Iranian Journal of Mathematical Sciences and Informatics
مجله علوم ریاضی و انفورماتیک
IJMSI
Basic Sciences
http://ijmsi.ir
1
admin
1735-4463
2008-9473
8
10.52547/ijmsi
14
8888
13
en
jalali
1389
8
1
gregorian
2010
11
1
5
2
online
1
fulltext
en
On the Pixel Expansion of Hypergraph Access Structures in Visual Cryptography Schemes
عمومى
General
پژوهشي
Research paper
<p>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.</p>
visual cryptography, secret sharing scheme, hypergraph, basis matrices, pixel expansion.
45
54
http://ijmsi.ir/browse.php?a_code=A-10-1-84&slc_lang=en&sid=1
Abbas
Cheraghi
`10031947532846002145`

10031947532846002145
Yes