A Novel Algorithm for Watermarking and Image Encryption

Natarajan Meghanathan, et al. (Eds): ITCS, SIP, JSE-2012, CS & IT 04, pp. 347–356, 2012.
© CS & IT-CSCP 2012 DOI : 10.5121/csit.2012.2132
A Novel Algorithm for Watermarking and
Image Encryption
Rakesh S1
, Ajitkumar A Kaller2
, Shakshari B C3
and Annappa B4
Department of Computer Science and Engineering, National Institute of
Technology Karnataka, Surathkal
1
rakeshsmysore@gmail.com
2
ajitkaller@gmail.com
3
shadsbellekere@gmail.com
4
annappa@ieee.org
ABSTRACT
Digital watermarking is a method of copyright protection of audio, images, video and text. We
propose a new robust watermarking technique based on contourlet transform and singular value
decomposition. The paper also proposes a novel encryption algorithm to store a signed double
matrix as an RGB image. The entropy of the watermarked image and correlation coefficient of
extracted watermark image is very close to ideal values, proving the correctness of proposed
algorithm. Also experimental results show resiliency of the scheme against large blurring attack
like mean and gaussian filtering, linear filtering (high pass and low pass filtering) , non-linear
filtering (median filtering), addition of a constant offset to the pixel values and local exchange of
pixels .Thus proving the security, effectiveness and robustness of the proposed watermarking
algorithm.
KEYWORDS
Image Watermarking, Contourlet Transform, singular value decomposition, Correlation, Image
Entropy.
1. Introduction
Digital watermarking primarily means inserting a copyright information into a cover work and is
proposed as a solution to illegal copying and tampering of the original data. The digital
watermark embedded need not be hidden and should be robust against intentional and non-
intentional attacks. The existing transform domain techniques locate regions of high frequency or
middle frequency to embed information. The transforms usually selected for digital watermarking
are Discrete Cosine Transform (DCT), Discrete Fourier Transform (DFT) and Discrete Wavelet
Transform (DWT) [4][5]. Of the proposed algorithms so far wavelet domain algorithms perform
better than DCT based algorithms. It has been proved that wavelets are good at representing
discontinuities in one dimension or point singularities [2]. But, since in higher dimensions there
are more types of singularities which wavelets fail to represent, we need to go for transforms like
curvelets and contourlets for better performance. Curvelet transform was defined in the
continuum space R2 and its discretization is a challenge when critical sampling is desired .
Contourlet transform was proposed as an improvement on curvelet transform using a double filter
bank structure. [1] Contourlet transform possess all features of wavelets and also shows a high

348 Computer Science & Information Technology (CS & IT)
degree of directionality and anisotropy. One of the unique properties of contourlet transform is
that we could have any number of directional decompositions at every level of resolutions [3].
Thus making it a one of the suitable technique for watermarking [8][9],[10].
The paper also proposes a novel method of image encryption, which is just an optional
intermediate layer for multimedia data security. Also the normalized correlation coefficients
(NCC) between the original watermark image and the extracted image after different attacks were
calculated. The results show high improvement detection reliability using proposed method. The
rest of the paper covers a brief introduction to contourlet transform and SVD in Section 2 and 3.
Section 4 explains the proposed algorithm. Experimental results and conclusion are included in
Section 5 and 6 respectively.
2. Contourlet Transform
It is transformation technique which is used in image analysis for capturing contours and fine
details in images. The contourlet transform is composed of basic functions oriented in multiple
scales at different directions with flexible aspect ratios, making it a multi resolution and multi
directional transformation. This frame work forms a basis with small redundancy unlike other
transform techniques in image processing. Contourlet representation contains basis elements
oriented at variety of directions much more than few directions that are offered by other separable
transform technique. One way to obtain a sparse expansion for images with smooth contours is
first apply a multistage wavelet like transform to capture the edge points, and then local
directional transform to gather the nearby edge points into contour segments. With this insight,
one can construct a double filter bank structure shown in figure 1(a) where the laplacian
pyramidal filter is used to capture the point discontinuities, followed by a directional filter bank to
link point discontinuities into linear structures. The result is an image expansion using basic
elements like contour segments, and thus it is named contourlet transform.
Figure 1.Block Diagram of Contourlet Filter Bank
The directional decomposition is implemented through an l-level tree structured decomposition
that leads to 2l sub bands with wedge shaped frequency partition. Fig. 2 shows the directional
decomposition at every level obtained using contourlet transform. The no of directional
decompositions can be chosen different and it makes this transform unique.
3. Singular Value Decomposition
Singular value decomposition (SVD) is a technique to obtain low dimensional representation for
high dimensional data, which can be further processed for data compression and data de-noising.
If A is any M x N matrix, it is possible to find a decomposition of the form A=U S VT
, Where U

