Fz2510901096

Anantha Kumar Kondra, Smt. U. V. Ratna Kumari / International Journal of Engineering
Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com
Vol. 2, Issue 5, September- October 2012, pp.1090-1096
An Improved (8, 8) Colour Visual Cryptography Scheme Using
Floyd Error Diffusion
Anantha Kumar Kondra*, Smt. U. V. Ratna Kumari**
*(Department of Electronics and Communications, University College of Engineering, JNTUK, Kakinada)
** (Department of Electronics and Communications, University College of Engineering, JNTUK, Kakinada)

ABSTRACT
Visual cryptography (VC) is the simplest on cryptography where n images are encoded in a
and a perfect way to provide the security to the way that only the human visual system can decrypt
confidential information. VC in color images the hidden message without any cryptographic
encrypts a color secret message into n color computations when all shares are stacked together.
halftone image shares. In earlier VC schemes in Visual cryptography is a very secure and unique way
order to recover the secret image, one has to to protect secrets. Visual cryptography has two
collect a set of qualified shares and print them important features. The first feature is its perfect
onto transparencies. However this VC scheme secrecy, and the second feature is its decryption
shows good results for black and white or gray method which requires neither complex decryption
scale images, but not with the Color Images due to algorithms nor the aid of computers. Consider a
its color structure. Using the concept of visual binary secret image B and a set of n participants
information pixel (VIP) synchronization and sharing B. A k out of n visual secret sharing scheme
error diffusion to attain a color visual encrypts B into n transparencies (called shares)
cryptography encryption method that produces which are distributed to the n participants one by one
meaningful color shares with high visual quality. in such a way that only when k or more shares are
Now a days the biggest challenge is to provide the stacked together can the participants see B by their
security in order to protect the confidential visual system; while any group of less than k shares
information from Security threats. In this paper obtains nothing about B.
we introduce a new solution which helps to Visual cryptography proposed by Naor and
identify the error in the shares and to verify the Shamir [1] discloses the possibility for using human
Authentication. Using CRC algorithm and Color visual ability to perform the decryption process.
VC scheme and error diffusion method generates Neither computational devices nor cryptographic
the quality shares and diffuses the errors and knowledge is required for the decryption process.
provides the security from threats like With such an interesting characteristic that the
Modification ,Fabrication ,Interception and shows decryption process is by the human visual system
the good results compared to the previous only, instead of any computational device, visual
schemes and increases the security level. cryptography attracts much attention from
researchers. In particular, it is much useful in
Keywords - Colour Meaningful Shares, Cyclic situations where computing devices are not available
Redundancy Check, Binary Information, Visual or not possible to use. Naor and Shamir [1] first
Cryptography Scheme, Error Diffusion, Secret presented k out of n visual secret sharing schemes,
Sharing. which ensure that the secret is concealed from
groups of less than k participants, while it can be
I. INTRODUCTION seen by groups of at least k participants when they
Visual Cryptography is a perfect way to stack their shares altogether. Since this pioneer
provide the security for the confidential information. research, many theoretical results on the
Initially it was introduced by Kafri and Keren in construction or contrast (the relative difference
1987 [1] where binary pictures were considered in between the reconstructed white and black pixels in
the encryption of pictures by two random grids. The the superimposed image) of visual secret sharing
encryption of a secret picture or shape into two schemes for binary images have been proposed in
random grids which are printed on transparencies the literature [4, 5, 6, 7]. Some studies [8, 9, 10]
such that the areas containing the secret information focused on the practical realization of visual
in the two grids are inter-correlated. Similar idea that cryptographic schemes for gray-level or color
the decryption needs only human visual ability, Naor images.
and Shamir initially used the terminology, visual A new method called extended visual
cryptography[1], which is defined as the study of cryptography (EVC) was developed by Ateniese[2].
secret (crypto) writing (graphy) and the study of In which shares contains not only the secret
mathematical techniques related to aspects of information but are also some meaningful images.
information security. Visual cryptography is based Hyper graph colorings are used in constructing

