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) 2 out of 2 Scheme (4 subpixels) 3 out of 3 Scheme 2 out of 6 Scheme Extensions Applications References

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)

2 out of 2 Scheme (4 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.

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

Divide image into two parts:

Key:

a transparency

Cipher:

a printed page

Separately, they are random noise

Combination reveals an image

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

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)

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.

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

Pixels are split:

n shares per pixel:

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

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.

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

Model

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

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:

m = n

White pixel - a random column-permutation of:

Black pixel - a random column-permutation of:

2 out of 2 Scheme (2 subpixels) 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.

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.

2 out of 2 Scheme (2 subpixels) If black, then randomly choose between one of the two rows for black.

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

2 out of 2 Scheme (2 subpixels)

2 out of 2 Scheme (2 subpixels) Example:

Example:

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

The two subpixels per pixel variant can distort the aspect ratio of the original image

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)

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 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

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

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

3 out of 3 Scheme (4 subpixels) 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

With same 2 x 2 array (4 subpixel) layout

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 }

Any 2 or more shares out of the 6 produced

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

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

Pixel range from 0 (white) to 255 (black)

Encode pixel with a half-circle

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

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  

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 - 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

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.

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

Verheul and van Tilborg ’s method

Extensions - Color VC 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

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.

Extensions - Color VC Rijmen and Preneel ’s method Pattern1 Pattern1 Pattern2 Pattern2 Combined Result Combined Result

Rijmen and Preneel ’s method

Extensions - Color VC

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

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

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

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