Remainder with Threshold Substitution Data Hiding Scheme: Counterexamples and Modification
Keywords:
Data hiding scheme, Remainder with threshold substitution, Cover Image, Pixel, Secret Embedding, Secret ExtractionAbstract
A well-known data hiding scheme, Remainder with Threshold substitution (RT), is analyzed. RT uses a threshold value, T, and two moduli numbers, m_u, and m_l, m_l<m_u, to embed secret data into a cover image. RT does not impose any divisibility constraints on the selection of the parameters, T, m_u, and m_l, and its correctness (i.e., the data extracted are always the same as the data embedded) is not proved. By counterexamples constructing, we show that RT works for them incorrectly. Also, RT scheme uses pseudo-random number generator (PRNG) to define a pixel for embedding of the next secret bit portion. PRNG can produce repeated values leading to the repeated embedding into the same pixel, thus overwriting previously embedded secret and preventing its correct extraction. We modify RT scheme (by imposing divisibility constraints on the threshold, moduli values, and PRNG), and prove correctness of the modification. Note that in the reported experiments on RT, its parameters used, T=160, and (m_l, m_u) from {(4, 8), (16, 32)}, exactly satisfy our constraints, and, thus, the scheme may be correct for such settings.
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