Visual cryptography1

CONTENTS

 INTRODUCTION TO CRYPTOGRAPHY
 INTRODUCTION TO VISUAL CRYPTOGRAPHY
 OVERVIEW OF VISUAL CRYPTOGRAPHY
 TYPES OF VISUAL CRYPTOGRAPHY
 ADVANTAGES
 DISADVANTAGES
 APPLICATIONS
 CONCLUSION
 REFERENCES

INTRODUCTION

What is Cryptography ?

Plain Text/image Encryption Cipher

Plain Text /image Decryption Channel

VISUAL CRYPTOGRAPHY

What is Visual Cryptography ?

 Visual cryptography is a cryptographic technique which
allows visual information (pictures, text, etc.) to be
encrypted in such a way that the decryption can be
performed by the human visual system.

 Visual cryptography was pioneered by Moni Naor and
Adi Shamir in 1994

Suppose the data D is divided into n shares
 D can be constructed from any k shares out of n

 Complete knowledge of k-1 shares reveals no
information about D
 k of n shares is necessary to reveal secret data.

EXAMPLE

 6 thieves share a bank account
 They don’t trust one another
 The thieves split up the password for the account in such
a way that:
 Any 3 or more thieves working together can have access
to account, but NOT < 3.

OVERVIEW OF V.C
Share1

Stacking the share
reveals the secret

Share2

Encryption Decryption

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’s

 S1 : handles the black pixels
 All 2k-1 columns have an odd number of 1’s

BASIS MATRICES
 The two matrices S0,S1 are called basis matrices,
if the two collections C0,C1 as defines in [1] are
obtained by rearranging the columns of S0,S1
satisfy the following condition:

the row vectors V0,V1 obtained by performing
OR operation on rows i1,i2,…..iv of S0,S1
respectively, satisfy
ω(V0) ≤ tX - α(m). m and ω(V1) ≥ tX

 Where tx is the threshold to visually interpret pixel as
black or white.

tX = min(ω(V1(M)))

 α(m) is the contrast or relative difference

α(m) = {min(ω(V1(M))) - max(ω(V0(M)))} / m

Example: the basis matrices and the collections of the encoding
matrices in the conventional (2,2) scheme can be written as:

Here, the pixel expansion is m=2. For any matrix M ∈ C0, the row
vector V0= OR (r1,r2) satisfies ω(V0) =1. For any M ∈ C1, the row
vector V1= OR (r1,r2) satisfies ω(V1) =2.

The threshold is given by:

tX = min(ω(V1(M))) = 2

Having a relative difference:

α(m) = {min(ω(V1(M))) - max(ω(V0(M)))} / m = 1/2

IMPLEMENTATION

FIG 1

 A pixel P is split into two sub pixels in each of the two
shares.
• If P is white, then a coin toss is used to randomly choose
one of the first two rows in the figure above.
• If P is black, then a coin toss is used to randomly choose
one of the last two rows in the figure above.
 Then the pixel P is encrypted as two sub pixels in each
of the two shares, as determined by the chosen row in the
figure. Every pixel is encrypted using a new coin toss.
 Now let's consider what happens when we superimpose
the two shares.
• If P is black, then we get two black sub pixels when we
superimpose the two shares;

 If P is white, then we get one black sub pixel and one white
sub pixel when we superimpose the two shares.
 Thus, we can say that the reconstructed pixel (consisting of
two sub pixels) has a grey level of 1 if P is black, and a grey
level of 1/2 if P is white. There will be a 50% loss of contrast
in the reconstructed image, but it is still visible.

EXAMPLE OF TWO-OUT-OF-TWO VC SCHEME:

 The secret image (a) is encoded into (b) & (c) two
shares and
 (d ) is decoded by superimposing these two shares with
50% loss of contrast.
 The decoded image is identified, although some contrast
loss is observed.
 Due to pixel expansion the width of the decoded image is
twice as that of the original image.

2 OUT OF 2 SCHEME (4 SUB PIXELS)
 Each pixel encoded as
 a 2x2 cell
 in two shares
 Each share has 2 black, 2 white sub pixels
 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

2 out of 2 Scheme (4 subpixels)

Horizontal shares Vertical shares Diagonal shares

2 out of 2 Scheme (4 sub pixels)

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

share1

share2

stack

4 0
1 5

random

2 OUT OF 6 SCHEME
 Any 2 or more shares out of the 6 are required to decrypt
the image.

Share1 Share2 Share3 Share4 Share5 Share6

2 shares 3 shares 4 shares 5 shares 6 shares


 With same 2 x 2 array (4 sub pixel) layout
 All of the three shares are required to decrypt the image.

