# ABSTRACT one of the images.1 The secret image

ABSTRACT

Intent of this paper is to study the performance of
the traditional visual cryptography schemes and XOR Based VCS on the basis of
quality of reconstructed image and type of shares generated. The visual
cryptography scheme (VCS) is a scheme which encodes a secret image into several
shares, and only qualified sets of shares can recover the secret image
visually, other sets of shares cannot get any information about the content of
the secret image. XOR-Based visual cryptography is capable to overcome the drawbacks of the visual cryptography scheme
(VCS) the large pixel expansion of each share image and the small contrast of
the recovered secret image.

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Keywords

Visual
Cryptography, Image share, Pixel Expansion, Alignment, superimposing

1.
INTRODUCTION

In Visual
cryptography mainly visual information is encrypted using encryption algorithm
but here there is no need of decryption algorithm to reveal the visual
information. Here the decryption process is done simply by human visual system.
During the encryption process we simply add some noise in the original image to
hide the original information and during the decryption process we reduce the
noise to unhide the original information. The technique was proposed by Moni
Naor and Adi Shamir in 1994.Visual Cryptography uses two transparent images.
They demonstrated a visual secret sharing scheme, where an image was broken up
into n shares so that only someone with all 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. One image contains random
pixels and the other image contains the secret information. It is impossible to
retrieve the secret information from one of the images.1

The
secret image is composed of black and white pixels. The original secret image
can be recovered by superimposing the two share images together. The underlying
operation of such a scheme is the logical operation OR. Generally, a(k,n)-VCS
takes a secret image as input, and outputs share images that satisfy two
conditions: First, any k out of n share images can recover the secret image;
second, any less than k share images cannot get any information about the
secret image. Similar models of visual cryptography with different underlying
operations have been proposed, such as the XOR operation introduced in 2–6,
and the NOT operation introduced in 7,which uses the reversing function of
the copy machines.

2.     PRELIMINARIES

In a VCS, there
is a secret image which is encrypted into some share images. The secret image
is called the original secret image for clarity, and the share images
are the encrypted images (and are called the transparencies if they are printed
out). When a qualified set of share images (transparencies) are stacked
together properly, it gives a visual image which is almost the same as the
original secret image; we call this the recovered secret image. In the
case of black and white images, the original secret image is represented as a
pattern of black and white pixels. Each of these pixels is divided into
subpixels which themselves are encoded as black and white to produce the share
images. The recovered secret image is also a pattern of black and white
subpixels which should visually reveal the original secret image if a qualified
set of share images is stacked. In this paper, we will focus on the black and
white images, where a white pixel is denoted by the number 0 and a black pixel
is denoted by the number 1. The easiest way to implement Visual Cryptography is
to print the two layers onto a transparent sheet. When the random image
contains truly random pixels it can be seen as a One-time Pad system and will
offer unbreakable encryption.

Table 1. Basic Encoding Idea in Naor and
Shamir’s               Scheme

Naor and
Shamir’s1 proposed encoding scheme to share a binary image into two shares Share1
and Share2 . If pixel is white one of the above two rows of Table 1 is chosen
to generate Share1 and Share2. Similarly If pixel is black one of the below two
rows of Table 1 is chosen to generate Share1 and Share2. Here each share pixel
p is encoded into two white

and two black
pixels each share alone gives no clue about the pixel p whether it is white or black.
Secret image is shown only when both shares are superimposed.
Various
parameters are recommended by researchers to evaluate the performance of visual
cryptography scheme. Naor and Shamir 1 suggested two main parameters: pixel
expansion m and contrast ?. Pixel expansion m refers to the number of subpixels
in the generated shares that represents a pixel of the original input image. It
represents the loss in resolution from the original picture to the shared one.
Contrast ? is the relative difference in weight between combined shares that
come from a white pixel and a black pixel in the original image.

3.
VISUAL CRYPTOGRAPHY SCHEME

The visual
cryptography scheme (VCS), introduced by Naor and Shamir in 1994 2 is a type
of secret sharing scheme which can split secret information into n shares
and recover them by superimposing the shares. In VCS, the secret to be hidden
is a black and white image and each share is compromised of groups of m black
and white subpixel used to recover a pixel of the secret image. It is assumed
that a white pixel in a share is transparent and a black pixel is opaque. It is
impossible to get any information about the secret images from shares
individually. The other advantage of VCS is that, unlike other cryptography
techniques, this secret recovery does not need difficult computations. The
secret information can easily be recovered with enough shares and requires
human vision instead of special software or hardware devices. Naor and Shamir
proposed a k out of n scheme and assumed that the image or
message is a collection of binary 1 and 0 displayed as black and white pixels. According
to their algorithm, the secret image is turned into n shares and the
secret is revealed if any k of them are stacked together. So the image
remains hidden if fewer than k shares are stacked together 5.

