On the Maximality of Secret Data Ratio in CPTE Schemes

Abstract

Based on the ring of integers modulo 2^r, Chen-Pan-Tseng (2000) introduced a block-based scheme (CPT scheme) which permits in each block F of size m ×n of a given binary image B to embed $r =\lfloor {\rm log}_2(k+1)\rfloor$. secret bits by changing at most two entries of F, where k = mn. As shown, the highest number of embedded secret bits for at most two bits to be changed in each block of k positions of F in any CPT-based schemes is rmax = $\lfloor {\rm log}_2(1+k (k+1)/2)\rfloor$, approximately 2r-1, twice as much as r asymptotically, and this can reached approximately in our CPTE1 scheme by using modules on the ring Z ₂ of integers modulo 2. A new modified scheme-CPTE2 to control the quality of the embedded blocks, in the same way as Tseng-Pan’s method (2001), is established. Approximately, CPTE2 scheme gives 2r-2 embedded bits in F, twice as much as r-1 bits given by Tseng-Pan’ scheme, while the quality is the same.