November 22, 2019

## I. to 100%. II. BASIC VISUAL CRYPTOGRAPHY SCHEMES 2.1

I. INTRODUCTION

Visual cryptography is a
cryptographic technique. It makes visual information to be encrypted in such a
way that decryption becomes the task of the user to decrypt by means of sight

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One of the best-known techniques
has been credited to Naor and
Shamir, who developed it in 1994. An image was split into n shares so that only someone with all the n shares could decrypt the image, while any n ? 1 shares revealed no information about the original image. Each
share was printed on a separate transparency, and decryption was performed by
overlaying the shares. When all n
shares were overlaid, the original image would appear. Several generalizations
of the basic scheme which included k-out-of-n visual cryptography are
available. 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%.

II.  BASIC VISUAL CRYPTOGRAPHY SCHEMES

2.1
(2, 2) VISUAL CRYPTOGRAPHY SCHEME

In (2, 2) Visual Cryptography
Scheme, original image is divided into 2 shares. Each pixel in original image
is represented by non-overlapping block of 2 or 4 sub-pixels in each share.
Anyone, having only one share will not be able to reveal any secret
information. Both the shares are required to be superimposed to reveal the
secret image.3

In this technique,
each pixel in original image is represented by two sub-pixels in each share.
While reading the pixels in original image, if a white pixel is encountered,
one of the first two rows in Figure 2.1 is selected with probability 0.5, and
the shares are assigned 2 pixel blocks as shown in the third and fourth columns
in Figure 2.1. Similarly, if a black pixel is encountered, one of the last two
rows is selected

with probability 0.5, from which
a sub-pixel block is assigned to each share.

Two shares when superimposed, if
two white pixels overlap, the resultant pixel will be white and if a black
pixel in one share overlaps with either a white or black pixel in another
share, the resultant pixel will be black. This implies that the superimposition
of the shares represents the Boolean OR function. 2

Each pixel of the original image
is divided into two sub-pixels in each share. The last column in Figure 2.1
shows the resulting sub-pixel when the sub-pixels of both the shares in the
third and fourth columns are superimposed.

Figure
2.1: 2 out of 2 using sub pixels per original pixel

2.2 (K, N) VISUAL
CRYPTOGRAPHY SCHEME

In (2, 2) visual cryptography,
both the shares are required to reveal secret information. If one share gets
lost due to some technical problem, secret information cannot be revealed. So
there is a restriction of keeping all the shares secure to reveal information
and user can not afford to lose a single share.

In (k, n) visual cryptography
scheme, n shares can be generated from original image and distributed. Original
image is recognizable only if k or more shares stacked together, where value of
k is between 2 to n. If fewer than k shares stacked together, original image
cannot be recognized. It gives flexibility to user. If user loses some of the
shares still secret information can be revealed, if minimum k number of shares
is obtained.2

2.3 MULTIPLE SECRET
SHARING SCHEME

The previous researches in visual
cryptography were focused on securing only one image at a time. Wu and Chen
were first researchers, who developed a visual cryptography scheme to share two
secret images in two shares.

In this scheme, two secret binary
images can be hidden into two random shares, namely A and B, such that the
first secret can be seen by stacking the two shares, denoted by A?B, and the second secret can be
obtained by rotating A by 90 degree anti-clockwise. J Shyu implemented a scheme
for multiple secrets sharing in visual cryptography, where more than two secret
images can be protected at a time in two shares. 1

2.4 HALFTONE VISUAL
CRYPTOGRAPHY SCHEME

Halftone visual cryptography uses
half toning technique to create shares. Halftone which is a reprographic
technique simulates continuous tone imagery through the use of dots, which may
vary either in size, in shape or in spacing. Zhi Zhou, Gonzalo R. Arce, and
Giovanni Di Crescenzo proposed halftone visual cryptography.In halftone visual
cryptography a secret binary pixel is encoded into an array of sub pixels,
called as halftone cell, in each of the ‘n’ shares. By using halftone cells with
an correct size, visually agreeable halftone shares can be obtained. It
maintains good contrast and security and increases quality of the shares.5

2.5
VISUAL CRYPTOGRAPHY SCHEME FOR GREY IMAGES

All previous visual cryptography
schemes were only limited to binary images. These techniques were capable of
doing operations on only black and white pixels. It is not sufficient for real
life applications. Chang-Chou Lin, Wen- Hsiang Tsai proposed visual
cryptography for gray level images. In this scheme a dithering technique is
used to convert gray level image into approximate binary image. Then presented
visual cryptography schemes for binary images are used to make the shares.

2.6
VISUAL CRYPTOGRAPHY SCHEME FOR COLOR IMAGES

Visual cryptography schemes were
applied to only black and white images till year 1997. Verheul and

Van Tilborg proposed first color
visual cryptography scheme.

In this visual cryptography
scheme one pixel is distributed into m sub pixels, and each sub pixel is
divided into c color regions. In each sub pixel, there is exactly one color
region colored, and all the other color regions are black.

2.7 EXTENDED VISUAL
CRYPTOGRAPHY SCHEME

Shares are created as random
patterns of pixel traditionally. These shares look like a noise. Noise-like
shares arouse the attention of hackers, as hacker may suspect that some data is
encrypted in these noise-like images. So it becomes prone to security related
issues. It also becomes difficult to manage noise-like shares, as all shares
look alike. Nakajima, M. and Yamaguchi, Y., developed Extended visual
cryptography scheme (EVS).6

An extended visual cryptography
(EVC) provide techniques to create meaningful shares instead of random shares
of traditional visual cryptography and help to avoid the possible problems,
which may arise by noise-like shares in traditional visual cryptography. Thus
the information can be transmitted securely.

2.8
SEGMENT BASED VISUAL CRYPTOGRAPHY SCHEME

schemes were based on pixels in the input image. The limitation of pixel based
visual cryptography scheme is loss in contrast of the reconstructed image,
which is directly proportional to pixel expansion. Bernd Borchert proposed a
new scheme which is not pixel-based but segment-based.

It is useful to encrypt messages
consisting of symbols represented by a segment display. For example, the
decimal digits 0, 1,….,9 can be represented by seven-

segment display.

segment-based encryption is that, it may be easier to adjust the secret images
and the symbols are potentially easier to recognize for the human eye and it
may be easier for a non-expert human user of an encryption system to understand
the working.3

2.9
VISUAL CRYPTOGRAPHY SCHEME FOR GENERAL ACCESS

In (k, n) visual cryptography
scheme, all n shares have equal importance. Any k out of n shares can reveal
the secret information. It may compromise the security of system. To overcome
this problem, G. Ateniese, C. Blundo, A. DeSantis, and D. R. Stinson extended
(k, n) visual cryptography model to general access structure. 3

In general access structure
scheme, given set of n shares is divided into two subsets namely qualified and
forbidden subset of shares as per the importance of shares. Any k shares from
qualified subset of shares can reveal secret information, but less than k
shares from qualified subset of shares can not reveal any secret information.
Even k or more shares from forbidden set can’t reveal secret information. 2applied to these regions .5 2.12PROGRESSIVEVISUAL
CRYPTOGRAPHY SCHEME In (k, n) visual secret sharing
scheme, it is not possible to recover the secret image though one less than k
shares are available. This problem is solved in progressive visual cryptography
scheme developed by D. Jin, W. Q. Yan, and M. S. Kankanhalli. In progressive visual
cryptography scheme, it is not necessary to have at least k shares out of n, as
in (k, n)
secret
sharing scheme. If more than one share obtained, it starts recovering the 