A new partial image encryption method for document images using variance based quad tree decomposition

International Journal of Electrical and Computer Engineering (IJECE)
Vol. 10, No. 1, February 2020, pp. 786~800
ISSN: 2088-8708, DOI: 10.11591/ijece.v10i1.pp786-800  786
Journal homepage: http://ijece.iaescore.com/index.php/IJECE
A new partial image encryption method for document images
using variance based quad tree decomposition
C. R. Revanna1
, C. Keshavamurthy2
1
Research Scholar at Jain University, Bangalore, India
1
Faculty of ECE, Government Engineering College, Ramanagara, Karnataka, India
2
Professor, Department of ECE, SRSIT, Bangalore, Karnataka, India
Article Info ABSTRACT
Article history:
Received Feb 18, 2018
Revised Aug 21, 2019
Accepted Sep 27, 2019
The proposed method partially and completely encrypts the gray scale
Document images. The complete image encryption is also performed to
compare the performance with the existing encryption methods. The partial
encryption is carried out by segmenting the image using the Quad-tree
decomposition method based on the variance of the image block. The image
blocks with uniform pixel levels are considered insignificant blocks and
others the significant blocks. The pixels in the significant blocks are
permuted by using 1D Skew tent chaotic map. The partially encrypted image
blocks are further permuted using 2D Henon map to increase the security
level and fed as input to complete encryption. The complete encryption is
carried out by diffusing the partially encrypted image. Two levels of
diffusion are performed. The first level simply modifies the pixels in
the partially encrypted image with the Bernoulli’s chaotic map. The second
level establishes the interdependency between rows and columns of the first
level diffused image. The experiment is conducted for both partial and
complete image encryption on the Document images. The proposed scheme
yields better results for both partial and complete encryption on Speed,
statistical and dynamical attacks. The results ensure better security when
compared to existing encryption schemes.
Keywords:
MSE
NPCR
PSNR
SSIM
UACI
Copyright © 2020 Institute of Advanced Engineering and Science.
All rights reserved.
Corresponding Author:
C. R. Revanna,
Research Scholar at Jain University, Bangalore, India
Faculty of ECE, Government Engineering College,
Ramanagara, Karnataka, India.
Email: revannacr2008@gmail.com
1. INTRODUCTION
The storage and exchange of images with high definition, redundancies and correlation of an
important document at a higher rate of transmission itself takes a longer time and the encryption of such
images takes additional computational time too. This requires a balance between security and
synchronization for real time applications. In such situations, where high definition, low memory and low
power are the limitations of the resources, partial encryption of the data is advantageous than encrypting an
entire image. Partial encryption helps in reducing the computations and bandwidth. The document images
consist of correlated and uncorrelated parts. Encryption of only the correlated part suffices than encrypting
the complete image. The core idea of partial encryption is to first identify the significant pixels or region of
pixels and then encrypt that region. Partial encryption also includes encryption of data with different security
levels to suit end user customer requirement. A significant region from the complete image may be selected
either statistically or dynamically for partial encryption to fulfill security and computational time for real
time applications. So the partial encryption increases the efficacy of encryption by reducing computation
size. To ensure a good security level a minimal data of 12.5% has to be encrypted [1].

Int J Elec & Comp Eng ISSN: 2088-8708 
A new partial image encryption method for document images using variance based quad ... (C R Revanna)
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In [2], the authors proposed a bit-level scrambling algorithms to scramble bit positions. It is also said
that the proposed algorithm provides flexibility to select any image as the input source image, any
decomposition technique for obtaining the bit plane, any decomposed bit plane as the security key bit plane
and any scrambling technique for the bit-level permutation. In [3], a chaotic system based partial image
encryption is proposed. The proposed scheme includes bit plane decomposition of source image.
After decomposing, the significant bit plane are selected for encryption. Encryption is achieved by generating
the pseudorandom number sequence using chaotic system.
In [4], a chaotic based partial grey sale image encryption is proposed. It is observed that the authors
proposed a bit plane decomposing method for encryption. The various bit planes (significant and
insignificant) are identified based on autocorrelation threshold of different binary planes. The key sequence
obtained by chaotic map is used to encrypt the correlated bit planes. In [5], both selective and complete
image encryption using the sequence of chaotic map. At first the chaotic map is used to generate a key to
completely encrypt the plain image. Second, for the same input image selective portion is encrypted.
Finally the complete and selective encrypted results are combined by XOR operation to achieve better
security. A new technique called graph coloring problem (GCP) for partial encryption of medical image is
proposed in [6]. The GCP technique is used to select the optimal positions of the pixels from the input
medical image. In [7], researchers presented a partial image encryption technique based shuffling the pixels
within a block. Pixels shuffling are achieved based on the sequence of chaotic map. By selecting varied block
size, data encryption quantum can be varied.