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meaningful binary shares. Since hyper graph securable and meaningful shares and is free of the
colorings are constructed by random distributed previously mentioned limitations. The method is
pixels, the resultant binary shares contain strong simple and efficient. It relies on two fundamental
white noise leading to inadequate results. Wang principles used in the generation of shares, namely,
generalized the Ateniese’s scheme using error diffusion and VIP synchronization. Error
concatenation of basis matrices and the extended diffusion is a simple and efficient algorithm for
matrices collection to achieve more simpler image halftone generation.
deviation of basis matrices[12]. Nakajima extended The quantization error at each pixel is
EVC to a scheme with natural grayscale images to filtered and fed to future inputs. The error filter is
improve the image quality[13]. Zhou et al. used half designed in a way that the low frequency differences
toning methods to produce good quality halftone between the input and output images are minimized
shares in VC[14]. Fu generated halftone shares that and consequently it produces pleasing halftone
carry visual information by using VC and images to human vision. Synchronization of the
watermarking methods[4]. Myodo proposed a VIPs across the color channels improves visual
method to generate meaningful halftone images contrast of shares. In color VC schemes, due to
using threshold arrays. Wang et. al. produced random matrix permutation the colors of encrypted
halftone shares showing meaningful images by using pixels and the contrast can be degraded. In grayscale
error diffusion techniques. This scheme generates VC schemes, it does not affect the visual quality;
more pleasing halftone shares owing to errors however, in color schemes, independent execution of
diffused to neighbor pixels. random matrix permutation for each color channel
Visual secret sharing for color images was can cause color distortion by placing VIPs at random
introduced by Naor and Shamir[1] based upon cover positions in sub pixels which finally degrades the
semi groups. Rijimen presented a 2-out-of-2 VC visual quality. VIP synchronization prevents the
scheme by applying the idea of color mixture. color and contrast of original images from
Stacking two transparencies with different colors degradation even with matrix permutation.
rises a third mixed color. Hou shares by applying The rest of this paper is organized as
halftone methods and color decomposition. Hou follows: Section II provides previous methods about
decomposed the secret color image into three (Red, standard VC, the extended VC scheme, and the
Green and Blue) halftone images. He then devised fundamentals of halftone techniques for easy
three colored 2-out-of-2 VC schemes which follow understanding of the proposed VC method. Section
the subtractive model for color mixture by exploiting III describes the proposed encryption method
some of the existing binary VC schemes. All of the including the VC matrix ,CRC bits and Binary value
previously mentioned methods, however, discuss adding method and a halftone process to generate
color schemes for 2-out-of-2 or 2-out-of-2 secret final shares. Section IV shows experimental results
sharing where the reconstructed colors are of the new method and comparisons with previous
interpreted by some mixing rules of colors. The approaches to prove its effectiveness. In Section V,
general construction of a k-out-of-n VC scheme for we discuss topics about image quality, security and
the color shares was first introduced by Verheul[16]. advantages of our scheme, and concluded this paper
He proposed a k-out-of-n VC scheme for a -colored .
image with pixel expansion q k-1, where devised II. PREVIOUS WORK
schemes for color q>=c Koga and Yamamoto used In this section, we give a brief description
a lattice structure to define the mixing result of of VC, extended VC, color models in VC and an
arbitrary two colors. All of these VC schemes for error diffusion quantization.
color images produce random pattern shares. Even 2.1 Basic Visual Cryptography
though the decrypted messages show messages with Generally (k, n)-VC scheme encrypts a
various colors, it is more desirable to generate secret message into shares to be distributed to n
meaningful shares which are less suspicious of participants. Each share shows noise-like random
encryption. Other approaches to color VC black and white patterns and does not reveal any
attempting to generate meaningful color shares information of the secret image by itself. In a k -out-
include. Ching-Nung Yand and Tse-Shih Chen n of scheme, access to more than k shares allows one
proposed a VCS for color images based upon an to recover the secret image by stacking them
additive color mixing method[18]. In this scheme, together, but access to less than k shares is not
each pixel is expanded by a factor of three. sufficient for decryption. A black and white (k,n)-
This scheme suffers from pixel expansion VC scheme consists of two collections of nxm
problem in the size of encrypted shares. In order to binary matrices S0 and S1 , having elements denoted
reduce the size of encrypted shares Inkoo Kang by 1 for a black pixel and 0 for a white pixel. To
proposed the VC for color image using visual encrypt a white (black) pixel, a dealer randomly
information pixel (VIP) synchronization with error chooses one of the matrices in S0(S1) and distributes
diffusion technique[11]. This paper introduces a new its rows to the n participants. More precisely, a
color VC encryption method which leads to produce

