Correspondence between steganographic protocols and error correcting codes

Year 2017, Volume: 4 Issue: 2 (Special Issue: Noncommutative rings and their applications), 197 - 206, 10.01.2017

M’hammed Boulagouaz Mohamed Bouye

https://doi.org/10.13069/jacodesmath.284966

Abstract

In this work we present a correspondence between the steganographic systems and error correcting
codes. We propose a new steganographic protocol based on 3-error-correcting primitive BCH codes.
We show that this new protocol has much better parameters than protocols which we get from
Hamming codes or from the 2-error-correcting primitive BCH codes, for high levels of incorporation.

Keywords

Steganographic protocol, Hamming distance, Linear correcting code, Covering radius, Parity matrix, BCH code

References

• [1] E. Assmus, H. Mattson, Some 3–error–correcting BCH codes have covering radius 5, IEEE Trans. Inform. Theory 22(3) (1976) 348–349.
• [2] R. Crandall, Some notes on steganography, available at http://dde.binghamton.edu/download/ Crandall_matrix.pdf, 1998.
• [3] J. Fridrich, D. Soukal, Matrix embedding for large payloads, IEEE Trans. Inf. Forensics Security 1(3) (2006) 390–395.
• [4] T. Helleseth, All binary 3–error–correcting BCH codes of length $2^m-1$ have covering radius 5, IEEE Trans. Inform. Theory 24(2) (1978) 257–258.
• [5] J. van der Horst, T. Berger, Complete decoding of triple–error–correcting binary BCH Codes, IEEE Trans. Inform. Theory 22(2) (1976) 138–147.
• [6] F. J. Mac Williams, N. Sloane, The Theory of Error Correcting Codes, Amsterdam, Netherlands, North–Holland, 1966.
• [7] C. Munuera, Steganography and error–correcting codes, Signal Process. 87(6) (2007) 1528–1533.
• [8] A. Westfeld, F5—A Steganographic Algorithm, Lecture Notes in Comput. Sci. 2137 (2001) 289–302.