Visual CryptoGraphy

-- Pallavi Khandekar

What is VC?

• Secret sharing scheme.

• Visual Cryptography (VC) was introduced by Moni Naor and Adi Shamir in Eurocrypt (1994).

• Used to encrypt written text/ pictures etc in a perfectly secure way.

• Decoding is done by human visual system, without any computation.

Secret Sharing Scheme

• Method of dividing a secret amongst a group of participants.

• Each of the participants get a share of the secret.

• Sufficient number of shares combined reveals the secret.

Share 1

Share 2

Share 1 +Share 2

Example - k by n Scheme (k,n)

• Consider data D (text / image) divided into – n number of shares (D1, D2 …. Dn)– k or more shares when overlapped reveals information

about the data– k-1 or fewer shares when overlapped reveal no

information about the data

• If k = n then all participants are required to reconstruct the secret.

Preliminary Notations

• n = Group size

• k = Threshold

• m = number of pixels in a share. (loss in resolution from the original image to the recovered image)

• ɑ = the relative difference in the weight between the combined shares that come from a white pixel and a black pixel in the original image. Represents loss in contrast.

Preliminary Notations (contd..)

• C0 = Collection of n × m Boolean matrices for shares of white pixel.

• C1 = Collection of n × m Boolean matrices for shares of black pixel.

• V = ORed k rows.

• H(V) = Hamming weight.

• d = number in [1,m]

Example 2 by 2 scheme (2 subpixels)

Partition for black and white pixels in 2 by 2scheme.

Example 2 by 2 scheme (2 subpixels)

• n = 2

• m = 2

• k = 2

• V0 = [0,1] or [1,0]

This scheme can be explained by below values

• V1 = [1,1] or [1,1]

• H(V0 ) = 1

• H(V1) = 2

• ɑ = H(V1) - H(V0 ) / m = 1/2

Implementation• Platform: .Net Framework 3.5

• Language: C#

• Reason for selecting .Net:– Previous experience working on .Net.– It is optimal for developing and demonstrating application through UI.– .NET also has lot of support for image acquisition and manipulation.

• Other Platforms: Matlab, Python etc

DEMO

Technique Used

0 01 1

S0

S1

S0

S1

White Pixel Black Pixel

Results for Text

Results for Image

Result for Image (contd..)

2 by 2 scheme with 4 sub pixels

Horizontal shares Vertical shares Diagonal shares

Results in 2 by 2 scheme (2 subpixels)

• The secret image I is encoded into Share1 & Share2 two shares.

• D is decoded by superimposing these two shares with 50% loss of contrast. (ɑ = ½)

• 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.

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.

• Due to pixel expansion the width of the decoded image is twice as that of the original image. Leads to loss of information due to change in aspect ratio.

• Additional processing is required for colored images.

Application• Biometric security

• Watermarking

• Steganography

• Remote electronic voting

• 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

References

• http://en.wikipedia.org/wiki/File:Visual_crypto_animation_demo.gif

• http://users.telenet.be/d.rijmenants/en/visualcrypto.htm

• http://www.cs.nccu.edu.tw/~raylin/UndergraduateCourse/ComtenporaryCryptography/Spring2009/VisualCrypto.pdf

Thank you!

Questions?