XOR-Based Visual Cryptography - Visual Cryptography and Secret Image Sharing - page 171

Reconstruction phase

TABLE 6.5
Reconstruction of participant 1 and 2 using Hu and Tzeng [10] algorithm.
First run

Second run

Pixel U = (T + A) A

T = t 1 t 2 A = A 1 + A 2

Black (110101) (001111) (110000)

White (000101) (001111) (000000)

TABLE 6.6
Reconstruction of participant 1 and 3 using Hu and Tzeng [10] algorithm.
First run Second run

Pixel U = (T + A) A

T = t 1 t 3 A = A 1 + A 3

Black (011011) (111100) (000011)

White (010100) (111100) (000000)

TABLE 6.7
Reconstruction of participant 2 and 3 using Hu and Tzeng [10] algorithm.
First run Second run

Pixel U = (T + A) A

T = t 2 t 3 A = A 2 + A 3

Black (101110) (110011) (001100)

White (010001) (110011) (000000)

6.5 Secret Sharing Scheme Using Boolean Operation
This section gives an introduction to some methods using an XOR Boolean
operation directly without using basis matrices to construct secret sharing
schemes. The algorithms of three schemes: the probabilistic (2;n) secret shar-
ing scheme, (n;n) secret sharing scheme, and (k;n) secret sharing scheme will
be described.
Consider a secret image A with size N R N C . Each pixel of A can take
any one of c different colors or gray levels. Image A is represented by an
integer matrix A. A = [a ij ] N R N C , where i = 1; 2; ;N R , j = 1; 2; ;N C ,
and a ij 2 f0; 1; ;c 1g. We have c = 2 for a binary image and c = 256
for grayscale image with one byte per pixel. In a color image with one byte
per pixel, the pixel value can be an index to a color table, thus, c = 256.
In a color image using an RGB model, each pixel has three integers: R(red),