Image contrast
and the number of subpixels of the shares and recovered image are two main
parameters in visual cryptography schemes. The number of subpixels represents
expansion of the image and should be as small as possible, while the contrast,
which is a relative difference between the maximum value of Hamming weight for
a black pixel and the minimum value of Hamming weight for white pixel, needs to
be as large as possible 4. Some researchers have focused on contrast
degradation and introduced methods to improve the contrast of the reconstructed
secret image.

3.1
The Basic Model

The basic 2 out
of 2 visual cryptography model consists of a secret message encoded into two transparencies,
one transparency representing the ciphertext and the other acting as a secret
key. Both transparencies appear to be random dots when inspected individually
and provide no information about the original clear text. However, by carefully
aligning the transparencies, the original secret message is reproduced. The
actual decoding is accomplished by the human visual system.

Naor and Shamir
further describe the visual cryptography scheme as a visual secret sharing
problem in which the secret message can be viewed as nothing more than a
collection of black and white pixels. Each pixel in the original image is
represented by at least one subpixel in each of the n transparencies
or shares generated. Each share is comprised of collections of m black
and white subpixels where each collection represents a particular original
pixel. An example of the encoding of white and black pixels in a 2 out of 2
scheme can be seen in Figure 1. Here two shares out of the two generated would
be needed to recover the original image. Since only two shares are generated, n
= 2. Figure 1 represents a single white or black pixel in the original
image and subpixel assignments that would be given to shares #1 and #2
respectively. The number of subpixels per share used to represent the original
pixel is four (m = 4). Finally, Figure 1(d) represents the overall
visual effect when shares #1 and #2 are correctly aligned on top of one
another. Notice that when the shares in this example are combined the original
black pixel is viewed as black, however, the original white pixel takes on a
grey scale.

The structure
obtained from either white or black pixel representation in Figure 1 can be
described by an n x m Boolean matrix Sp where
p ? {white, black}. Any given element of the matrix S say
sij, is considered to be 1 iff the jth subpixel in the ith
transparency is black. When the n transparencies are properly
aligned, the resulting black subpixels are the Boolean OR of the columns for
each row i1, i2, … , in of S.
Shares #1 and #2 of Figure 1 would represent i1 and i2
respectively. Therefore, the following 2 x 4 Boolean matrices would be derived:

Swhite = { {1, 0, 0, 1},
{1, 0, 0, 1}} and

Sblack = { {1, 0, 0, 1},
{0, 1, 1, 0} }.

The matrix
elements represent share assignments for share #1 and share #2 respectively Since
m subpixels constitute one original pixel and the overall visual
effect of a black subpixel in any one of the shares causes that particular
subpixel when combined to become black, inspection of the grey level is the
method of determining the original color of a pixel.

3.2     Algorithm

Encryption:

Step 1: Input the image with
secret image.

Step 2: Initialize two
collections of n x m Boolean matrices S0 and
S1. S0 acts as a pool of matrices from which to randomly choose
matrix S to represent a white pixel while S1 acts
as a pool of matrices from which to randomly choose matrix S to
represent a black pixel.

Step 3: Using the
permutated basis matrices, each pixel from the secret image will be encoded
into two subpixels on each participant’s share. A black pixel on the secret
image will be encoded on the ith participant’s share as the ith row
of matrix S1, where a 1 represents a black subpixel and a 0 represents a
white subpixel. Similarly, a white pixel on the secret image will be encoded on
the ith participant’s share as the ith row of matrix S0.

Decryption :

Stacking all the
qualified participant’s share and ORing the stacked pixel to reconstructed the
image.

We illustrated it
with 2-out-of-2 scheme. In the 2-out-of-2scheme, every secret pixel of the
image is converted into two shares and recovered by simply stacking two shares
together. This is equivalent to using the OR operation between the shares. As
illustrated in Table1 4, 4 subpixels are generated from a pixel of the secret
image in a way that 2 subpixels are white and2 pixels are black. The pixel
selection is a random selection from each pattern. For example, when the
corresponding pixel is white, one of the first six rows of Table 2 is randomly
selected to encode the pixel into2 shares. It is easy to see that knowing only
one share value does not reveal the other share and the secret image pixel.
However superimposing all the shares reveals the corresponding binary secret
image.

Experimental
result

Figure 1 shows an
example of Traditional Visual Cryptography scheme applying the (2,2) with
4-subpixels layout visual secret sharing scheme, where the share images are
larger than the original secret image in each dimension. That is, the share
uses 4 subpixel for the original pixel. As illustrated in Figure1, (a) is the
secret image, (b) and (c) are two random shares, and (d) shows the reconstructed
image from superimposing the two shares.

Table 2.

(2,2) VISUAL CRYPTOGRAPHY SCHEME

Here it is
applied to binary image. However, the shortcomings of visual cryptography are
as salient as its merits.

(a)

(b)

(c)

(d)

Fig
1.  (a) Original Image (b) Share 1 (c)
Share 2 (d) Reconstructed Image

There are three
main drawbacks in visual cryptography:

It results in a
loss of resolution. The restored secret image has a resolution lower than that
of the original secret image.Its background
contrast is lost.Its original
formulation is restricted to binary images. For color images, some additional
processing such as halftoning and color-separation are required.The
superimposition of two shares is not easy to perform unless some special
alignment marks are provided. The manual alignment procedure can be tedious
especially for high resolution images.