Computer Science & Information Technology (CS & IT)
and V are orthogonal matrices of order M x M
x N having positive elements λi (i=1,2,3,..n) called singular values
subjected to transpose, scaling, flipping,
same as that of matrix A, making singular values of an image have very good stability i.e. when a
small perturbation is added to an image, the values do not change significantl
employed for image watermarking [8], [9
Figure 2.Contourlet Transform Decomposition
4. Proposed Algorithm
The proposed approach for watermarking of still images is based on a hybrid combination of
contourlet transform and singular value decomposition
to ensure additional security. The detailed steps involved are explained below
4.1. Watermark Embedding
Embedding the watermark image
camouflaged onto the original image, followed by encoding the intermediate double image into
an RGB image. This image is prone to various statistical attacks, so the image is shuffled and
scrambled to reduce correlation. Further individual pixel values are encrypted to increas
4.1.1. Step 1
In this step watermark image is embedded to the original image to get the transformed
watermarked image
Step i. Apply contourlet transform to the original image to decompose into sub bands (CTO).
Step ii. Do the same with the watermark image to decompose into sub bands (CTW).
and V are orthogonal matrices of order M x M and N x N, and the diagonal matrix S is of order M
(i=1,2,3,..n) called singular values. Even though the matrix A is
flipping, rotation or translation the singular values still remain the
making singular values of an image have very good stability i.e. when a
small perturbation is added to an image, the values do not change significantly. Thus it was
oyed for image watermarking [8], [9].
Figure 2.Contourlet Transform Decomposition
contourlet transform and singular value decomposition. Also the intermediate image is encrypted
The detailed steps involved are explained below.
Embedding the watermark image is a four step procedure. First the watermark
original image, followed by encoding the intermediate double image into
scrambled to reduce correlation. Further individual pixel values are encrypted to increas
watermark image is embedded to the original image to get the transformed
pply contourlet transform to the original image to decompose into sub bands (CTO).
watermark image to decompose into sub bands (CTW).
349
is of order M
. Even though the matrix A is
ranslation the singular values still remain the
making singular values of an image have very good stability i.e. when a
y. Thus it was
the intermediate image is encrypted
watermark image is
original image, followed by encoding the intermediate double image into
scrambled to reduce correlation. Further individual pixel values are encrypted to increase entropy.
watermark image is embedded to the original image to get the transformed
pply contourlet transform to the original image to decompose into sub bands (CTO).

Step iii. Apply SVD to low frequency sub band (CTO{1}) of contourlet transformed original
image.
[U S VT
] = SVD(CTO{1}) (1)
Step iv. Modify matrix S so obtained, by salting it with the values of low frequency sub band of
contourlet transformed watermark image.
S’ = S + α CTW{1} (2)
Where α being the scaling factor.
Step v. Reverse the operation in 3 to get the low frequency sub band of watermarked image.
CTT{1}=U*S’*VT
(3)
Step vi. To get other of other sub bands of the watermarked image, add the corresponding sub
bands of CTW to that of CTO, with the same scaling factor
CTT{i}{j}=CTO{i}{j}+ α CTW{i}{j} (4)
where i=2 to 5 and j=3 if i=2 else 2^(i-1).
Step vii. Apply inverse contourlet transform using the modified coefficients (CTT) to obtain the
watermarked image.
4.1.2. Step 2
The watermarked image so obtained is prone to attacks (resizing, median filtering, histogram
equalization, sharpening, etc..), also as its values range from [-1000.000 +1000.000], it has to be
converted to suitable format for storage and data transfer. So we propose the following novel
image encryption algorithm, which results in low correlation and high entropy. Here, we convert
the signed double watermarked image (IW) into an RGB unsigned 8 bit image (IW’), by the
following:
If IW(x1,y1) < 0
s = sqrt(IW(x1,y1)*(-1))
else
s = sqrt(IW(x1,y1))
end
f = floor((sim-floor(sim))*100)
d = floor(sim)
r = round(IW(x1,y1)-(d+f)^2)*100)
IW’(x1,y1,1) = d
IW’(x1,y1,3) = r
If IW(x1,y1) < 0
IW’(x1,y1,2) = 100+f
else
IW’(x1,y1,2) = f
end
Here, IW’( : , : , i) represents R,G,B as i=1,2,3 respectively. Now if we can notice, square root of
positive pixel values of IW is calculated and the decimal part is stored in red component of IW’
and the fraction part rounded to two decimal places (storing 3 decimal places would require more
than 8 bits, so we stick to 2) is stored in green component, also its clear that these values do not
exceed 100, so if the original pixel values in IW was negative, 100 is added, which acts as a sign

