Generalization and analysis of the paper folding method for steganography

Authors:
Weiming Zhang;Jiufen Liu;Xin Wang;Nenghai Yu
Affiliations:
School of Information Science and Technology, University of Science and Technology of China, Hefei, China;Department of Information Research, Zhengzhou Information Science and Technology Institute, Zhengzhou, China;Department of Information Research, Zhengzhou Information Science and Technology Institute, Zhengzhou, China;School of Information Science and Technology, University of Science and Technology of China, Hefei, China
Venue:
IEEE Transactions on Information Forensics and Security
Year:
2010

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Abstract

Wet paper codes (WPCs) are designed for steganography, in which the sender and recipient do not need to share the changeable positions. In this paper, we propose the N-page construction for wet paper coding, which can generate a family of WPCs following the upper bound on embedding efficiency from one single WPC. The Paper Folding method, one of our previous methods, is a special case of the N-page construction with N = 2k. We deduce recursions for calculating embedding efficiency of N-page construction, and obtain explicit expression on embedding efficiency of 2k-page construction. Furthermore, we derive the limit of distance between the embedding efficiency of 2k -page construction and the upper bound of embedding efficiency as k tends to infinity. Based on the limit, we analyze how the embedding efficiency is influenced by the proportion of wet pixels (wet ratio) in the cover, showing that embedding efficiency only drops about 0.32 as the wet ratio increases to 0.9999.