Clever Geek Handbook

Generalized visual cryptography algorithm

Spoiler

If you don't have time to read everything, after describing the classic scheme, you can go straight to the section on the practical application of visual cryptography.





Introduction

Consider a visual cryptography scheme proposed by Moni Naoru and Adi Shamir [2, 3]. The main idea of ​​the scheme is that two plates are generated to transmit the secret image, each separately looking like white noise and carrying no information about the secret image. To decode a message, it is enough to superimpose two plates on top of each other. Thus, the decoding process does not require any special equipment. The material is taken from the article "Generalized Visual Cryptography Scheme with Completely Random Shares". [one]





Although the plates look like white noise, the sequence of pixels that make up them is not statistically random, since, based on the circuit design, each plate contains an equal number of white and black pixels. The article proposes to generalize the scheme in such a way that both plates will not only look random, but will also pass statistical tests for randomness.





Terms

In the process of coding one plate called the base , which is generated by a secret image independently, the other - the coding . The coding plate is a function of the secret image and the base plate.





Each pixel of the secret image corresponds to nxn pixels that form a tile. The base plate and the coding plate are formed from the tiles. In our case, the tile will be 2 x 2. We will refer to the base plate tile as the base tile and the coding plate tile as the coding tile. The base plate is generated from randomly selected tiles. Examples of 2 x 2 tiles with all sorts of combinations of black and white pixels can be seen in Figure 1.





Figure 1: 2x2 squares with every possible mix of white and black pixels
Figure 1: 2x2 squares with every possible mix of white and black pixels

Classic scheme

. , , . , . 2.





Figure 2: Demonstration of overlapping squares during decoding
2:

- 2 x 2, 2 , 2 . , , 2 x 2, , - .





, 3.





Figure 3: Secret image to be encoded across 2 plates
3: , 2

, , , . .





4a. .





Figure 4: (a) classical algorithm (b) random (c) almost random
4: (a) (b) (c)

, . 5; .





Figure 5: (a) classical algorithm (b) random (c) almost random
5: (a) (b) (c)

, , . , . c , . .





, 16 ( 1). , . . 5b. , , .





4b. , . , , . , . , , . , , 2 x 2, 2 x 2. -2 . : -1. . +, , . +1 +2 . , . . .





. -2 , , 1 1. -1 , , 2, 3, 5 9, . .





  1. .





  2. .





, 1 5c. , , , 5b. , 4c, , , 4b. - 1 . , , .





. 1 ( ). , ( 7).





2 , . , 6, . , . , , - 2 . , , , , 5d. , , .





Figure 6: The shadow of classified information is visible
6:

. , , , 5a, 5b, . , , , .





, 1. , . P- . , , . , . . 4 8 . , , .





Table 1: Results of randomness tests for coding and base plates.
1: .

. 7, , : 7a, 7b, - 1 7c, - 2 7d.





Figure 7: distribution of tiles in coding
7:

, , - 1 , 7c, 1/15 ( , ), 1. 1 ( ) , 16 ( ) .





. 2. , , . . - 1 , .





Table 2: Dispersion of tile spawn rate
2:

, . , 16 6 . , 1 . , . , , .





, , , . - 1 .





. , , . -2, -1 - , +1, +2 . 8. (a) - , (b) - 1, (c) - 2.





Figure 8: Visualization of decoding errors
8:

, . 1 .





.





  • " - ." [4]



    : - , 16 . , . , , . .





  • " ." [5]



    : . , . , - , . . , , . , . , . RGB (2, 2).





  • , - . " ". [6]



    : (, ), , . , , . ( ), , , ; .





  • - ( - ). " - ad-hoc ". [7]



    : (MANET) , , , (WSN), , , , . - , , . - . , . , (2, 2). , - . - , , , . . -, . , , . (FP) .





. . - , , . , . , . , , , . , , . , , .





  1. : Orłowski A., and Chmielewski L. J. "Generalized Visual Cryptography Scheme with Completely Random Shares"





  2. M. Naor and A. Shamir. 1995. Visual Cryptography





  3. M. Naor and A. Shamir. 1997. Visual Cryptography II





  4. Orłowski A., and Chmielewski L. J. Randomness of Shares Versus Quality of Secret Reconstruction in Black-and-White Visual Cryptography





  5. Orłowski A., and Chmielewski L. J. Color Visual Cryptography with Completely Randomly Coded Colors





  6. Arun Ross, Asem A Othman Visual Cryptography for Biometric Privacy





  7. Vimal Kumar, Rakesh Kumar Detection of phishing attack using visual cryptography in ad hoc network











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