Computer Science & Information Technology (CS & IT) 351
indicator and later can be subtracted during decryption. Since we are considering only square
root rounded to 2 decimal places, there will always be fractional error part, which is stored in blue
component.
4.1.3. Step 3
Image Scrambling and Shuffling -
Step i. Divide the whole image IW’ into 16x16 size blocks, B1, B2, . . ., Bn.
Step ii. Apply Cat map within block Bi by the following equation:
൤
‫′ݔ‬
‫′ݕ‬
൨=ቂ
1 1
1 2
ቃ ቂ
‫ݔ‬
‫ݕ‬ቃ
(5)
Where (x,y) are original coordinates of IW’ and (x’,y’) are new shuffled coordinates . After
repeating this step for n times we get partially shuffled image IW’’ (x, y).
Step iii. Then uniform scrambling is applied onto the image IW’’ where the pixels in the same
block of original image is distributed into all the blocks of scrambled image and the every block
has one pixel at least, without regarding to the order of the pixels appearance, accordingly all the
pixels in the same block of scrambled image come from different blocks of original image. Figure
below shows that all the pixels in the first block of the original image are distributed into all the
blocks of the scrambled image. Thus, the ideal block numbers is N for an original image of size
NxN. After scrambling, the resultant would be a new image IW’’’.
Figure 3. Uniform Image Scrambling
Step iv. Apply Cat map to IW’’’ to shuffle the pixels of the whole image. Steps i to iv are
repeated n times to get the finally shuffled image IS. In our case we performed 3 iterations were
performed to get the shuffled image.
4.1.4. Step 4
Image so shuffled is encryption to increase entropy. Encryption is performed on the image IS of
size NxN using secret keys Z and L, to get the encrypted image IE using the following proposed
algorithm-
for x = 1 to N
for y = 1 to N
KB1=mod(10^14*Z,256)
Z=L*Z*(1-Z)
KB2=mod(10^14*Z,256)
Z=L*Z*(1-Z)

IE(x,y)= mod(IS(x,y)+KB1,256)
IE(x,y)= xor(IE(x,y),KB2)
end
end
In our case, the keys Z and L were taken to be 0.3915 and 3.9985 respectively. The above method
uses modulus operation, restricting the encrypted values less than 256 and thus making it 8 bit
encrypted image. The above steps ie., shuffling, scrambling and encryption had to be performed
separately for the three RGB components of the image IW’. Also the proposed approach results in
very high entropy close to the ideal value 8.
4.2. Water Mark Extraction
The encrypted image IE first has to be decrypted then the watermark image is extracted, the
following three steps explain the decryption process and step 4, the watermark extraction process.
4.2.1. Step1
The image IE is decrypted by the following snippet, using the same keys Z and L used during
encryption ( 0.3915 and 3.9985 respectively) -
for x = 1 to N
for y = 1 to N
KB1=mod(10^14*Z,256)
Z=L*Z*(1-Z)
KB2=mod(10^14*Z,256)
Z=L*Z*(1-Z)
ID(x,y)= xor(IE(x,y),KB2)
ID(x,y)= mod(ID(x,y)-KB1,256)
end
end
The resultant would be the decrypted image ID, having the pixel values same as that of original
image, but correlation between adjacent pixel still not being the same due shuffling.
4.2.2. Step 2
Now the shuffling and scrambling performed during watermark embedding process has to be
nullified to get back the intermediate RGB watermarked image.
Step i. Apply inverse of the transformation matrix used in embedding process to shuffle the pixels
of the whole image. During watermark embedding, Arnold Cat transformation used ቂ
1 1
1 2
ቃ as
mapping matrix, thus here its inverse ቂ
2 −1
−1 1
ቃ is used as transformation matrix to get the
partially de-shuffled image ID’.
Step ii. Now the block wise shuffling and scrambling effect on the pixels performed during
process has to be nullified. For this Then divide the whole image ID’ into 16x16 size blocks, B1,
B2, . . ., Bn. And the pixels uniformly scattered across the image amongst different blocks has to
be brought back to their respective block. This is reverse of image scrambling operation
performed in step 3.ii of watermark embedding mechanism.

