Modules Over Rings of Small Characteristics and Maximality of Data Hiding ratio in CPTE Schemes

Introduced CPT scheme as a block-based hiding scheme based on the ring of the integers modulo 2^r, which permits to embed r = ⌊log₂(k+1)⌋ secret bits in F by changing at most two entries, while the highest number of secret bits in any CPT-based schemes is MSDR₂ = ⌊log₂(1+k (k+1)/2)⌋, approximately 2r-1. This ratio can be reached approximately in our proposed CPTE1 scheme by using modules on the ring Z₂ of integers modulo 2, as an instance of application of modules over rings of small characteristics. As a consequence, a new modified scheme-CPTE2 is to control the quality of stego-images. The CPTE2 scheme gives 2r-2 embedded bits approximately, more than r-2 bits by Tseng-Pan’s scheme, while the quality is the same.