Constructing Good Covering Codes for Applications in Steganography

Product perfect codes and steganography

“…The definition of covering codes and the relations between covering codes and steganography were studied in [1], where it is described the good performance of some covering codes used in steganography.…”

“…Remember that for a Hamming code [n, n − t], where n = 2 t − 1, it is easy to compute the embedding rate t/n = t 2 t −1 and the average distortion R a /n = 1/2 t (see (1), where ρ = 1 and a 1 = n).…”

Asymptotic Behavior of the ZZW Embedding Construction

“…By inspecting this construction for the Hamming code H 1 , which corresponds to the trivial embedding method that embeds one bit in one pixel using on average Figure 1. This family outperforms all known embedding schemes constructed from structured covering codes (both linear and non-linear [1]) designed to have a small covering radius to bound the worst case of the number of embedding changes. Code families of sparse random constructions [4] follow the bound even closer.…”

“…By mapping the individual pixels of the cover to elements of a finite field, for example, by associating a bit (or q-ary symbol from finite field F q ) with each pixel value 1 , one can formulate the problem of maximizing embedding efficiency within the framework of coding theory [3], [8]. In particular, it is known that a q-ary linear code C with length n, dimension k, parity check matrix H, and covering radius R can be used to communicate n − k q-ary symbols (or (n − k) lg q bits) in a cover consisting of n elements by making at most R changes in the following manner.…”

“…The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies, either expressed or implied, of AFOSR or the U. S. Government. Jessica Fridrich is Professor at the Department of Electrical and Computer Engineering, Binghamton University, NY 13902 USA (607-777-6177; fax: 607-777-4464; e-mail: fridrich@binghamton.edu) 1 A popular way is to use the least significant bit of the pixel value or, in general, the modulo q operation.…”