Editing Visual cryptography (section)

== (2, ''n'') visual cryptography sharing case ==
[[File:visual_cryptography_3_choose_2.svg|thumb|upright=1.25|Any two transparencies printed with black rectangles, when overlaid reveals the message, here, a letter A (gridlines added for clarity)]]
Sharing a secret with an arbitrary number of people, ''n'', such that at least 2 of them are required to decode the secret is one form of the visual secret sharing scheme presented by [[Moni Naor]] and [[Adi Shamir]] in 1994. In this scheme we have a secret image which is encoded into ''n'' shares printed on transparencies. The shares appear random and contain no decipherable information about the underlying secret image, however if any 2 of the shares are stacked on top of one another the secret image becomes decipherable by the human eye.

Every pixel from the secret image is encoded into multiple subpixels in each share image using a matrix to determine the color of the pixels. 
In the (2, ''n'') case, a white pixel in the secret image is encoded using a matrix from the following set, where each row gives the subpixel pattern for one of the components:

{all permutations of the columns of} : <math>\mathbf{C_0 = }  \begin{bmatrix}
1 & 0 & ... &0 \\
1 & 0 & ... & 0 \\
...\\ 
1 & 0 & ... &0 \end{bmatrix}.</math>

While a black pixel in the secret image is encoded using a matrix from the following set:

{all permutations of the columns of} : <math> \mathbf{C_1 =}\begin{bmatrix}
1 & 0 & ...& 0 \\
0 & 1 & ... & 0 \\
... \\
0 & 0 & ...& 1 \end{bmatrix}.</math>

For instance in the (2,2) sharing case (the secret is split into 2 shares and both shares are required to decode the secret) we use complementary matrices to share a black pixel and identical matrices to share a white pixel. Stacking the shares we have all the subpixels associated with the black pixel now black while 50% of the subpixels associated with the white pixel remain white.