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formal definition of the black and white (k, n) -VC Where 𝑥(𝑝,𝑞) = 𝑥 𝑖 𝑝,𝑞 1, 𝑥 𝑖 𝑝,𝑞 2 , 𝑥 𝑖 𝑝,𝑞 3 є {0,1}3
𝑖
scheme is given next. denotes the binary vector at the ith bit-level with i=1
The security condition ensures that any less denoting the most significant bit.
than k shares cannot get any information of the
secret image other than the size of the secret image. 2.4 Error Diffusion
Based upon the principle of VC, extended VC has Error diffusion is a simple yet efficient way
been proposed whose shares take meaningful images to halftone a grayscale image. The quantization error
rather than random noise-like patterns to avoid at each pixel is filtered and fed into a set of future
suspicion. inputs. Fig. 3 shows a binary error diffusion diagram
where f(m, n) represents the pixel at (m, n) position
2.2 Extended Color Visual Cryptography of the input image. d(m, n) is the sum of the input
Generally, a (n, n ) –EVC scheme takes a pixel value and the diffused errors, g(m, n) is the
secret image and n original images as input and output quantized pixel value. Error diffusion consists
produces n encrypted shares with approximation of of two main components.
original images that satisfy the following three The first component is the thresholding
conditions: block where the output g(m ,n) is given by
• all the shares are required to recover the secret 1, 𝑖𝑓 𝑑 𝑚, 𝑛 ≥ 𝑡(𝑚, 𝑛)
image; 𝑔 𝑚, 𝑛 =
0, 𝑜𝑡𝑕𝑒𝑟𝑤𝑖𝑠𝑒
• any less than shares cannot obtain any information The threshold t(m, n) can be position
of the secret image; dependant. The second component is the error filter
• all the shares are meaningful images; encrypted h(k, l) where the input e(n, m) is the difference
shares and the recovered secret image are colored. between d(m ,n) and g(n ,m). Finally, we compute
Denote Scc1,c2,....cn as the collection of d(m, n)
matrices from which the dealer chooses a matrix to
encrypt, where C,C1,........Cn є{0,1}. for i=1,.....n, Ci 𝑑 𝑚, 𝑛 = 𝑓 𝑚, 𝑛 − 𝑕 𝑘, 𝑙 𝑒(𝑚 − 𝑘, 𝑛 − 𝑙)
is the bit of the pixel on the ith original image and is 𝑘,𝑙

the bit of the secret message. For a black and c Where 𝑕 𝑘, 𝑙 є 𝐻 , H is a2-D filter. A
white(k ,n) -EVC scheme, we have to construct 2^n widely used filter is the error weight originally
pairs of such collection (S0c1,c2,....cn , S1c1,c2,....cn ) , one proposed by Floyd and Steinberg
1 ∗ 7
for each possible combination of white and black 𝑕 𝑘, 𝑙 = ×
pixels in the n original images. 16 3 5 1

2.3 Color Models
There are two models namely additive and
subtractive color models, which are widely used to
describe the constitutions of colors. In the additive
color model, the three primary colors are red, green,
and blue (RGB), with desired colors being obtained
by mixing different RGB channels. By controlling Fig 1 Block Diagram Of Floyd Error Diffusion
the intensity of red, green, blue channels, we can Technique
modulate the amount of red, green, blue in the
compound light. The more the colors are mixed, the where * is the current processing pixel. The
more the brightness of the light. When mixing all
recursive structure of the block diagram indicates
red, green and blue channels with equal intensity,
that the quantization error e(m, n) depends upon not
white color will result. The computer screen is a
only the current input and output but also the entire
good example of the additive color model. In the
past history. The error filter is designed in such a
subtractive model, color is represented by applying
way that the low frequency difference between the
the combination of colored lights reflected from the
input and output image is minimized. The error that
surface of an object. The more the pigments are
is diffused away by the error filter is high frequency
added, the lower the intensity of the light is and, or “blue noise.” These features of error diffusion
thus, the darker the light is. This is the reason it is produce halftone images that are pleasant to human
called the subtractive model. Red, Green, and Blue eyes with high visual quality.
are the three primitive colors of pigment which
cannot be composed from other colors. The color
printer is a typical application of the subtractive III. ENCRYPTION OF SECRET IMAGE WITH
model and, hence, the VC model of Naor and COLOR IMAGES USING VC MATRICES (S0,S1)
Shamir is also of such kind. the color of the pixel AND ERROR DIFFUSION
X(p,q) can be expressed in a binary form as In this section, we describe the encryption
𝑋(𝑝,𝑞 ) = 8 𝑥(𝑝,𝑞) 28−𝑖
𝑖 method for color meaningful shares with a VIP
𝑖=1
synchronization and error diffusion. First, we

