visual 999
TRANSCRIPT
-
8/6/2019 Visual 999
1/36
Visual Cryptography
UNDER THE GUIDENCE OF
B.NAGA RAJU sir
V.S.K.chaitanya(08NG1A1225)P.Durga rao (08NG1A1206)
P.Sai kavitha (08NG1A1224)
CH.snehith (08NG1A1233)
-
8/6/2019 Visual 999
2/36
Introduction Visual cryptography (VC) was introduced
by Moni NaorandAdi Shamirat
EUROCRYPT 1994.
It is used to encrypt written material
(printed text, handwritten notes, pictures,
etc) in a perfectly secure way. The decoding is done by the human visual
system directly, without any computation
cost.
-
8/6/2019 Visual 999
3/36
Introduction Divide image into two parts:
Key:
a transparency Cipher:
a printed page
Separately, they are randomnoise
Combination reveals animage
Simple example
-
8/6/2019 Visual 999
4/36
kout of
nsharing problem Extended to kout ofn sharing problem
For a set P ofn participants, a secret image S isencoded into n shadow images called shares
(shadows), where each participant in P receives oneshare.
The original message is visible if any k or more ofthem are stacked together, but totally invisible if
fewer than k transparencies are stacked together (oranalysed by any other method)
-
8/6/2019 Visual 999
5/36
Model
Assume the message consists of a collection ofblack and white pixels and each pixel is handledseparately.
Each share is a collection ofm black and whitesubpixels.
The resulting picture can be thought as a [nxm]Boolean matrixS = [si,j]
si,j = 1 if the j-th subpixel in the i-th share is black. si,j = 0 if the j-th subpixel in the i-th share is white.
-
8/6/2019 Visual 999
6/36
Pixels are split:Pixels are split:
mm
nn shares per pixel:per pixel:
mm
nn
Share 1
Share 2
Share n
Pixel Subpixels
si,j
Model
-
8/6/2019 Visual 999
7/36
Model
The grey level of the combined share is
interpreted by the visual system:
as black if
as white if .
is some fixed threshold and
is the relative difference.
H(V) is the hamming weight of the OR
combined share vector of rows i1,in in S
vector.
md ee1 0"a
dVH u)(
amdVH )(
-
8/6/2019 Visual 999
8/36
mm
mm
: V: V
H(V)H(V)
H(V)H(V) uu mmBB
H(V)H(V) mmWW
mmWW
-
8/6/2019 Visual 999
9/36
Model
-
8/6/2019 Visual 999
10/36
General kout ofkScheme
Matrix size = k x2k-1
S0 : handles the white pixels
All 2k-1 columns have an even number of 1s
No two krows are the same
S1 : handles the black pixels
All 2k-1 columns have an odd number of 1s No two krows are the same
C0/C1 : all the permutation of columns in S0/S1
-
8/6/2019 Visual 999
11/36
2 out of n Scheme
m = nm = n
White pixelWhite pixel -- a random columna random column--permutation of:permutation of:
Black pixelBlack pixel -- a random columna random column--permutation of:permutation of:
0001
0001
0001
0001
.
/1///
.
.
.
1000
0100
0010
0001
.
/1///
.
.
.
-
8/6/2019 Visual 999
12/36
2 out of 2 Scheme (2 subpixels)
Black and white image: each pixel
divided in 2 sub-pixels
Randomly choose between black andwhite.
If white, then randomly choose one of
the two rows for white.
-
8/6/2019 Visual 999
13/36
2 out of 2 Scheme (2 subpixels)
If black, then randomly choose between one of
the two rows for black.