Computer Science & Information Technology (CS & IT) 353
Step iii. The transformation matrix used in step i, is applied once again on each of the blocks B1,
B2,.., Bn to de-shuffle the image block wise. Steps i to iii are repeated the same number of
iterations performed during embedding process to finally remove all the shuffling and
scrambling, fetching image IWD. Also the above 2 steps of de-shuffling and decrypting has to be
performed separately on the RGB components of the encrypted image to get the original RGB
watermarked image.
4.3.3. Step 3
Now the RGB watermarked image IWD so obtained has to be converted back to intermediate
signed double watermarked image. According to the encoding algorithm, the red component of
image represents decimal part of square root of required double value, green component the
fractional part and blue component represents fractional error. This information is used to decode
as shown by the following algorithm,
If IWD(x,y,2) >= 100
IWD’(x,y)=-1;
IWD(x,y,2)=IWD(x1,y1,2)-100;
else
IWD’(x,y)=1;
end
// Above takes care of sign
IWD’(x,y)=IWD’(x,y)*((IWD(x,y,1)+IWD(x,y,2)/100)^2+IWD(x,y,3))
Here x and y are pixel coordinated of the image and they range from 1 to N, since assuming IWD
is of size NxNx3. Thus finally IWD’ is the decrypted watermarked image obtained, also NCC
(Normalized Correlation Coefficient) between IW (watermarked image during embedding
process) and IWD’ is very close to 1, proving correctness of the proposed encryption-decryption
algorithm.
4.4.4. Step 4
Watermark Extraction is done by the following steps
Step i. Apply contourlet transform to the watermarked image to decompose into sub bands (CTT).
Step ii. Do the same with the original image to decompose into sub bands (CTO).
Step iii. Apply SVD to low frequency sub band (CTO{1}) of contourlet transformed original
image.
[U S VT
] = svd(CTO{1}) (6)
Step iv. To extract the values of low frequency sub band of contourlet transformed watermark
image, originally salted during embedding we perform the following operations
S’’=inv(U)*CTT{1}*inv(VT
)
CTW’{1} = (S’’ - CTO{1}) / α
(7)
(8)
Here CTW’ is the extracted low frequency sub band.
Step v. Extracting the other frequency sub bands follows the following equation
CTW’{i}{j}=(CTT{i}{j}- CTO{i}{j}) / α (10)
where i=2 to 5, j=3 if i=2 else 2^(i-1)

Step vi. Finally apply inverse contourlet transform using the extracted coefficients (CTW’) to
obtain the extracted watermark image.
5. Experimental Results
In the experiments that we have tested, we used the original image as shown in the figure(4)(a)
and watermark shown in figure(4)(b). Both are gray scale images of size 512 x 512 pixels. The
normalized correlation coefficient without attack is obtained to be 0.9919, which very close to
ideal value 1 as shown in figure(4)(c). Also the intermediate encrypted RGB watermarked image
shown in figure(4)(d) has an ideal entropy of 8, which is the required. Normalized Correlation
Coefficient is calculated using the equation (11) and entropy by the equation (12). MATLAB was
used for testing the robustness of the proposed approach. Various attacks that was used to test
robustness of the proposed watermark algorithm are erode, dilate, open, close, const value added
and subtracted, motion filter, gaussian blur, sharpening, weiner filter, high pass filter, low pass
filter and mean filter. The results of the various above attacks are shown in table 1.
Entropy is calculated by the equation below
Entropy =∑(p(k) ∗ log(1/p(k))) (11)
where p(k) is the probability of occurrence of a pixel with gray scale value k.
And Normalized Correlation Coefficient is calculated by the equation
NCC =
∑ ∑ ூ′(௫,௬)ூ(௫,௬)ಿ
ೣసబ
ಾ
೤సబ
ට∑ ∑ ூ′(௫,௬)మ ∑ ∑ ூ(௫,௬)ಿ
ೣసబ
ಾ
೤సబ
మಿ
ೣసబ
ಾ
೤సబ
(12)
where I is the mean centred watermark image, I’ is the extracted mean centred watermark image,
and both are of size MxN
Figure 4. Step involved in Watermark Embedding and Extraction
Table 1. NCC for various Attacks