In [8], a partial grayscale enciphering based on the chaotic map is proposed. The grayscale image is
decomposed into eight binary planes. Scrambling is done for most significant bit planes. The Chaotic
sequence generated by the Skew tent map is used to scramble the planes. The scrambled bit planes are
encrypted to obtain cipher image. In [9], authors proposed a transform domain approach for partial image
encryption. Four sub-bands are arrived at by applying DWT for the input plain image. The low frequency
sub-band is encrypted by the sequence generated by the Logistic chaotic map. At last encrypted low
frequency band and non-encrypted high frequency band are combined and inverse discrete wavelet transform
is applied to obtain the cipher image. Discrete Cosine Transform (DCT) based partial encryption of color
image is proposed in [10].
The DCT is applied for the input source image for all three planes. Then the encryption is performed
by the sequence generated by the Logistic chaotic map. The encrypted planes are combined and inverse DCT
is applied to obtain cipher image. In [11], the authors proposed an enciphering technique based on two levels
of permutation and substitution. For every input source image, a dynamic key is generated which results in
the basis of encryption processes. Then, a nonlinear S-box method is used for image substitution which is
followed by a matrix multiplication which is performed for image diffusion. These two processes finally
results in a cipher image. In [12], proposed a technique which combines both partial encryption and image
compression. The compression is achieved by the quad tree and SPHIT image compression techniques.
Only 13-27% of the quad tree compressed data and less than 2% of the SPHIT compressed data is partially
encrypted for security. In [13] an efficient selective image encryption technique combining saw tooth filling,
selected pixels, non-linear chaotic map and SVD(singular value decomposition) is proposed. Image
scrambling is done using the saw tooth filling, whereas significant pixels are selected based on the pixels of
interest. Finally, diffusion is performed on the more weighted pixels using chaotic map and singular value
decomposition as the key. A substitution box [S-box] and linear fractional transform technique is proposed in
[14] for partial image encryption. The proposed technique uses a lifting wavelet transform in frequency
domain, which provides a sensitive information that can be encrypted by the sequence generated from chaotic
map. The dual process of confusion and diffusion are carried out via permutation, diffusion and substitution
process. In [15], a partial image encryption using DCT and light weight stream technique is proposed.
By considering the basic fundamental attacks like statistical attack, replacement attack and differential attack,
DCT Coefficients based transformation technique is proposed. In [16], a partial image encryption based on
bit plane decomposition is proposed. The input source image is segmented into eight bit planes.
Then the significant binary bit plane is considered for encryption. Using the tent chaotic map, a key sequence
is obtained for encryption.
In [17], a non-adaptive partial encryption of grayscale image is performed using Chaotic map is
proposed. The input source image is sub-divided into eight binary planes. By the Tent map method applying
pseudorandom sequences, four significant bit planes are encrypted. The partial image encryption is obtained
by scrambling using non sinusoidal wavelets is proposed in [18]. Kekre’s Walsh Sequence procedure is used
to scramble the image in the transform domain (wavelet). The transform domain helps in preventing
the attacks by statistical means. In [19], a partial encryption technique is proposed. Encryption in both Spatial
and transform domain has been deployed in this case. The bit plane decomposition technique is used for
encrypting the image in spatial domain. At last, the ratio of encryption time and encoding time is calculated

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Int J Elec & Comp Eng, Vol. 10, No. 1, February 2020 : 786 - 800
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to illustrate the speed performance. In [20], a DCT based partial color image encryption is presented.
The DCT is used to select the significant regions in three different planes from the color image.
Then the selected regions are encrypted or diffused using the Arnold chaotic map which results in
cipher image.
From the literature review, there is a need to encrypt the Document images partially to synchronize
with the real time applications and increase the security level for hand held devices and other less
computationally capable gadgets. When an image is viewed as a whole with blocks, the blocks with uniform
pixel intensity levels (Histogram) exhibit less meaningful information in the image but blocks with unequal
pixel intensity levels exhibit more intelligent information and are referred to as significant regions. There is
a need to identify blocks with unequal intensity levels. The proposed method uses a different approach to find
the significant regions and encrypt only those regions. For identifying the significant regions, the image is
segmented into blocks by taking variance as a parameter for Quad-tree Segmentation technique. This method
decomposes an image into significant and insignificant blocks. It is enough to encrypt only the significant
blocks to partially encrypt an image. The block size is a preset value, depending on the requirement based on
the level of security. The partial encryption is performed using a chaotic system. The proposed work is also
extended for complete encryption using mixed chaotic system.
