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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)

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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.

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Introduction Divide image into two parts:

Key:

a transparency Cipher:

a printed page

Separately, they are randomnoise

Combination reveals animage

Simple example

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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)

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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.

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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

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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 )(

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mm

mm

: V: V

H(V)H(V)

H(V)H(V) uu mmBB

H(V)H(V) mmWW

mmWW

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Model

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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

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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///

.

.

.

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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.

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If black, then randomly choose between one of

the two rows for black.

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Example:

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+

The two subpixels per pixel variant can

distort the aspect ratio of the original

image

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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)

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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

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Horizontal shares Vertical shares Diagonal shares


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share1

share2

stack

pixel

4

1

0

5

random

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

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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


0011 1100 0101 1010 0110 1001

horizontal shares vertical shares diagonal shares

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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)

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2 out of 6 Scheme

Any 2 or more shares out of the 6 produced

1100

1100

1100

1100

11001100



0110

0011

0101

1001

1010

1100

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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

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Extensions - Four Gray Levels

Each pixel encoded as

A 3x3 cell

3 black, 6 transparent

Combine to 3, 4, 5, or 6 black

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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

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Extensions - Continuous Gray level

Each pixel encoded as 33% black circle

Combine for any gray from 33% to 67% black

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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.

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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.

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Four

subpixels

Four

regions

CombinedOne pixel on

four- color

image


Verheul and van Tilborgs method

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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.

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Rijmen and Preneels method

Pattern1 Pattern1Pattern2 Pattern2Combined

Result

Combined

Result

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Applications

Remote Electronic Voting

Anti-Spam Bot Safeguard

Banking Customer Identification Message Concealment

KeyManagement

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THANKYOU

Visual 999

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