Visual cryptography

to be encrypted in such a way that the decrypted information appears as a visual image.

One of the best-known techniques has been credited to Moni Naor and Adi Shamir, who developed it in 1994.

When all n shares were overlaid, the original image would appear.

There are several generalizations of the basic scheme including k-out-of-n visual cryptography,[2][3] and using opaque sheets but illuminating them by multiple sets of identical illumination patterns under the recording of only one single-pixel detector.

Normally, there is an expansion of space requirement in visual cryptography.

But if one of the two shares is structured recursively, the efficiency of visual cryptography can be increased to 100%.

[6][7] Other antecedents are in the work on perception and secure communication.

[8][9] Visual cryptography can be used to protect biometric templates in which decryption does not require any complex computations.

When these complementary pairs are overlapped, they will appear dark gray.

When these matching pairs are overlapped, they will appear light gray.

However, without the other component, a component image reveals no information about the original image; it is indistinguishable from a random pattern of ■□ / □■ pairs.

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} :

While a black pixel in the secret image is encoded using a matrix from the following set: {all permutations of the columns of} :

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.

[11] We know that 2 shares are enough to decode the secret image using the human visual system.

For instance, colluding participants may examine their shares to determine when they both have black pixels and use that information to determine that another participant will also have a black pixel in that location.