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describe the VC matrix derivation method for VIP є {S0C1...Cn [i], S1C1...Cn
3
synchronization from a set of standard VC matrices. [i]}
We then introduce an error diffusion process to where 1≤ i ≤ n; p'= p. m-x (mx-1);
produce the final shares. The halftone process is q'= q. m-y (my-1) , m= m-x. m-y
independently applied to each Red (R), Green (G), m-x, m-y are non negative integers decide the aspect
and Blue (B) color channel so each has only one bit ratio encrypted color shares. the matrix Sc c1...cn [i]
per pixel to reveal colors of original images. A secret shows the ith row of the matrix Sc c1...cn. X is the
message is half toned ahead of the encryption stage. image pixel and Xi (p',q') shows the corresponding
pixel on the color channels position at (p', q') and the
3.1 Visual Pixel Synchronization sub pixels takes one of the rows in Soc1...cn or S1c1...cn
VIPs are pixels on the encrypted shares that according to the bit value of corresponding message
have color values of the original images, which pixel color channel.
make the encrypted shares meaningful. In each of
the m sub pixels of the encrypted share, there are ƛ 3.3 Share generation Via Error Diffusion
number of VIPs, denoted as Ci and the remaining Using matrices S0,S1 processed across the
(m-ƛ) pixels deliver the message information of the all color channels after half toning algorithm is
secret message image. Here each sub pixel m carries applied to generate the final encrypted shares.
visual information as well as message information,
while other methods extra pixels are needed in
addition to the pixel expansion to produce
meaningful shares. Since each VIP is placed at the
same bit position in sub pixels across the three color
channels, VIP represents accurate colors of the
original image
Fig. 3.3 Block Diagram to generate half toned
Images
3.2 Flow Chart For Encryption of Secret Image
Fig. 3(a) shows a binary error diffusion
diagram designed for our scheme. To produce the i th
halftone share, each of the three color layers are fed
into the input. The process of generating halftone
shares via error diffusion is similar to that shown in
Fig.1 except that Fi.j(m, n) is a (m, n) i th pixel on the
input channel j(1≤ i ≤ n, 1≤ j ≤ 3) of ith share.
Fig. 3(b) depicts this process. 1s and 0s in
black are message information pixels that should not
be modified and those are in red are VIPs that are
already defined by the error diffusion. The Ci are
also VIPs whose values are to be decided by
referring the corresponding pixel values of original
images and errors from neighboring pixels when the
error filter window comes. Non Ci elements,
however, still affect di,j(m, n) and the quantization
error ei,j(m, n) when they are calculated in the
Fig 2 Flow Chart for Encryption of Secret Image filter window. The non elements may increase
quantization errors added to the shares, but in turn,
The Secret image and Color images are these errors are diffused away to neighboring pixels.
processed using half toning method and the leads to The visual quality of shares via error diffusion can
produce the half toned images. be improved through edge enhancement methods. So
the remedy for the apparent blurring of edges caused
X ( p ,q )   x R , xG ,xB 
 ( p ,q ) ( p ,q ) ( p ,q )   ,1
0  by the error diffusion algorithm is to apply an edge
3
 
Here p, q lies in between ((1,k1),(1,k2)) sharpening filter prior to half toning such that
respectively. here X that represents the pixel of the Xisharp [n]=X[n]-β(ψ[n]*X[n])
secrete image and p,q represents the location of the
pixel. The 3 binary bits xR(p,q) , xG(p,q), xB(p,q) which Where X[n] stands for the original image,
represents the values for Red ,Green, Blue color ψ[n] is a digital Laplacian filter, * denotes
channels respectively. each message pixel encrypted convolution and β is a scalar constant (β >0)
and expanded to sub pixel of length m and the regulating the amount of sharpening with larger β
encoded share i as leading to a sharper image Xisharp Consequently,
error diffusion produces high quality halftone
X(p1 , q1) i =[xR (p1 , q1) , xG( p1 , q1) , xB(p1 ,q1)] i

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images. 3.5 CRC checking and Authentication Checking
at the Receivers side
At the receivers side, all the shares are
collected from the communication channel. through
the secured channel the VC matrices S0,S1,key and
the checker value will be received from the source.
once the shares are collected at the receivers end it
will processed in a reverse process of encryption .
the binary information and crc bits were extracted
first from the shares. using the key the crc bits were
processed and the result which is equals to check
value. if the result not equal to the check value that
shows some error in the share and retransmission of
the share is needed.