2. RESEARCH METHOD
2.1. Quad tree segmentation
The Quad tree method is applied for the division of an image into blocks/regions by applying
recursion [21]. The partitioned blocks are arranged in the form of hierarchal tree structure. The root block is
called as parent block and the partitioned blocks are called as child blocks. The parent block is segmented
into four (quad) equally sized sub-blocks and each sub-block is subjected to a test. A block is checked to see
if the criterion for homogeneity is met, if it meets, then no further division is made and the node is left
undivided and is called as a leaf node. If the criterion is not met, then divide the block into four sub blocks or
regions and apply the test criteria again. The above procedure is performed until each sub-block obeys
the criteria. Therefore each node/parent is either have no children or has four children. Hence the quad tree
decomposing technique partitions the image into sub blocks or regions that are more homogeneous than
the image itself. The least block size is variable one and depends on the requirements that suit the application.
The decomposing lasts when Quad tree reaches its minimum size [22].
The quad tree decomposition is shown in the Figure 1 with a tree diagram. The root node indicates
the whole image, this node is partitioned into equally sized four sub-blocks if it fails to satisfy the criteria of
homogeneity. The leaf node indicates a block satisfies the homogeneity criteria.
Figure 1. (a) Sample Image, (b) Quad Tree Decomposition Structure
2.2. Image Decomposition Criteria
The quad tree decomposition is made with variance of the image as the criteria. The variance of
a block is calculated by computing the mean of the pixels in that block. The variance equation can be
given as
𝑉(𝑥) =
1
𝑛
× ∑ [𝑥𝑖 − µ(𝑥)]2𝑛
𝑖=1 . (1)

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where µ(𝑥) is the mean of that block.
µ(𝑥) =
1
𝑛
× [∑ 𝑥𝑖].𝑛
𝑖=1 (2)
The variance of the parent block calculated first and the variance of the partitioned children blocks
are determined individually. Now check for the variance of the individual block, if it is greater than its parent
block, then decompose the child block further. Otherwise the child block is left as a leaf block/node with no
further division. This results in decomposing the image with unequal size partitioned blocks. Figure 2 is an
example of a picture document which is decomposed into smaller blocks. A 4 × 4 decomposed Lena image is
represented in Figure 2(a). Figure 2(b) represents the corresponding mapped blocks.
Figure 2. (a) Quad Tree Decomposition with Block Size 4 × 4,
(b) Decomposed Blocks mapped for Lena image
2.3. Chaotic Map
2.3.1. Skew tent map
This chaotic map is one dimensional in nature. It is also called as asymmetric tent map.
Mathematically, it is given by
𝑥 𝑛+1 = 𝑈(𝑥 𝑛) ∶= {
𝑥 𝑛
𝑎
, 𝐼𝑓 𝑥 𝑛 ∈ [0, 𝑎],
1−𝑥 𝑛
1−𝑎
, 𝐼𝑓 𝑥 𝑛 ∈ [𝑎, 1].
(3)
where 𝑎 is control parameter ranges from [0, 1] and xn is the state of system whose value ranges from [0, 1].
At 𝑎= 0.5, 𝑈(𝑥 𝑛) becomes a regular tent map. Further details can be had on this map in [23].
2.3.2. Bernoulli map
This chaotic map is also one dimensional in nature. General formula for Bernoulli map can be
written as follows
𝑥 𝑘+1 = (𝑏 𝑥 𝑘)𝑚𝑜𝑑 1 𝑤ℎ𝑒𝑟𝑒 𝑥 ∈ [0, 1]. (4)
The control parameter of Bernoulli map (i.e., b) should be taken in the range of 1 to 5 to keep
chaotic behavior [24, 25]. For 𝑏 = 2, Eq. 4 can be written as follows
𝑥 𝑘+1 = (2 𝑥 𝑘)𝑚𝑜𝑑 1 ∶= {
2𝑥 𝑛, 𝐼𝑓 𝑥 𝑛 ∈ [0,
1
2
],
2𝑥 𝑛 − 1, 𝐼𝑓 𝑥 𝑛 ∈ [
1
2
, 1] .
(5)
where 𝑥0 = 0.2709 is taken as the initial value. Further details can be had on this map in [26].
2.3.3. Henon map
In discrete time dynamic systems Henon map exhibit good chaotic behavior. It takes the point
(𝑋 𝑘,𝑌𝑘) in the space and maps it to a new point.
Mathematically it can formulated as
𝑥 𝑘+1 = 𝑦 𝑘 − 1 + 𝑎𝑦 𝑘
2
, (6)

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𝑦 𝑘+1= 𝑏𝑥 𝑘. (7)
The initial value 𝑥0 ∈ (0, 1) and 𝑦0 ∈ (0, 1) can be used as the key for the system (𝑥0, 𝑦0). The Henon map
mainly depends on two parameters 𝑎 and 𝑏, the research results show that the value for 𝑎 = 1.4 and 𝑏 = 0.3,
the Henon map exhibits chaotic nature [27].
