Modules over rings of characteristic 2 and its application to maximality of secret data ratio in CPTE schemes - Thanh, Nguyễn Hải; Huy, Phan Trung (Journal of Computer Science and Cybernetics, 2012)
Based on the ring of integers modulo 2r, 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 =<span lang="VI" style="color: black; font-family: Symbol; font-size: 10pt; mso-bidi-font-weight: bold; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman"; mso-char-type: symbol; mso-symbol-font-family: Symbol;">ëlog2(q+1)<span lang="VI" style="color: black; font-family: Symbol; font-size: 10pt; mso-bidi-font-weight: bold; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman"; mso-char-type: symbol; mso-symbol-font-family: Symbol;">û secret bits by changing at most two entries of F, where q=m.n . As shown, the highest number of embedded secret bits for at most two bits to be changed in each block of q positions of F in any CPT-based schemes is rmax=<span lang="VI" style="color: black; font-family: Symbol; font-size: 10pt; mso-bidi-font-weight: bold; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman"; mso-char-type: symbol; mso-symbol-font-family: Symbol;">ëlog2(1+q(q+1)/2)<span lang="VI" style="color: black; font-family: Symbol; font-size: 10pt; mso-bidi-font-weight: bold; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman"; mso-char-type: symbol; mso-symbol-font-family: Symbol;">û, approximately 2r-1. In this paper we introduce a CPTE scheme based on modules over the ring of characterisctic 2 such as Z2 which permits ratio of secret data to be reached approximately rmax, twice as much as CPT asymptotically.