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August  2012, 6(3): 273-285. doi: 10.3934/amc.2012.6.273

Wet paper codes and the dual distance in steganography

1. 

Department of Applied Mathematics, University of Valladolid, Avda Salamanca SN, 47014 Valladolid, Castilla

2. 

Computer Science Laboratory, École Polytechnique, 91 128 Palaiseau CEDEX, INRIA Saclay, ÎIle de France

Received  March 2011 Revised  January 2012 Published  August 2012

In 1998 Crandall introduced a method based on coding theory to secretly embed a message in a digital support such as an image. Later, in 2005, 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 embedding solutions and point out the relationship between wet paper codes and orthogonal arrays.
Citation: Carlos Munuera, Morgan Barbier. Wet paper codes and the dual distance in steganography. Advances in Mathematics of Communications, 2012, 6 (3) : 273-285. doi: 10.3934/amc.2012.6.273
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show all references

References:
[1]

in "Transactions on Thirteenth IMA International Conference on Cryptography and Coding,'' Springer-Verlag, Berlin, Heidelberg, (2011), 244-258. Google Scholar

[2]

in "Transactions on Data Hiding and Multimedia Security III,'' Springer-Verlag, (2008), 1-22. doi: 10.1007/978-3-540-69019-1_1.  Google Scholar

[3]

J. Sys. Sci. Compl., 21 (2008), 191-208. doi: 10.1007/s11424-008-9103-0.  Google Scholar

[4]

Random Struc. Algor., 16 (2000), 209-232. doi: 10.1002/(SICI)1098-2418(200003)16:2<209::AID-RSA6>3.0.CO;2-1.  Google Scholar

[5]

R. Crandall, Some notes on steganography,, \url{http://os.inf.tu-dresden.de/ westfeld}, ().   Google Scholar

[6]

in "Information Hiding 9th International Workshop,'' Springer-Verlag, (2007), 130-144. Google Scholar

[7]

IEEE Trans. Signal Proc., 53 (2005), 3923-3935. doi: 10.1109/TSP.2005.855393.  Google Scholar

[8]

in "Proceedings of Information Hiding,'' Springer-Verlag, 2005. doi: 10.1007/b104759.  Google Scholar

[9]

in "Proceedings of the Forty-Third Annual Allerton Conference On Communication, Control and Computing,'' (2005), 1521-1538. Google Scholar

[10]

IEEE Trans. Inform. Forens. Secur., 1 (2006), 102-110. doi: 10.1109/TIFS.2005.863487.  Google Scholar

[11]

in "Proceedings of 1996 Tactical Communications Conference,'' (1996), 397-406. Google Scholar

[12]

Westview Press, New York, 1994. Google Scholar

[13]

Springer-Verlag, New York, 1999.  Google Scholar

[14]

Ph.D thesis, Espoo, Finland, 2006. Google Scholar

[15]

Cambridge University Press, Cambridge, 1999.  Google Scholar

[16]

North-Holland Publishing Co., Amsterdam, 1977.  Google Scholar

[17]

MinT, Online database for optimal parameters of $(t, m, s)$-nets, $(t, s)$-sequences, orthogonal arrays, linear codes, and OOAs,, available at \url{http://mint.sbg.ac.at/}, ().   Google Scholar

[18]

IEEE Trans. Inform. Theory, 40 (1994), 2092-2099. doi: 10.1109/18.340488.  Google Scholar

[19]

IRE Trans. Inform. Theory, 8 (1962), 58. doi: 10.1109/TIT.1962.1057670.  Google Scholar

[20]

in "Proceedings 8th ACM Workshop on Multimedia and Security,'' (2006), 214-223. Google Scholar

[21]

in "Proceedings 10th ACM Workshop on Information Hiding,'' Springer-Verlag, (2007), 145-158. Google Scholar

[22]

IEEE Trans. Inform. Theory, 39 (1993), 239-242. doi: 10.1109/18.179365.  Google Scholar

[23]

Congressus Numerantium, 92 (1993), 105-110.  Google Scholar

[24]

Algoritmica, 56 (2010), 605-620. doi: 10.1007/s00453-008-9192-0.  Google Scholar

[25]

IEEE Trans. Inform. Theory, 18 (1972), 825-826. doi: 10.1109/TIT.1972.1054904.  Google Scholar

[26]

Springer-Verlag, New York, 1982. Google Scholar

[27]

IEEE Trans. Inform. Theory, 37 (1991), 1412-1418. doi: 10.1109/18.133259.  Google Scholar

[28]

in "Proceedings 10th International Workshop on Information Hiding,'' Springer-Verlag, (2008), 60-71. Google Scholar

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