Visual Cryptography

Visual Cryptography (OR) Reading Between the Lines Ecaterina Valică http://students.info.uaic.ro/~evalica/

Agenda
Introduction
k out of n sharing problem
Model
General k out of k Scheme
2 out of n Scheme
2 out of 2 Scheme (2 subpixels)
3 out of 3 Scheme
2 out of 6 Scheme
Extensions
Applications
References

Introduction
Visual cryptography (VC) was introduced by Moni Naor and Adi Shamir at EUROCRYPT 19 94 .
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.

Introduction
Divide image into two parts:
Key:
a transparency
Cipher:
a printed page
Separately, they are random noise
Combination reveals an image
Simple example

Extended to k out of n sharing problem
For a set P of n participants, a secret image S is encoded into n shadow images called shares (shadows), where each participant in P receives one share.
The original message is visible if any k or more of them are stacked together, but totally invisible if fewer than k transparencies are stacked together (or analysed by any other method)
k out of n sharing problem

Model
Assume the message consists of a collection of black and white pixels and each pixel is handled separately.
Each share is a collection of m black and white subpixels.
The resulting picture can be thought as a [ n x m ] Boolean matrix S = [s i,j ]
s i,j = 1 if the j-th subpixel in the i-th share is black.
s i,j = 0 if the j-th subpixel in the i-th share is white.

Model
Pixels are split:
Pixel Subpixels s i,j m
n shares per pixel:
m n Share 1 Share 2 Share n

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 i 1 ,…i n in S vector.
Model

Stacking Model: Stacking & Contrast m m : V H(V) H(V)  m B H(V)  m W m W < m B contrast = (m B -m W )/m

General k out of k Scheme
Matrix size = k x 2 k-1
S 0 : handles the white pixels
All 2 k -1 columns have an even number of 1’s
No two k rows are the same
S 1 : handles the black pixels
All 2 k -1 columns have an odd number of 1’s
No two k rows are the same
C 0 /C 1 : all the permutation of columns in S 0 /S 1

2 out of n Scheme
m = n
White pixel - a random column-permutation of:
Black pixel - a random column-permutation of:

Black and white image: each pixel divided in 2 sub-pixels
Randomly choose between black and white.
If white, then randomly choose one of the two rows for white.

If black, then randomly choose between one of the two rows for black.

Example:

2 out of 2 Scheme (2 subpixels) +
The two subpixels per pixel variant can distort the aspect ratio of the original image

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)

6 ways to place two black subpixels in the 2 x 2 square
White pixel: two identical arrays
Black pixel: two complementary arrays

Horizontal shares Vertical shares Diagonal shares 2 out of 2 Scheme (4 subpixels)

share1 share2 stack pixel random 0 1 2 3 4 5 0 1 2 3 4 5 4 1 0 5

With same 2 x 2 array (4 subpixel) layout
C 0 ={ 24 matrices obtained by permuting the columns of } C 1 ={ 24 matrices obtained by permuting the columns of } 0011 1100 0101 1010 0110 1001 horizontal shares vertical shares diagonal shares

3 out of 3 Scheme (4 subpixels) Original Share #1 Share #2 Share #3 Share #1+#2+#3 Share #1+#2 Share #2+#3 Share #1+ #3

2 out of 6 Scheme
Any 2 or more shares out of the 6 produced
C 0 ={ 24 matrices obtained by permuting the columns of } C 1 ={ 24 matrices obtained by permuting the columns of }

2 out of 6 Scheme Share#1 Share#2 Share#3 Share#4 Share#5 Share#6 2 shares 3 shares 4 shares 5 shares 6 shares

Extensions - Four Gray Levels
Each pixel encoded as
A 3x3 cell
3 black, 6 transparent
Combine to 3, 4, 5, or 6 black

Pixel range from 0 (white) to 255 (black)
Encode pixel with a half-circle
Extensions - Grey Scale Encryption Share #1 Share #2 Stacked Color White Gray Black

Extensions - Continuous Gray level
Each pixel encoded as 33% black circle
Combine for any gray from 33% to 67% black

Ateniese et al., 2001
Send innocent looking transparencies, e.g. Send images a dog, a house, and get a spy message with no trace.
Extensions - Extended VC  

Extensions - Color VC
Verheul and van Tilborg ’s 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 C 1 , only the region belonged to C 1 will have the color. Other regions are left black.

Verheul and van Tilborg ’s method
Four subpixels Four regions Combined One pixel on four- color image

Rijmen and Preneel ’s 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.

Rijmen and Preneel ’s method
Pattern1 Pattern1 Pattern2 Pattern2 Combined Result Combined Result

Applications
Remote Electronic Voting
Anti-Spam Bot Safeguard
Banking Customer Identification
Message Concealment
Key Management

References
Naor and Shamir, Visual Cryptography, in A dvances in Cryptology - Eurocrypt ‘94
www.cacr.math.uwaterloo.ca/~dstinson/visual.html
http://homes.esat.kuleuven.be/~fvercaut/talks/visual.pdf
http:// www.cse.psu.edu/~rsharris/visualcryptography/viscrypt.ppt

References
http://netlab.mgt.ncu.edu.tw/computersecurity/2002/ppt/%E5%BD%A9%E8%89%B2%E8%A6%96%E8%A6%BA%E5%AF%86%E7%A2%BC%E5%8F%8A%E5%85%B6%E6%87%89%E7%94%A8.ppt
http://163.17.135.4/ imgra /PPT/200500022.ppt

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Visual Cryptography

by Ecaterina Valica

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