Fig. 3 (a) Block diagram of error diffusion with
share encryption.
(b)Visualization of error diffusion with VIP

3.4 Adding binary information and CRC bits
The information will send from the source
to destination via communication channel. in that
process it might be chance of attack of the intruder
whether he can change the information or misguide
the people at the receivers side. so in order to protect
from the security threats and detect the errors and to
identify the shares to retransmit the shares from the
source we added binary information which tells the Fig 3.5 Color share values with binary
secret information and to detect the error and for the information(0001) and CRC bits for R
authentication purpose we added CRC bits to the plane..similarly G and B.
shares and transmitted to the destination through the
communication channel.

Fig. 3.4 Block Diagram for Encryption process and
adding CRC bits
A represents the Secret image and B
represents the Color Shares C shows the half toned
Resultants. After generating the shares Binary
Information and CRC bits added to the shares, which
are extracted first and verified with key at receiver
side. Fig 3.6 Flow Chart for CRC , Authentication
checking at the receivers side.

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If all the shares are verified with CRC checking key 4.3 Reconstructed Secret Image from meaning full
and then test for the Authentication checking. in Shares
each share the added binary information which
represents by 8 bits, in that last 4 bits shows the part
information that is order of the part of secret image.
which helps to reconstruct the secret image from the
shares at the destination side. And the first 4bits
represents the authentication check bits. these check
bits are collected from the shares according to the
binary information in order and processed with the
CRC key .if the result of the process and checker
value is equal then Authentication Verified unless it
shows that Authentication failed that means an Fig:4.3 Reconstructed Secret image(8,8)VCS
attack of Intruder on the information.
TABLE I
IV. SIMULATION RESULTS COMPARISON OF (4,4) AND (8,8) COLOUR VC SCHEME
This section presents the information Images (4,4)VCS (8,8)VCS
regarding input secret image for encryption,
1st Image(PSNR) 12.0650 dB 12.0650 dB
meaningful shares or half toned shares used for
encryption process and reconstructed image. 2nd Image(PSNR) 12.5358 dB 12.5358 dB
3rd Image(PSNR) 13.7786 dB 13.7786 dB
4.1 Original Secret Image for (n out of n) VCS 4th Image(PSNR) 15.7007 dB 15.7007 dB
5th Image(PSNR) - 12.0378 dB
Fig:4.1 Secret Image Requirement for Meaningful Meaningful
Encryption Shares Shares
4.2 Colour Images for (n out of n) VCS for No. of Shares Required
All All
Encryption for Decryption
Reconstructed Image
23.5705dB 25.4563dB
PSNR
Mean Error 6.0383e+005 1.7202e+006
Quality & Clarity(by
Good High
vision)
1 2 3 4 Security High Very High
Computation
High Very High
Complexity
Hard ware
High High
Implementation
5 6 7 8
Fig: 4.1, The actual secret image which
(a) represents the confidential information that we want
to send in secure way to the destination. Fig: 4.2 (a),
The coloured images which plays the key role for
the secure transmission of information. Fig: 4.3 (b),
After applying to half toning the generated shares for
the encryption of secret information .
1 2 3 4 Fig : 4.3, After the Half toning process the
generated shares encrypted using VC matrices
(S0,S1). that means the secret information is
embedded into the shares which are called as
meaning full shares. At the receiver side all the
shares are collected and using the VC matrices S0,S1
5 6 7 8 the information is extracted from the meaning full
(b) shares. and thus forms the reconstructed secret
Fig:4.2 (a) Actual Colour Images for Encryption Of image which showed in figure 4.3. from the figure 4
SI which shows that how binary values and crc bits
(b) After Encryption of SI the Meaningful Shares embedded into color channels and at receiver side

