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Advances in Mathematics of Communications (AMC)
 

$\mathbb{Z}_2\mathbb{Z}_4$-additive perfect codes in Steganography

Pages: 425 - 433, Volume 5, Issue 3, August 2011      doi:10.3934/amc.2011.5.425

 
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Helena Rifà-Pous - Department of Computer Science and Multimedia, Universitat Oberta de Catalunya, 08018-Barcelona, Spain (email)
Josep Rifà - Department of Information and Communications Engineering, Universitat Autònoma de Barcelona, 08193-Bellaterra, Spain (email)
Lorena Ronquillo - Department of Information and Communications Engineering, Universitat Autònoma de Barcelona, 08193-Bellaterra, Spain (email)

Abstract: Steganography is an information hiding application which aims to hide secret data imperceptibly into a cover object. In this paper, we describe a novel coding method based on $\mathbb{Z}_2\mathbb{Z}_4$-additive codes in which data is embedded by distorting each cover symbol by one unit at most ($\pm 1$-steganography). This method is optimal and solves the problem encountered by the most efficient methods known today, concerning the treatment of boundary values. The performance of this new technique is compared with that of the mentioned methods and with the well-known rate-distortion upper bound to conclude that a higher payload can be obtained for a given distortion by using the proposed method.

Keywords:  Steganography, $\mathbb{Z}_2\mathbb{Z}_4$-additive perfect codes.
Mathematics Subject Classification:  Primary: 68P30; Secondary: 94A60, 94B60.

Received: May 2010;      Revised: March 2011;      Available Online: August 2011.

 References