2.4. Partial image encryption
The resultant decomposed image blocks of minimum size (variable) are scrambled using a Skew tent
chaotic map. The partial encryption is performed detailed below.
1. Generate the chaotic sequences using the Skew tent map for each block size.
2. The chaotic sequence generated for a particular block size is used to confuse that block as follows.
a. Convert the generated chaotic sequences for the block size into natural numbers by multiplying with
a factor of 1015
(precision of real numbers) and obtain a unique index value whose range lies within
the block size (Perform Modulus).
b. Scramble/permute the various pixels within each block based on the index values generated in
the previous step.
3. The steps 1 and 2 are repeated for all the block sizes generated.
The block diagram of the partial and complete encryption is shown in Figure 3 (a). The resultant
partial encryption is referred as the first level confusion. The sequence of actions on the Document image is
pictorially depicted in Figure 3 (b). The partially encrypted results for the Lena image with block sizes
of 8 × 8, 16 × 16 and 32 × 32 are shown in Figure 4 (a), 4 (b) and 4 (c) respectively.
Figure 3 (a). Block diagram of proposed scheme
Figure 3 (b). Flow diagram of proposed document image segmentation using quad tree

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Figure 4. Partially Encrypted Lena images for (a) Block Size equal to 8 × 8, (b) Block Size equal to 16 × 16,
(c) Block Size equal to 32 × 32, (d) Second level confused image
2.5. Complete image encryption
The proposed scheme can be further extended for complete image encryption by the addition of
second level confusion and diffusion. In diffusion, where the pixel values are modified according to
the sequence generated by the chaotic map including, establishing interdependency between the pixels.
Diffusion is carried out at the first and second levels.
2.5.1. Second level confusion
1. Divide the partially encrypted image into non-overlapping blocks of size equal to the least level for which
the partially encrypted block size is considered.
2. Generate chaotic sequence using 2D Henon map equal to number of blocks.
3. Permute the blocks according to sequence generated by Henon map. The resultant matrix is ‘C’.
Figure 4 (d) depicts the second level confused image obtained after the partial encryption.
2.5.2. First level diffusion
1. Generate the chaotic sequence using the Bernoulli’s map of size [1, M × N].
2. The generated sequence is converted into integer by multiplying with a factor of 1015
and modulus it with
255. Arrange this sequence of integers in order to obtain the matrix ‘A’ of size M × N.
3. The matrix ‘B’ which is the result of first level of diffusion is arrived by XORing the pixels of the
partially encrypted image (from Section 2.4) with the corresponding pixels (elements) of the matrix ‘A’
obtained in the previous step.
2.5.3. Second level diffusion
To establish more interdependency between the neighboring pixels
1. Convert the input image matrix I of size M × N into an array 𝑋 𝑛 .Where n= 1, 2, 3………. M × N.
2. Establish forward row wise interdependency as shown Figure 5 such that
𝑋 𝑛
′
∶= {
𝑋 𝑛, 𝑓𝑜𝑟 𝑛 = 0,
𝑋 𝑛 ⊕ 𝑋 𝑛−1
′
, 𝑓𝑜𝑟 𝑛 = 1,2,3… . . 𝑀 × N.
(8)
3. Establish backward row wise interdependency as shown Figure 5 such that
𝑋 𝐾
′′
∶= {
𝑋 𝐾
′
, 𝑓𝑜𝑟 𝐾 = 𝑀 × N,
𝑋 𝐾
′
⊕ 𝑋 𝐾+1
′′
, 𝑓𝑜𝑟 0 < 𝐾 < 𝑀 × N.
(9)
4. Arrange 𝑋 𝐾
′′
into a matrix J of size M × N, arrange elements of J into an array 𝑋𝑙
′′′
using column wise
progressive scan method.

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5. Establish column wise pixel inter dependency as shown Figure 5 such that
𝑋𝑙
′′′
∶= {
𝑋𝑙
′′
, 𝑓𝑜𝑟 𝑙 = 0,
𝑋𝑙
′′
⊕ 𝑋𝑙−1
′′′
, 𝑓𝑜𝑟 𝑙 = 1,2,3… . . 𝑀 × N.
(10)
6. Arrange 𝑋𝑙
′′′
into a matrix ‘D’ of size M × N.
7. The second level diffused image is the resultant matrix ‘E’ (Cipher Image as shown in Figure 6(b))
obtained by XORing the first level diffused image ‘B’ with matrix ‘D’ obtained in step 6.
Figure 5. Interdependency matrix generation Figure 6. (a) Input plain lena image, (b) Complete
cipher image
2.6. Complete image decryption
The decryption is the reverse process of encryption. To decipher the encrypted image the following
steps are followed.
