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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
INTRODUCTION

What is Cryptography ?

Plain Text/image    Encryption     Cipher



Plain Text /image     Decryption     Channel
TYPES OF CRYPTOGRAPHY:
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)
2 OUT OF 2 SCHEME (4 SUB PIXELS)

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
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
3 OUT OF 3 SCHEME (4 SUB PIXELS)




   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.
Visual cryptography1
Visual cryptography1
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 cryptography1
Visual cryptography1
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 .
Visual cryptography1
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.
Visual cryptography1
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
Visual cryptography1
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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Visual cryptography1

  • 1. CONTENTS  INTRODUCTION TO CRYPTOGRAPHY  INTRODUCTION TO VISUAL CRYPTOGRAPHY  OVERVIEW OF VISUAL CRYPTOGRAPHY  TYPES OF VISUAL CRYPTOGRAPHY  ADVANTAGES  DISADVANTAGES  APPLICATIONS  CONCLUSION  REFERENCES
  • 2. INTRODUCTION What is Cryptography ? Plain Text/image Encryption Cipher Plain Text /image Decryption Channel
  • 4. 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
  • 5. 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.
  • 6. 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.
  • 7. OVERVIEW OF V.C Share1 Stacking the share reveals the secret Share2 Encryption Decryption
  • 8. 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
  • 9. 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
  • 10. 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
  • 11. 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.
  • 12. 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
  • 13. IMPLEMENTATION FIG 1
  • 14. 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;
  • 15. 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.
  • 17.  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.
  • 18. 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)
  • 19. 2 OUT OF 2 SCHEME (4 SUB PIXELS) 6 ways to place two black subpixels in the 2 x 2 square
  • 20. 2 out of 2 Scheme (4 subpixels) Horizontal shares Vertical shares Diagonal shares
  • 21. 2 out of 2 Scheme (4 sub pixels)
  • 22. pixel 0 1 2 3 4 5 0 1 2 3 4 5 share1 share2 stack 4 0 1 5 random
  • 23. 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
  • 24. 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
  • 25. 3 OUT OF 3 SCHEME (4 SUB PIXELS) Original Share 1 Share 2 Share 3 Share 1+2+3 Share 1+2 Share 2+3 Share 1+ 3
  • 26. 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
  • 27. 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.
  • 30. 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.
  • 31. 2) Creation of shares: Considering the case of (2,2)-VCS, the steps are:
  • 34. 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 .
  • 36. 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.
  • 38. 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
  • 40. 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.
  • 41. 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.
  • 42. 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
  • 43. 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.
  • 44. 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.
  • 45. 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