The biggest
advantage of traditional method is the hard copy of the shares will give the
same result as soft copy that too just by stacking the together.

4.     XOR-BASED VISUAL CRYPTOGRAPHY

A (k; n) visual
cryptography (VC) scheme 16 is a type of secret sharing scheme with the
special property that a secret image can be recovered visually by the human eye
and does not require any calculation on a computer. However, the recovered
secret image has low quality. In this case, some researchers attempt to
consider other different approaches to improve the quality (contrast)of the
recovered image. Lee et al. 2 presented a VC scheme using an XOR process to
share a binary image.

Based on the definition
of Naor and Shamir 6, Verheul and van Tilborg 10 gave a more general
definition. Following the notation from 16, 20, a definition of k out of n
XOR-based visual cryptography scheme is given by Tuyls in Reference 7. A (k,
n) VC scheme S =
(C0,C1) consists of two collections of n x m binary matrices C0 and C1.

TABLE
II

(2,2) XOR-BASED VISUAL CRYPTOGRAPHY SCHEME

To share a white
(black) pixel, the dealer randomly chooses one of the matrices in C0(C1) and
distributes its rows as shares among the n participants of the system.

Table 2 4,
shows that 4 subpixels are generated from a pixel of the secret image in a way
that 2 subpixels are white and 2 pixels are black. The pixel selection is a
random selection from each pattern. For example, when the corresponding pixel
is white, one of the first six rows of Table 2 is randomly selected to encode
the pixel into 2 shares.

4.1
Algorithm

Step 1: Input the image with
secret image.

Step 2: Initialize two
collections of n x m Boolean matrices S0 and
S1. S0 acts as a pool of matrices from which to randomly choose
matrix S to represent a white pixel while S1 acts
as a pool of matrices from which to randomly choose matrix S to
represent a black pixel.

Step 3: Using the
permutated basis matrices, each pixel from the secret image will be encoded
into two subpixels on each participant’s share. A black pixel on the secret
image will be encoded on the ith participant’s share as the ith row
of matrix S1, where a 1 represents a black subpixel and a 0 represents a
white subpixel. Similarly, a white pixel on the secret image will be encoded on
the ith participant’s share as the ith row of matrix S0.

Decryption :

Stacking all the
qualified participant’s share and XORing the stacked pixel to reconstructed the
image.

We illustrated it
with 2-out-of-2 scheme. In the 2-out-of-2scheme, every secret pixel of the
image is converted into two shares and recovered by simply stacking two shares
together. This is not equivalent to the OR operation between the shares but we
have to XOR the pixels. As illustrated in Table2 4, 4 subpixels are generated
from a pixel of the secret image in a way that 2 subpixels are white and2
pixels are black. The pixel selection is a random selection from each pattern.
For example, when the corresponding pixel is white, one of the first six rows
of Table 2 is randomly selected to encode the pixel into2 shares. It is easy to
see that knowing only one share value does not reveal the other share and the
secret image pixel. However superimposing all the shares reveals the
corresponding binary secret image.

Experimental
result

Figure 2 shows an
example of Traditional Visual Cryptography scheme applying the (2,2) with  4-subpixels layout visual secret sharing
scheme, where the share images are larger than the original secret image in
each dimension. That is, the share uses 4 subpixel for the original pixel. As
illustrated in Figure 2(a) is the secret image, (b) and (c) are two random
shares, and (d) shows the reconstructed image from superimposing the two
shares.

(a)

(b)

(c)

(d)

Fig.
2 (a) Original Image (b) Share 1 (c) Share 2 (d) Reconstructed XORed Image

5.
Comparison

Visual Cryptography has almost double pixels in its reconstructed image same as
XOR-Based Visual Cryptography. The Reconstructed image in traditional Visual
Cryptography had lost its original contrast specially in background but in
XOR-Based Scheme the contrast is regained. If the decryption is done by
software for stacking shares then both the method gives expected result but if
the hard copy of shares are to be stacked then traditional VCS will have same
output as softcopy but XOR-Based VCS will not have output as softcopy stacked.

VCS
type

Pixel
Expansion

Contrast

Softcopy Decryption

Hardcopy Decryption

More

Lost

Same
as algorithm

Same
as algorithm

XOR
Based

More

Retained

Same
as algorithm

Not
Same

CONCLUSION

Visual
cryptography scheme can store the secrecy of the image but the reconstructed
image quality is the concern to make it useful in the real world that
efficiently. If at the decryption end the computational of softcopy is possible
the XOR-Based method gives better output but if hardcopy is to be stacked and
it has to be done by human visual system then it will give the same result as
traditional VCS.XOR-Based VCS can be used in other algorithms of visual
cryptography to increase the reconstructed image quality.