1. The interdependency matrix ‘D’ which is shared (by sender) is XORed with the cipher image/matrix ‘E’
to obtain the first level diffused image ‘B’.
2. Generate the matrix ‘A’ using Bernoulli’s map with the same initial conditions and control parameters
used in encryption (As in Step 1 and 2 of Section 2.5.2).
3. The second level confused image is obtained by performing XOR of matrix ‘C’ with ‘B’.
4. Generate the Chaotic sequence using 2D Henon map with the same initial conditions and control
parameters to permute the non-overlapping blocks obtained at the second level confused image and thus
obtain the partially encrypted image.
5. Generate the chaotic sequence using Skew tent map with the same initial conditions and control
parameters as in section 2.4 and permute the pixels within the blocks generated out of Quad Tree
Decomposition. The resultant image obtained is the Original Plain image.
3. RESULTS AND ANALYSIS
To determine how much efficient the proposed encryption method to provide the security,
the performance analysis was developed in MATALAB R2014a software using a Laptop having 4GB RAM
and 80GB Hard disc. The simulation outputs of the proposed algorithm reveals that various gray scale images
of different sizes (512 × 512 and 256 × 256) are fed as the input plain image. The initial conditions and
the control parameters used are as shown in Table 1. The various block sizes used are 8×8, 16×16 and
32×32.
Table 1. Different maps with control parameters and initial conditions used as Keys
MAP SUB KEYS CONTROL PARAMETERS INITIAL CONDITIONS
Skew Tent Map k1 a = 0.5 x0 = 0.1
Bernoulli map K2 b = 2 x0 = 0.2705
Henon Map k3
a = 1.4 x0 = 0.6315477
b = 0.3 y0 = 0.18906343

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3.1. Mean square error and peak signal to noise ratio
The mean square error is nothing but the differences in intensity levels of pixels between input and
output image representing the noise level. For an ideally completely encrypted cipher image, the MSE value
is more but for the partially encrypted image, its value is moderate. MSE is calculated by using the equation
𝑀𝑆𝐸 =
∑ ∑ [𝑝𝑙𝑎𝑖𝑛(𝑖,𝑗)−𝑐𝑖𝑝ℎ𝑒𝑟(𝑖,𝑗)]2𝑁
𝑗=1
𝑀
𝑖=1
𝑀 × 𝑁
. (11)
The partial encryption is always not secure because only the correlated part of the image is
encrypted and the remaining part is left unencrypted. The amount of image encrypted determines
the confidentiality level. A better confidentiality level is obtained when a minimum of 12.5% of data
encrypted [1]. The proposed method yields 60% of encryption for a block size of 8×8.
% of encryption=
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑖𝑥𝑒𝑙𝑠 𝑒𝑛𝑐𝑟𝑦𝑝𝑡𝑒𝑑
𝑡𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑖𝑥𝑒𝑙𝑠
. (12)
The PSNR of the encrypted document image should be less than 30dB in order to prevent
the interceptor from extracting the plain image out of the noise present in the cipher image. Our method
yields a PSNR of 8.8925dB. PSNR is given by
𝑃𝑆𝑁𝑅 = 10𝑙𝑜𝑔10 (
2552
𝑀𝑆𝐸
). (13)
3.2. Histogram
Histogram is a pictorial way of depicting pixel distribution of varying intensity levels. It is plotted
as, the total number of pixels with varying intensity along the y-axis and the different intensity levels along
the x-axis. The histogram of plain and cipher image are shown in Figure 7. For a completely encrypted image
the histogram is flat, but the partially encrypted image has spikes in it and is same as that of the plain image
since, only the permutation of the pixels takes place. This depicts that any kind of statistical attack on
the completely encrypted image is impossible but for the partially encrypted image it may be possible.
Figure 7. Histogram of (a) Plain image, (b) Cipher image (complete encryption)
3.3. Correlation
A clearly visible image with proper brightness has its correlation coefficient equal to one, but for
the ciphered image it has a significantly reduced value (almost equal to zero). An encryption algorithm
generates a ciphered image with randomly distributed pixels of different intensities and has its correlation
coefficient between adjacent pixels close to zero. A set of 4000 pairs of two adjacent pixels in all directions
(horizontal, vertical and diagonal) were randomly selected to determine the correlation coefficient from
the plain and ciphered image. The correlation coefficient is given by
𝐶 𝑥𝑦 =
𝐶𝑂𝑉𝑅(𝑥,𝑦)
√𝑉(𝑥)√𝑉(𝑦)
. (14)

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where 𝐶𝑂𝑉𝑅(𝑥, 𝑦) is the Covariance between x and y. it is given by
𝐶𝑂𝑉𝑅(𝑥, 𝑦) =
1
𝑛
× ∑ 𝐸[(𝑥𝑖 − µ(𝑥))(𝑦𝑖 − µ(𝑦))]𝑛
𝑖=1 . (15)
where x and y are two adjacent pixels values in the image, V (x) is the variance of variable x and is given by
𝑉(𝑥) =
1
𝑛
× ∑ [𝑥𝑖 − µ(𝑥)]2
.𝑛
𝑖=1 (16)
µ(𝑥) is the mean of variable x.
