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) 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 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.

Introduction

Divide image into two parts: Key:

a transparency Cipher:

a printed page Separately, they are

random noise Combination reveals an

image

Simple example

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 [nxm] Boolean matrix S = [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.

Pixels are split:Pixels are split:

mm

n n shares per pixel: per pixel:

mm

nn

Share 1

Share 2

Share n

Pixel Subpixels

si,j

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 1 0a

Model

dVH )(

amdVH )(

mm

mm

: V: V

H(V)H(V)

H(V) H(V) m mBB

H(V) H(V) m mWW

mmWW < m < mBB

contrast = (mcontrast = (mBB-m-mWW)/m)/m

Stacking

Model: Stacking & Contrast

Model

General k out of k Scheme Matrix size = k x 2k-1 S0 : handles the white pixels

All 2k-1 columns have an even number of 1’sNo two k rows are the same

S1 : handles the black pixelsAll 2k-1 columns have an odd number of 1’sNo two k rows are the same

C0/C1 : all the permutation of columns in S0/S1

2 out of n Scheme

m = nm = n White pixel - a random column-permutation of:White pixel - a random column-permutation of:

Black pixel - a random column-permutation of:Black pixel - a random column-permutation of:

0001

0001

0001

0001

1000

0100

0010

0001

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.

2 out of 2 Scheme (2 subpixels)

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



Example:


+

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 toSolid blackHalf 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

}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


Horizontal shares Vertical shares Diagonal shares



share1

share2

stack

pixel

4

1

0

5

random

0 1 2 3 4 5 0 1 2 3 4 5


With same 2 x 2 array (4 subpixel) layout

0110

0101

0011C0={ 24 matrices obtained by permuting the columns of }

1001

1010

1100C1={ 24 matrices obtained by permuting the columns of }

0011 1100 0101 1010 0110 1001

horizontal shares vertical shares diagonal shares

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

1100

1100

1100

1100

1100

1100

C0={ 24 matrices obtained by permuting the columns of }

C1={ 24 matrices obtained by permuting the columns of }

0110

0011

0101

1001

1010

1100

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

Extensions - Four Gray Levels

Each pixel encoded asA 3x3 cell3 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

Share #1 Share #2 Stacked Color

White

Gray

Black

Extensions - Grey Scale Encryption

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 methodFor 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 regions are left black.

Four subpixels

Four regions

CombinedOne pixel on four- color image


Verheul and van Tilborg’s method


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 Pattern2Combined

ResultCombined

Result


Applications

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

References

Naor and Shamir, Visual Cryptography, in Advances 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

Visual Cryptography

Technology

scheme share

subpixels black

black subpixels

white subpixels

subpixels original share

c subpixels

pixel subpixels s i

black pixels