizes results to systematic codes, and explores their connection to orthogonal arrays.

Findings

Derived conditions for guaranteed embedding success

Extended analysis to systematic codes

Connected wet paper codes with orthogonal arrays

Abstract

In 1998 Crandall introduced a method based on coding theory to secretly embed a message in a digital support such as an image. Later Fridrich et al. improved this method to minimize the distortion introduced by the embedding; a process called wet paper. However, as previously emphasized in the literature, this method can fail during the embedding step. Here we find sufficient and necessary conditions to guarantee a successful embedding by studying the dual distance of a linear code. Since these results are essentially of combinatorial nature, they can be generalized to systematic codes, a large family containing all linear codes. We also compute the exact number of solutions and point out the relationship between wet paper codes and orthogonal arrays.