µ(𝑥) =
1
𝑛
× ∑ 𝑥𝑖
𝑛
𝑖=1 . (17)
The correlation coefficient for the completely ciphered image was found close to zero in all
the directions and a value between 0 and 1 for the partially encrypted image. This represents that
the algorithm is resistant against statistical attacks. The correlation coefficients for Plain and cipher image in
three different directions are shown in Figure 8.
Figure 8. Correlation: (a-c) Correlation for Plain image in three different directions (Horizontal, Vertical and
Diagonal), (d-f) Correlation for Cipher image block with size 8×8 in three different directions (Horizontal,
Vertical and Diagonal), (g-i) Correlation for Cipher image block with size 16×16 in in three different
directions (Horizontal, Vertical and Diagonal) and (j-l) Correlation for Complete Encrypted Cipher image in
three different directions (Horizontal, Vertical and Diagonal)

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3.4. Key space analysis
It’s a measure of the total different keys that are used in the encryption and decryption process.
The different secret key K is a combination of sub keys k1, k2 and k3 which are taken from the various maps
with their initial conditions and the system parameters used in the system as shown in the Table 1. The sub
keys k1, k2 and k3 are extracted from Skew Tent Map, Bernoulli’s Map and Henon Map respectively.
Consider the precision taken for the keys is of the order of 10-15
. Then the total key space used is (1014
) z
,
where z is the number of initial conditions and system parameters used in all the sub keys (z=8). This results
in a very large key space and is sufficiently large to resist the attacks. For an encryption scheme based on
chaos, the key space should be greater than the 2200
≈1030
[28] to withstand or resistant with the brute-force
attack. The proposed method yields a key size of 10112
which is very much greater than 1030
.
3.5. Key sensitivity test
An encryption algorithm is said to be good if it produces a completely different plain image for
a tiny change in the key K, without making any changes in the ciphered image. A plain image of size
512 × 512 is subjected to an encryption key K= {k1, k2, k3} where k1, k2 and k3 are the sub keys. The correct
key value K=K1= {0.5, 0.1, 2, 0.2705, 1.4, 0.6315477, 0.3, 0.18906343} for which the decrypted image is as
shown in Figure 9a. It is observed that the deciphered image is exactly same as that of the plain image.
For a small change in the key K= K2 = {0.5, 0.1, 2, 0.2705, 1.9, 0.6315477, 0.6, 0.18906343}, K = K3 = {0.5,
0.1, 5, 0.1, 1.4, 0.6315477, 0.3, 0.18906343} and K= K4 = {0.3, 0.2, 2, 0.2705, 1.4, 0.6315477, 0.3,
0.18906343} for which the decrypted images are entirely different from that of the plain image is shown in
Figure 9b, 9c and 9d respectively. A tiny change in the value of key produces a completely different plain
image for the same input cipher image. Hence the algorithm is key sensitive.
Figure 9. Decryption: (a) Cipher Image Decrypted with Correct Key K1, (b-d) Decrypted using wrong Keys
[(b) with K2, (c) with K3, and (d) with K4]
3.6. NPCR AND UACI
An interceptor can make a tiny modification in the plain image and observe the changes in
the output ciphered image. By doing so, the significant relationship between the input and output images can
be observed. If it is observed that significant changes taken place in the ciphered image for a tiny change in
the plain image, it means that the interceptor can extract the key used for the encryption and crack
the algorithm. To check for the efficiency of this algorithm two parameters are calculated. They are NPCR
and UACI. The ideal value for NPCR and UACI are 100 and 33.33 respectively [29].
NPCR =
∑ 𝑊(𝑖,𝑗)𝑖,𝑗
𝑀 × 𝑁
×100. (18)
where M and N are the width and height of the image. 𝑊(𝑖, 𝑗) Can be defined as
𝑊(𝑖, 𝑗) ∶= {
1, 𝐼𝑓 𝐶𝑖𝑝1(𝑖, 𝑗) ≠ 𝐶𝑖𝑝2(𝑖, 𝑗),
0, 𝐼𝑓 𝐶𝑖𝑝1(𝑖, 𝑗) = 𝐶𝑖𝑝2(𝑖, 𝑗).
where
𝐶𝑖𝑝1(𝑖, 𝑗) Grey value of cipher image and
𝐶𝑖𝑝2(𝑖, 𝑗) Grey value of new cipher image
UACI =
1
𝑀 × 𝑁
× ∑
𝑎𝑏𝑠(𝐶𝑖𝑝1(𝑖,𝑗)−𝐶𝑖𝑝2(𝑖,𝑗))
255𝑖,𝑗 ×100. (19)
The results of the above tests for both partial and complete are shown in the Table 2 and Table 3. The results
reveal that the algorithm is better than the existing methods.