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

TYPES OF VISUAL CRYPTOGRAPHY
o Halftone visual cryptography

o Colour visual cryptography

o Visual Cryptography with Perfect Restoration

o Multiresolution Visual Cryptography

o Progressive Multiresolution Visual
Cryptography

HALFTONE VISUAL CRYPTOGRAPHY
 A halftone image is made up of a series of dots rather than a
continuous tone.
 These dots can be different sizes, different colors, and sometimes
even different shapes.
 Larger dots are used to represent darker, more dense areas of the
image, while smaller dots are used for lighter areas.

COLOUR VISUAL CRYPTOGRAPHY
1) Color half toning:
we can do the color channel splitting first and then do
the grayscale half toning for each channel

or we can do the colour half toning first followed by the
splitting.

2) Creation of shares:
Considering the case of (2,2)-VCS, the steps are:

VISUAL CRYPTOGRAPHY WITH PERFECT
RESTORATION

 The half toning method degrades the quality of the
original image.
 In this technique both gray and colour images are
encoded without degradation.
 It retains the advantages of traditional visual
cryptography.
 Here the stacking operation involves only XOR ing .

MULTIRESOLUTION VISUAL
CRYPTOGRAPHY

 In traditional (k;n) visual cryptography, we only
construct an image of single resolution if the threshold k
number of shares are available.

 Progressive visual cryptography scheme in which we not
only build the reconstructed image by stacking the
threshold number of shares together, but also utilize the
other shares to enhance the resolution of the final image.

PROGRESSIVE MULTIRESOLUTION VISUAL
CRYPTOGRAPHY

 In PMRVCS, the shares are ordered and merged in such
a way that as more shares are used, the bigger is the
spatial resolution of the reconstructed image.
 A (n,n)-PMRVCS is defined as follows:

Let I be the original image, S0,S1…Sn are the shares
created. For k =1,2...,n-1, image Ik can be reconstructed
by merging S0,S1…….Sk

ADVANTAGES

 Simple to implement
 Decryption algorithm not required (Use a human Visual System).
So a person unknown to cryptography can decrypt the message.
 We can send cipher text through FAX or E-MAIL
 Lower computational cost since the secret message is recognized
only by human eyes and not cryptographically computed.

DISADVANTAGES

 The contrast of the reconstructed image is not
maintained.
 Perfect alignment of the transparencies is troublesome.

 Its original formulation is restricted only to binary
images. For coloured images additional processing has to
be done.

APPLICATIONS

 Biometric security
 Watermarking

 Steganography

 Printing and scanning applications

 Bank customer identification
 Bank sends customer a set of keys in advance
 Bank web site displays cipher
 Customer applies overlay, reads transaction key
 Customer enters transaction key

CONCLUSION
 Among various advantages of Visual Cryptography
Schemes is the property that VCS decoding relies purely
on human visual system, which leads to a lot of
interesting applications in private and public sectors of
our society.
 Visual Cryptography is used with short messages,

therefore giving the cryptanalyst little to work with.
 It can be used with other data hiding techniques to
provide better security.

 Since Visual Cryptography uses short message,
public keys can be encrypted using this method. Visual
Cryptography has proved that security can be attained
with even simple encryption schemes.

REFERENCES

 Zhongmin Wang, Arce, G.R., Di Crescenzo, G., "Halftone Visual
Cryptography Via Error Diffusion", Information Forensics and
Security, IEEE Transactions on, On page(s): 383 - 396 Volume: 4,
Issue: 3, Sept. 2009
 Z. Zhou , G. R. Arce and G. Di Crescenzo "Halftone visual
cryptography", IEEE Trans. Image Process., vol. 15, pp.2441
2006
 ”Progressive visual cryptography”, Duo Jin, Wei-Qi Yan, Mohan S.
Kankanhalli , SPIE Journal of Electronic Imaging (JEI/SPIE) on
Nov.15, 2003, revised on Oct.26, 2004.
 “Security of a Visual Cryptography Scheme for Color Images”, Bert
W. Leung, Felix Y. Ng, and Duncan S. Wong, Department of
Computer Science, City University of Hong Kong, Hong Kong,
China

Visual cryptography1

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