.svg){kind=logo}
LIST DECODING OF GOPPA CODES IN STEGANOGRAPHY
Keywords:
steganography, error-correcting codes, Goppa codes, list-decoding, digital communications, finite fieldsDOI:
https://doi.org/10.17654/0972555526002Abstract
Matrix encoding (or syndrome coding) represents a general coding theory process applied on steganographic schemes to reduce distortion during embedding and improve embedding efficiency and security. The disruption of statistic properties of the cover object is not considerable when a smaller number of embedding changes occur, and the steganographic security of schemes utilizing matrix embedding seems to be better. As a result, embedding efficiency, which is the number of bits integrated on the number of changes introduced into the cover-object, has become a very important parameter in the field of steganography. In this article, we propose a new steganographic scheme by investigating the possibility of remotely transferred hidden information and subsequently increasing the embedding efficiency, and extending steganography construction and error correcting code. In this approach, we utilize the list-decoding algorithm up to the Johnson radius for binary Goppa codes to hide a message in a cover image. We evaluate the embedding efficiency of our approach, and then use it to compare our method with the previous works and the theoretical upper bound.
References
[1] R. Crandall, Some notes on steganography, 1998. Available at
http://os.inf.tu-dresden.de/westfeld/crandall.pdf.
[2] A. Westfeld, High capacity despite better steganalysis (F5 – A steganographic algorithm), Lecture Notes in Comput. Sci., Vol. 2137, Springer-Verlag, 2001, pp. 289-302.
[3] R. Zhang, V. Sanchev and H. J. Kim, Fast BCH syndrome coding for steganography, S. Katzenbeisser and A.-R. Sadeghi, eds., Information Hiding 2009, IH’2009, LNCS 5806, Springer-Verlag, Berlin, Heidelberg, 2009, pp. 48-58.
[4] Y. Kim, Z. Duric and D. Richards, Modified matrix encoding technique for minimal distortion steganography, J. L. Camenisch, C. S. Collberg, N. F. Johnson and P. Sallee, eds., IH 2006, LNCS, Vol. 4437, 2007, pp. 314-327.
[5] C. Fontaine and F. Galand, How Reed-Solomon codes can improve steganographic schemes, EURASIP Journal on Information Security 2009 (2009), Article ID 274845. doi:10.1155/2009/274845.
[6] C. Munuera, Steganography and error-correcting codes, Signal Processing 87 (2007), 1528-1533.
[7] W. Zhang and S. Li, A coding problem in steganography, Designs, Codes and Cryptography 46(1) (2008), 67-81.
[8] H. Rifïà-Pous and J. Rifïà, Product perfect codes and steganography, Digtal Signal Processing 19(4) (2009), 764-769.
[9] Madhu Sudan, Decoding of Reed-Solomon codes beyond the error-correction bound, Journal of Complexity 13(1) (1997), 180-193.
[10] Peter Elias, Error-correcting codes for list decoding, Information Theory, IEEE Transactions on 37(1) (1991), 5-12.
[11] V. Guruswami and M. Sudan, Improved decoding of Reed-Solomon and algebraic geometry codes, Information Theory, IEEE Transactions on 45(6) (1999), 1757-1767.
[12] D. Augot, M. Barbier and A. Couvreur, List-decoding of binary Goppa codes up to the binary Johnson bound, IEEE, ITW’11, 2011.
[13] H. J. Highland, Data encryption: a non-mathematical approach, Comput. Secur. 16 (1997), 369-386.
[14] H. Jouhari and E. M. Souidi, A novel embedding scheme based on Walsh Hadamard transform, Journal of Theoretical and Applied Information Technology 32 (2011), 55-60.
[15] V. Guruswami, List Decoding of Error-Correcting Codes, Winning Thesis of the 2002 ACM Doctoral Dissertation Competition, Volume 3282 of Lectures Notes in Computer Science, Springer, 2004.
Downloads
Published
Issue
Section
License
Copyright (c) 2025 PUSHPA PUBLISHING HOUSE, PRAYAGRAJ, INDIA
This work is licensed under a Creative Commons Attribution 4.0 International License.
_________________________________
Attribution: Credit Pusha Publishing House as the original publisher, including title and author(s) if applicable.
Non-Commercial Use: For non-commercial purposes only. No commercial activities without explicit permission.
No Derivatives: Modifying or creating derivative works not allowed without written permission.
Contact Pusha Publishing House for more info or permissions.