Attack
Erode
Open
Const value added
Motion filter
Sharpening
Low pass filter
Mean filter
The proposed algorithm works well for
figure(5). The extracted watermark image has a NCC of 0.9717 which is appreciable. Also the
quality of extracted watermark survives after several attacks, but in some cases the quality and
texture degrades as shown in the figure(
(a)
Figure 5. (a) Original Watermark Image
(a)
Figure 6.Extracted Watermark after (a
6. Conclusion
We proposed a new approach for watermarking of still images bas
contourlet transform and singular value decomposition concepts, also imparting a novel image
encryption for multi-media data security. The proposed
information is robust and the experimental results
large blurring by mean and Gaussian filtering
NCC Attack NCC
0.9821 Dilate 0.9627
0.9886 Close 0.9899
0.9898 Const value subtracted 0.9905
0.9893 Gaussian blur 0.9865
0.9818 Weiner filter 0.9906
0.9904 High pass filter 0.9897
0.9899
The proposed algorithm works well for more complicated watermark images also,
. The extracted watermark image has a NCC of 0.9717 which is appreciable. Also the
texture degrades as shown in the figure(6)
(a) (b)
igure 5. (a) Original Watermark Image (b) Extracted Watermark Image
(a) (b) (c) (d)
Extracted Watermark after (a)Erode (b) Dilate (c) Gaussian blur (d) Low pass f
We proposed a new approach for watermarking of still images based on a hybrid combination of
a data security. The proposed method of embedding the copyright
experimental results show that it has survived various
blurring by mean and Gaussian filtering, linear filtering (high pass filtering and low pass
355
as shown in
. The extracted watermark image has a NCC of 0.9717 which is appreciable. Also the
(d)
(d) Low pass filter
ed on a hybrid combination of
g the copyright
show that it has survived various attacks like
and low pass

filtering), non-linear filtering (median filtering), addition of constant offset to the pixel values,
local exchange of pixels and more. Future work will concentrate to extend the same to video and
audio watermarking, also making the method more practical that can be implemented in real life
applications.
7. References
[1] Minh N. Do, and Martin Vetterli, “The Contourlet Transform: An Efficient Directional
Multiresolution Image Representation” IEEE transaction on image processing,vol 14,issue no 12,pp
2091-2106,Dec 2005.
[2] E. J. Candes and D. L. Donoho. Curvelets- a surprisingly effective nonadaptive representation for
objects with edges. Saint-Malo Proceedings, 1999.
[3] Elham salahi ,M.Shahram Moin and Ahmad salahi “A new Visually Imperceptible and Robust Image
water marking Scheme in contourlet Domain” International conference on intelligent information
hiding and multimedia signal processing, 2008.
[4] C. T. Hsu and J. L. Wu. Multiresolution watermarking for digital images. IEEE Trans. on Circuit and
Systems, 45:1097– 1101, Aug. 1998.
[5] D. Kundur and D. Hatzinakos. Towards robust logo watermarking using multiresolution image fusion
principles. IEEE Trans. on Image Processing, 6(1):185–198, Feb. 2004.
[6] R. Liu and T. Tan, “An SVD based watermarking scheme for protecting rightful ownership”, IEEE
Trans, Multimedia. Vol. 4 , no.1, pp.121-128, Mar. 2002.
[7] Alexander Sverdlov,Scott Dexter and Ahmet M.Eskicioglu “Robust DCT_SVD domain image
watermarking for copyright protection: embedding data in all frequencies”.
[8] Akhaee, M. A.; Sahraeian, S. M. E.; Marvasti, F. (2010): Contourlet-Based Image Watermarking
Using Optimum Detector in a Noisy Environment, IEEE Transactions on Image Processing, 19(4),
pp. 967-980.
[9] B.Chandra Mohan and S.Srinivas Kumar “ Robust Digital watermarking scheme using Contourlet
Transform” IJCSNS International journal of computer science and network security,Vol.8
No.2,February 2008.
[10] Khalighi, S.; Tirdad, P.; Rabiee H. R. (2009): A New Robust Non-Blind Digital Watermarking
Scheme in Contourlet Domain, IEEE Conference, pp. 20-25.

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