Reversible data hiding using reference points coding

A Two-Dimensional mKdV Linear Map and Its Application in Digital Image Cryptography

“…where α ∈ R. Thus, for all n ∈ N, the solution for Equation (12) lies in a level set of H(x, y : α).…”

“…Then, we focused on dynamics and bifurcations of the 2-dimensional mKdV map. Consider the two-dimensional mKdV map in Equation (12). The dynamics of mapping…”

“…Consider the two-dimensional mKdV map in Equation (12). The dynamics of mapping h α,1,1 is contained in the level sets of H(x, y : α).…”

“…. Now, we can use λ max (x 0 , y 0 ) to acquire the maximum LE for 2D nonlinear mKdV map in Equation (12). For α = −9.79 and the fixed point (x * , y * ) = (2.5571, 2.5571), we have…”

“…Two of the techniques were proposed in 2017 in [10,11]. In [11], the authors proposed an algorithm that involves scrambling pixel positions and changing the intensities of the pixels (see [12] for a different method in hiding an image using reference point coding to embed data in the spatial domain). In this article, a two-dimensional linear map derived from a partial discrete equation (partial discrete mKdV equation) with Consistency Around the Cube (CAC) properties will be discussed (see [13,14] for the construction of a generalized mKdV map and the investigation of its properties) and applied in cryptographic encoding algorithms for digital image data (see [15] for digital text data).…”