Visual Cryptography

1
Visual Cryptography

• Given By
• Moni Naor
• Adi Shamir
• Presented By
• Anil Vishnoi
• (2005H103017)

2
Contents

• Introduction
• Terminology
• The Model
• Efficient Solution for Small K and n
• K out of K scheme
• K out of n Scheme
• Conclusion
• Reference

3
Introduction

• Cryptography
• Plain Text Encryption Cipher Text
• Plain Text Decryption Channel

4
Visual Cryptography

• Plaintext (in form of image)
• Encryption (creating shares)
• Channel (Fax, Email)
• Decryption (Human Visual System)

5
Example

• Secret Image
• Share1
• Stacking the share
• reveals the secret
• Share2

6
Encoding of Pixels

• Original Pixel
• Share1
• Share2
• overlaid
• Note White is actually transparent

7
Computer Representation of pixels

• Visual Cryptography scheme represented in
  computer using n x m Basis matrices
• Original Pixel
• share1
• s1 s0 share2
• overlaid Image

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(2,2) Model

• 1. Construct two 2x2 basis matrices as
• s0 1 0 s1 1 0
• 0 1 1 0
• 2.Using the permutated basis matrices, each pixel
  from the secret image will be encoded into two
  sub pixels on each participant's share. A black
  pixel on the secret image will be encoded on the
  ith participant's share as the ith row of matrix
  S1, where a 1 represents a black sub pixel and a
  0 represents a white sub pixel. Similarly, a
  white pixel on the secret image will be encoded
  on the ith participant's share as the ith row of
  matrix S0.

9
Cont..

• 3. Before encoding each pixel from the secret
  image onto each share, randomly permute the
  columns of the basis matrices S0 and S1
• 3.1 This VCS (Visual Cryptography Scheme)
  divides each pixel in the secret image into m2
  sub pixels.
• 3.2 It has a contrast of a(m)m1 and a relative
  contrast of a(m)1/2.

10

• Queries?

11
Conclusion
12
Terminology

• PixelPicture element
• Grey Level The brightness value assigned to a
  pixel values range from black, through gray, to
  white.
• Hamming Weight (H(V)) The number of non-zero
  symbols in a symbol sequence
• V- Vector of 1 and 1 of any length
• A qualified set of participants is a subset of ?
  whose shares visually reveal the 'secret' image
  when stacked together.
• A forbidden set of participants is a subset of ?
  whose shares reveal absolutely no information
  about the 'secret' image when stacked together.

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Visual Cryptography (cont..)

• Visual Cryptography is a secret-sharing method
  that encrypts a secret image into several shares
  but requires neither computer nor calculations to
  decrypt the secret image. Instead, the secret
  image is reconstructed visually simply by
  overlaying the encrypted shares the secret image
  becomes clearly visible
• A Visual Cryptography Scheme (VCS) on a set ? of
  n participants is a method of encoding a 'secret'
  image into n shares such that original image is
  obtained only by stacking specific combinations
  of the shares onto each other.

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Terminology (cont)

• The relative contrast (also called relative
  difference) of a VCS is the ratio of the maximum
  number of black sub pixels in a reconstructed
  (secret) white pixel to the minimum number of
  black sub pixels in a reconstructed (secret)
  black pixel. So, the lower the relative contrast
  in a scheme, the better. Note the smallest
  relative contrast attainable in a VCS is 1/2,
  which is only achieved in a (2,2)-threshold VCS
• The contrast of a VCS is the difference between
  the minimum number of black sub pixels in a
  reconstructed (secret) black pixel and the
  maximum number of black sub pixels in a
  reconstructed (secret) white pixel.

15
The Model

• A solution to the k out of n visual secret
  sharing scheme consists of two collections of n x
  m Boolean (Basis) matrices S0 and S1. To share a
  white pixel, the dealer randomly chooses one of
  the matrices in S0 , and to share a black pixel,
  the dealer randomly chooses one of the matrices
  in S1. The chosen matrix defines the color of the
  m sub pixels in each one of the n transparencies
  for a original pixel. The solution is considered
  valid if the following three conditions are met
  
• 1. For any S in S0 , the or'' V of any k of
  the n rows satisfies H(V ) lt d-a.m
• 2. For any S in S1 , the or'' V of any k of
  the n rows satisfies H(V ) d.
• n-Total Participant
• k-Qualified Participant

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The Model (cont)

• 3. For any subset i1 i 2 i q of 1
  2 n with q lt k, the two collections of q
  x m matrices Dt for t e 0,1 obtained by
  restricting each n x m matrix in Ct (where t 0
  1) to rows i1 i2 iq are indistinguishable
  in the sense that they contain the same matrices
  with the same frequencies.
• Condition 3 implies that by inspecting fewer than
  k shares, even an infinitely powerful
  cryptanalyst cannot gain any advantage in
  deciding whether the shared pixel was white or
• black.

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Advantage of Visual Cryptography

• Simple to implement
• Encryption dont required any NP-Hard problem
  dependency
• 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
• Infinite Computation Power cant predict the
  message.

18
Basis Matrices

• Basis matrices are binary n x m used to encrypt
  each pixel in the secret image, where n is the
  number of participants in the scheme and m is the
  pixel expansion. The following algorithm is used
  to implement a VCS using basis matrices
• If the n x m basis matrices S1 (used to encrypt
  black pixels) and S0 (used to encrypt white
  pixels) for any VCS are given, the secret image
  SI is encrypted as follows

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Basic Matrices (Cont..)

• for each pixel p in SI
• if (p is black) Let R a random permutation of
  the columns of S1
• else Let R a random permutation of the
  columns of S0
• for each participant i (1 lt i lt n)
• The position on participant is share that
  corresponds to p is expanded into m pixels where
  each of these pixels j (1 lt j lt m) is black if
  Ri,j 1 and white if Ri,j 0.