Visual Cryptography

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contents

• INTRODUCTION to cryptography
• INTRODUCTION to visual cryptography
• Overview of visual cryptography
• Types of visual cryptography
• Advantages
• disadvantages
• APPLICATIONS
• CONCLUSION
• REFERENCES

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INTRODUCTION

• What is Cryptography ?
• Plain Text/image Encryption
  Cipher
• Plain Text /image Decryption Channel

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TYPES OF CRYPTOGRAPHY
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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

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• 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.

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• EXAMPLE
• 6 thieves share a bank account
• They dont 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 lt 3.

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• OVERVIEW OF V.C
• Share1
• Stacking the share
• reveals the secret
• Share2
• Encryption Decryption

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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 1s
• S1 handles the black pixels
• All 2k-1 columns have an odd number of 1s

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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
• ?(V0) tX - ??(m)? m and ?(V1) tX

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• Where tx is the threshold to visually interpret
  pixel as black or white.
• tX min(?(V1(M)))
• ?(m) is the contrast or relative difference
• ?(m) min(?(V1(M))) - max(?(V0(M)))
  ? m

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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 m2. For any matrix
M ? C0, the row vector V0 OR (r1,r2) satisfies
?(V0) 1. For any M ? C1, the row vector V1 OR
(r1,r2) satisfies ?(V1) 2.
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The threshold is given by
tX min(?(V1(M))) 2 Having a relative
difference ?(m) min(?(V1(M))) -
max(?(V0(M))) ? m 1/2

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IMPLEMENTATION
FIG 1
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• 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

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• 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.
  

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EXAMPLE OF TWO-OUT-OF-TWO VC SCHEME
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• 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.

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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)

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2 out of 2 Scheme (4 sub pixels)

• 6 ways to place two black subpixels in the 2 x 2
  square

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2 out of 2 Scheme (4 subpixels)
Horizontal shares
Vertical shares
Diagonal shares
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2 out of 2 Scheme (4 sub pixels)
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pixel
0
1
2
3
4
5
0
1
2
3
4
5
share1
share2
stack
random
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2 out of 6 Scheme

• Any 2 or more shares out of the 6 are required to
  decrypt the image.

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3 out of 3 Scheme (4 sub pixels)

• 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
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3 out of 3 Scheme (4 sub pixels)
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Types of visual cryptography

• Halftone visual cryptography
• Colour visual cryptography
• Visual Cryptography with Perfect Restoration
• Multiresolution Visual Cryptography
• Progressive Multiresolution Visual Cryptography

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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.

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Colour visual cryptography

• 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.

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

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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
  .

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Multiresolution Visual Cryptography

• In traditional (kn) 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.

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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,S1Sn are the
  shares created. For k 1,2...,n-1, image Ik can
  be reconstructed by merging S0,S1.Sk

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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.

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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.

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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

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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.

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• 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.

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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

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Thank you