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the similar way the the information extracted first [7] W. Q. Y, J. Duo, and M. Kankanhalli,
and checked with crc key. if the result checked “Visual cryptography for print and scan
successfully that means no error and identified the applications,” in Proc. IEEE Int. Symp.
part of Secret image according the binary value. Circuits Syst., 2004, pp. 572–575.
after that header bits (checker, from Fig:3.5) [8] C. Blundo, P. D’Arco, A. D. S. , and D. R.
collected from the all shares and verify with CRC Stinson, “Contrast optimal threshold visual
key ,if it shows that success Authentication proved cryptography schemes,” SIAM J. Discrete
unless need to retransmit the shares from the source. Math., vol. 16, no. 2, pp. 224–261, 2003.
The quality of the reconstructed image can be [9] L. A. MacPherson, “Gray level visual
measured in different ways. Here the following table cryptography for general access structrue,”
presents some quality measuring parameters using M. Eng. thesis, Univ. Waterloo, Ontario,
PSNR. Canada, 2000.
[10] C. Blundo, A. D. Santis, and M. Naor,
V. CONCLUSION “Visual cryptography for grey level
This paper develops an encryption method images,” Inf. Process. Lett., vol. 75, no. 6,
to construct color EVC scheme with VIP pp. 255–259, 2000.
synchronization and error diffusion for visual quality [11] Inkoo Kang, Gonnzoalo R..Arce, Heun-Kyu
improvement. VIPs synchronize the positions of Lee “Color Extened Visual Cryptography
pixels that carry visual information of original Using Error Diffusion” IEEE Trans,
images across the color channels so as to retain the Image Process., vol. 20 No.1, pp.132-
original pixel values the same before and after 145,2011.
encryption. Error diffusion is used to construct the [12] D.s Wang, F.Yi, and X.Li,”On general
shares such that the noise introduced by the preset construction for extended visual
pixels is diffused away to neighbors when encrypted cryptography schemes” Pattern Recognit.,
shares are generated. It is obvious that there is a pp.3071-3082,2009.
tradeoff between contrast of encryption shares and [13] M.Nakajima and Y. Yamaguchi, ”Extended
the decryption share; however, we can recognize the visual cryptography for natural images ,” J
colorful secret messages having even low contrast. WSCG vol. 10, no. 2, 2002.
Either VIP synchronization or error diffusion can be [14] Z. Zhou, G. R Arce, and G. D. Crescenzo,
broadly used in many VC schemes for color images. “ Halftone visual cryptography,” IEEE
In this paper has solved for the cryptanalysis which Trans . Image Process., vol 18, no. 8,pp.
is helpful in security analysis of confidential 2441-2453,Aug.2006.
information. As future work increase the no of share [15] C. N Yang, “ A note on efficient color
and range of CRC which leads to enhance the visual encryption,” J. Inf. Sci.Eng., vol. 18,
security level of the confidential information. pp.367-372,2002.
[16] E. R.Verheul and H.C.A vanTilborg,
REFERENCES ”Construction and properties of k out of n
[1] M. Naor and A. Shamir, “Visual visual secret sharing schemes, ” Des. Codes
cryptography,” in Proc. EUROCRYPT , Cryptogr., vol. 11, no. 2, pp. 179-196, May
1994, pp. 1–12. 1997.
[2] G. Ateniese, C. Blundo, A. D. Santis, and [17] H. Koga and H. Yamamoto, “ Proposal of a
D. R. Stinson, “Visual cryptography for lattice based visual secret sharing scheme
general access structures,” Inf. Comput., for color and gray –scale images, ” IEICE
vol. 129, no. 2, pp. 86–106, 1996. Trans. Fundamentals, vol.E81-A, no. 06,
[3] A. Houmansadr and S. Ghaemmaghami, “A pp. 1262-1269, Jun. 1998.
novel video watermarking method using [18] C. N Yang and T.S . Chen, "Visual
visual cryptography,” in Proc. IEEE Int. Cryptography .Scheme based on additive
Conf. Eng. Intell. Syst., 2006, pp. 1–5. color mixing," Pattern Recognit., vol. 41,
[4] M. S. Fu and O. C. Au, “Joint visual pp. 3114-3129,2008.
cryptography and watermarking,” in Proc.
IEEE Int. Conf. Multimedia Expo, 2004,
pp. 975–978.
[5] C. S. Hsu and Y. C. Hou, “Copyright
protection scheme for digital images using
visual cryptography and sampling
methods,” Opt. Eng., vol. 44, p. 077003,
2005.
[6] M. Naor and B. Pinkas, “Visual
authentication and identification,” Adv.
Cryptol., vol. 1294, pp. 322–336, 1997.

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