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3.7. Speed
The speed at which the encryption algorithm converts the plain image into a ciphered image is
instrumental for real time applications. This algorithm is executed using a system with its specifications
𝑘1 = 𝑎= 0.5 for skew tent map and 𝑘2 = 𝑥0 = 0.2709 for Bernoulli’s map. It is found that the encryption
speed is 133.723 m sec for partial and 622.517 m sec for complete encryption as in Table 2 and Table 3.
It’s compared with the other works in the Table 2 and found that this algorithm is more suitable for real time
applications.
Table 2. Comparison of proposed partial encryption results with existing work
INPUT IMAGE
[Reference]
PSNR ENTROPY
ENCRYPTION
(%)
EXECUTION
TIME (m sec)
MSE
HAND [6] 19.6400 NA 18.7300 NA NA
LENA [7] 29.8288 NA NA NA 67.6390
LENA [20] 10.1530 NA NA NA NA
HAND [PROPOSED] 10.9811 7.1062 NA NA NA
LENA [PROPOSED] 16.3585 7.4458 18.5941 133.72 1.099×103
(Note: NA= Not Applicable)
Table 3. Comparison of complete encryption results with existing work
Reference PSNR NPCR UACI Correlation EXECUTION
TIME (m sec)
ENTROPY
Horizontal Vertical Diagonal
[2] NA 96.4600 33.1000 0.0102 0.0053 0.0161 3500 NA
[14] NA 99.6493 33.4305 NA NA NA NA NA
[17] 8.9055 97.2387 22.2154 NA NA NA 398 NA
[29] 8.3581 100.00 33.4657 0.0220 -0.0215 -0.0215 71.2 7.9993
[30] NA 99.6390 27.7672 NA NA NA 7440 7.9978
[31] NA 99.6108 33.4679 -0.00465 -0.051 -0.016 NA 7.9992
[32] NA 99.6096 33.4595 -0.0127 0.0024 .0032 NA 7.9991
[33] NA 99.6084 33.4719 0.0083 0.0041 0.04 NA 7.9991
[Proposed
Paper]
8.3546 99.6487 33.4475 0.0218 0.0150 0.0197 622 7.9991
(Note: NA= Not Applicable)
3.8. Universal image quality index
Let x= {𝑥𝑖|𝑖 = 1,2, … … . . 𝑀 × 𝑁} and y= {𝑦𝑖|𝑖 = 1,2, … … . . 𝑀 × 𝑁} be the original and cipher
images respectively, then the quality index can be defined as
𝑈𝐼𝑄 =
4𝜎 𝑥,𝑦 𝑥𝑦
(𝜎 𝑥
2+𝜎 𝑦
2)×[(𝑥̅)2+(𝑦̅)2]
. (20)
where
𝑥̅ =
1
𝑀×𝑁
× ∑ 𝑥𝑖
𝑀×𝑁
𝑖=1 , (21)
𝑦̅ =
1
𝑀 × 𝑁
× ∑ 𝑦𝑖
𝑀 × 𝑁
𝑖=1 , (22)
𝜎𝑥
2
=
1
𝑀 × 𝑁
× ∑ (𝑥𝑖
𝑀 × 𝑁
𝑖=1 − 𝑥̅)2
, (23)
𝜎 𝑦
2
=
1
𝑀 × 𝑁
× ∑ (𝑦𝑖
𝑀 × 𝑁
𝑖=1 − 𝑦̅)2
, (24)
𝜎𝑥,𝑦 =
1
𝑀 × 𝑁
× ∑ (𝑥𝑖
𝑀 × 𝑁
𝑖=1 − 𝑥̅) × (𝑦𝑖 − 𝑦̅). (25)
3.9. Structural Similarity Index Measure
SSIM is a measure of structural similarity between plain image and the encrypted image,
mathematically it is represented as
𝑆𝑆𝐼𝑀 =
(2𝑥̅ 𝑦̅+𝑐1) × (2𝜎 𝑥,𝑦+𝑐2)
(𝑥̅2+𝑦̅2+𝑐1) × (𝜎 𝑥
2+𝜎 𝑦
2+𝑐2)
. (26)
where 𝑐1 and 𝑐2 are constants.

