RT - Journal Article
T1 - On the Pixel Expansion of Hypergraph Access Structures in Visual Cryptography Schemes
JF - IJMSI
YR - 2010
JO - IJMSI
VO - 5
IS - 2
UR - http://ijmsi.ir/article-1-140-en.html
SP - 45
EP - 54
K1 - visual cryptography
K1 - secret sharing scheme
K1 - hypergraph
K1 - basis matrices
K1 - pixel expansion.
AB - In a visual cryptography scheme, a secret image is encoded into n shares, in the form of transparencies. The shares are then distributed to n participants. Qualified subsets of participants can recover the secret image by superimposing their transparencies, but non-qualified subsets of participants have no information about the secret image. Pixel expansion, which represents the number of subpixels in the encoding of the secret image, should be as small as possible. Optimal schemes are those that have the minimum pixel expansion. In this paper we study the pixel expansion of hypergraph access structures and introduce a number of upper bounds on the pixel expansion of special kinds of access structures. Also we demonstrate the minimum pixel expansion of induced matching hypergraph is sharp when every qualified subset is exactly one edge with odd size. Furthermore we explain that the minimum pixel expansion of every graph access structure $P_{n}$ is exactly $lceil frac{ n+1}{2}rceil$. It indicates the lower bound mentioned in [4] is sharp.
LA eng
UL http://ijmsi.ir/article-1-140-en.html
M3 10.7508/ijmsi.2010.02.005
ER -