New Visual Secret Sharing Schemes With Non-Expansible Shadow Size Using Non-binary Sub Pixel

Ching-Nung YangYun-Hsiang LiangWan-Hsiang Chou

National Computer Symposium on Information security

Outline

介紹 NEVSS (Non-Expansible VSS) 介紹 Visual Cryptography 上的 Contrast 和 Security 結論

NEVSS vs. Conventional VSS

不同點 : 1. Addition “ADD” vs. Boolean “OR” 2. Non-Binary{W,G,B} vs. Binary{W,B} 3. Non-Expansible vs. Expansible

Non-Expansible Method

Original Image

Shadow Image I

-- A (2,2) NEVSS Scheme Example:

Shadow Image II

Non-Expansible Method

Pixel Value:

--0: white

--1: gray

--2: approximate black

--C0 is used to represent “white”.

--C1 is used to represent “black”.

可知 :

Shadow image: {white,gray}

target image: {white,gray,black}

-- A (2,2) NEVSS Scheme Example:

NEVSS--Contrast Definition-- a (2,2) NEVSS Scheme Example:

}1,1{)}0

1(),

1

0({

}2,0{)}1

1(),

0

0({

}0

1,

1

0{}{

}1

1,

0

0{},{

1,11

0,20,00

GG

GG

C

C

When stacking two shadows. The dominant color is “0” (white), because “0” is the biggest contrast among the colors “0”,”1”,”2” in λandγ. Pλand Pγare the probabilities of the dominant color in the set λandγrespectively. Now , Pλ=1/2, Pγ=0, the difference Pλ-Pγ=1/2, the holds the first and the second condition.

NEVSS--Security DefinitionWe randomly chooses one column matrix in C0 and C1. So for each shadow every pixel will be “0” (white) or “1” (gray) half and half, and one cannot see any thing from the shadow.

NEVSS

The major difference between two schemes is that our scheme uses non-binary operation and the conventional scheme uses Boolean operation.

他的結論

In this paper, we have presented new (2,2),(2,n), and (k,k) NEVSS schemes . However, the general method for constructing (k,n) NEVSS schemes may need the further studies.在 2001 年 , 提出動態式的 NEVSS

曾經

滄

海

難

為

水

我的結論

此篇論文 : Contrast and Security 不能兼顧

M. Naor and A. Shamir : 可同時兼顧 Contrast and Security 我認為我的論文也可同時兼顧 Contrast and Security

我的論文 Contrast : 已歸納在各個 scheme 中可擁有的最大 contrast, 也就是論文中的 T 值 Security : 由於 Shadow Image( 小學生 ) 和 Recovered Image( 高中生 ) 是處在 2個不同的 Grayleve 上 , 所以分享者最多只能知道 Recovered Image’s graylevel ( 國中生 , 高中生 , 大學生…… ) 必大於 Shadow Image.