-
8/6/2019 Visual 999
14/36
2 out of 2 Scheme (2 subpixels)
-
8/6/2019 Visual 999
15/36
2 out of 2 Scheme (2 subpixels)
Example:
-
8/6/2019 Visual 999
16/36
2 out of 2 Scheme (2 subpixels)
+
The two subpixels per pixel variant can
distort the aspect ratio of the original
image
-
8/6/2019 Visual 999
17/36
2 out of 2 Scheme (4 subpixels)
Each pixel encoded as
a 2x2 cell
in two shares (key and cipher)
Each share has 2 black, 2 transparent
subpixels
When stacked, shares combine to Solid black
Half black (seen as gray)
-
8/6/2019 Visual 999
18/36
2 out of 2 Scheme (4 subpixels)
6 ways to place two black subpixels in the 2 x 2
square
White pixel: two identical arrays
Black pixel: two complementary arrays
}1001
1001
0110
0110
1100
1100
0011
0011
1010
1010
0101
0101{0
!C
}
0110
1001
1001
0110
0011
1100
1100
0011
0101
1010
1010
0101{1
C
-
8/6/2019 Visual 999
19/36
Horizontal shares Vertical shares Diagonal shares
2 out of 2 Scheme (4 subpixels)
-
8/6/2019 Visual 999
20/36
2 out of 2 Scheme (4 subpixels)
-
8/6/2019 Visual 999
21/36
share1
share2
stack
pixel
4
1
0
5
random
0 1 2 3 4 5 0 1 2 3 4 5
-
8/6/2019 Visual 999
22/36
3 out of3 Scheme (4 subpixels)
With same 2 x2 array (4 subpixel) layout
0110
0101
0011
C0={ 24 matrices obtained by permuting the columns of }
1001
1010
1100
C1={ 24 matrices obtained by permuting the columns of }
0011 1100 0101 1010 0110 1001
horizontal shares vertical shares diagonal shares
-
8/6/2019 Visual 999
23/36
Original Share #1 Share #2 Share #3
Share
#1+#2+#3
Share #1+#2 Share #2+#3 Share #1+ #3
3 out of3 Scheme (4 subpixels)
-
8/6/2019 Visual 999
24/36
2 out of 6 Scheme
Any 2 or more shares out of the 6 produced
1100
1100
1100
1100
11001100
C0={ 24 matrices obtained by permuting the columns of }
C1={ 24 matrices obtained by permuting the columns of }
0110
0011
0101
1001
1010
1100
-
8/6/2019 Visual 999
25/36
Share#1 Share#2 Share#3 Share#4 Share#5 Share#6
2 shares 3 shares 4 shares 5 shares 6 shares
2 out of 6 Scheme
-
8/6/2019 Visual 999
26/36
Extensions - Four Gray Levels
Each pixel encoded as
A 3x3 cell
3 black, 6 transparent
Combine to 3, 4, 5, or 6 black
-
8/6/2019 Visual 999
27/36
Pixel range from 0 (white) to 255 (black)
Encode pixel with a half-circle
Share #1 Share #2 Stacked Color
White
Gray
Black
Extensions - Grey Scale Encryption
-
8/6/2019 Visual 999
28/36
Extensions - Continuous Gray level
Each pixel encoded as 33% black circle
Combine for any gray from 33% to 67% black
-
8/6/2019 Visual 999
29/36
Extensions - Extended VC
Ateniese et al., 2001
Send innocent looking transparencies, e.g. Send
images a dog, a house, and get a spy messagewith no trace.
-
8/6/2019 Visual 999
30/36
Extensions - Color VC
Verheul and van Tilborgs method
For a C-color image, we expand each pixel to C
subpixels on two images.
For each subpixel, we divide it to C regions. One
fixed region for one color.
If the subpixel is assigned color C1 , only the region
belonged to C1will have the color. Other regionsare left black.
-
8/6/2019 Visual 999
31/36
Four
subpixels
Four
regions
CombinedOne pixel on
four- color
image
Extensions - Color VC
Verheul and van Tilborgs method
-
8/6/2019 Visual 999
32/36
Extensions - Color VC
Rijmen and Preneels method
Each pixel is divided into 4 subpixels, with the color red,
green, blue and white.
In any order, we can get 24 different combination of colors.We average the combination to present the color.
To encode, choose the closest combination, select a
random order on the first share. According to the
combination, we can get the second share.
-
8/6/2019 Visual 999
33/36
Extensions - Color VC
Rijmen and Preneels method
Pattern1 Pattern1Pattern2 Pattern2Combined
Result
Combined
Result
-
8/6/2019 Visual 999
34/36
Extensions - Color VC
-
8/6/2019 Visual 999
35/36
Applications
Remote Electronic Voting
Anti-Spam Bot Safeguard
Banking Customer Identification Message Concealment
KeyManagement
-
8/6/2019 Visual 999
36/36
THANKYOU