797
3.10. Entropy
Information entropy is a measure of randomness in the image. The randomness of the image is based
on the probability of occurrence of the various gray levels in the image. An image with all pixels of equal
gray levels are equally probable represents highest randomness. Randomness of an image says how much
confidential the image is. It also represents the leakage of information. Entropy also finds the strength of
the cryptosystem. Information entropy is calculated using the formula
ET (m) = - ∑ 𝑝(𝑚𝑖)𝐿−1
𝑖=0 × 𝑙𝑜𝑔2(𝑝(𝑚𝑖)). (27)
Where ET is the entropy, L is the total number of grey level values and 𝑝(𝑚𝑖) is the probability of
occurrence of pixel at each grey level 𝑚𝑖. A gray scale image with 256 levels to be random, the entropy
should ideally be equal to 8. A ciphered image with its entropy value very close to 8 represents an extremely
random image and the negligible leakage. An entropy value less than 8 represents a predictable image which
threatens security. The proposed algorithm results in the entropy of 7.9991. This represents the uniformity of
the document. Hence our algorithm is better with respect to certainty of the document. Therefore this scheme
is capable of resisting the entropy base attacks.
3.11. Document image encryption
In the proposed encryption method the algorithm is subjected to different document images
containing text, picture and text with picture. The results obtained for partial and complete encryption for all
document types are shown in Figure 10. The security parameters obtained for all document types are
tabulated in Table 4 and Table 5 for partial and complete encryption respectively.
Figure 10. Encryption of Document Images: (a-d) Input Plain Document images, (e-h) Corresponding Partial
Encryption results, (i -l) second level confused image and (m-p) Corresponding Complete Encryption results

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798
Table 4. Partial encryption results for different document Images
Table 5. Complete encryption results for different document Images
3.12. NIST test analysis
There are different complexity measurement techniques to measure the randomness of a given
chaotic sequence. In this paper a NIST (National Institute of Standards and Technology) test Analysis has
been conducted in WINDOWS (WIN 7 OS) environment to quantitatively estimate the complexity of
different dimensional (2D and 1D) chaotic maps. The complexity of the proposed scheme can be assessed by
making use of NIST special publication [34]. There are 16 different statistical test of special publication [35].
The different statistical methods are 1. Mono bit test, 2. Frequency test within block 3.Runs test, 4. Longest
run ones test, 5. Binary matrix rank test, 6. Spectral test, 7. Non overlapping template matching test, 8.
Overlapping template matching test, 9. Universal statistical test, 10. Lempel-Ziv compression test, 11. Linear
Complexity test, 12. Serial test, 13. Approximate Entropy test, 14. Cumulative sums test, 15. Random
excursion test and 16. Random excursion variant test.
For each of these tests the value of P is calculated from a binary sequences generated by the multi-
dimensional chaotic maps (2D and 1D). Each P-value determines whether the produced sequence is random
in nature or not. A P-value equals to 1 determines a perfect randomness. If P is in the range of 0.01 to 1,
then the test indicates that the sequence produced in completely random in nature. The randomness of
the sequence generated by the proposed algorithm can be evaluated by converting the encrypted pixels Pi to
bit Pib. The NIST Test Analysis Table 6 shows that it is successful against statistical attacks and hence
the proposed method is feasible for cryptography applications.
Table 6. NIST test analysis
INPUT IMAGE MSE PSNR EXECUTION TIME (m sec) SSIM UIQ
DOC1 7.38155×102 19.3465 144.52 0.81468914 0.81468960
DOC2 1.7247×103 15.7636 134.08 0.6639804 0.66398114
DOC3 9.9899×102 16.8132 172.074 0.6363383 0.6363397
DOC4 5.9976×103 10.3509 170.34 0.00424 0.00423
P-Value
Statistical Analysis 2D Henon Map Bernoulli map 1D Skew Tent Map Status
Mono Bit Frequency Test 0.911722762 0.545081094 0.411058023 Success
Block Frequency Test 0.896651648 0.745444081 0.204953127 Success
Run Test 0.017473068 0.019475341 0.021192845 Success
Longest Run Ones 0.731976748 0.939505864 0.185557603 Success
Binary Matrix Rank Test 0.480372774 0.263197135 0.069933096 Success
Spectral Test 0.917508648 0.462602814 0.640251058 Success
No over Lapping Template Matching Test 0.981407246 0.594564267 0.397569266 Success
Overlapping Template Matching Test 0.835255129 0.241877465 0.473148082 Success
Universal Statistic Test 0.043523569 0.290658217 0.279569313 Success
Linear Complexity Test 0.790994918 0.394483897 0.904411584 Success
Serial Test 0.982153254 1.000000000 1.000000000 Success
Approx. Entropy Test 1.000000000 0.971174997 0.962333535 Success
Cumulative Sums Test Forward 0.966310137 0.932836878 0.521342232 Success
Cumulative Sums Test Reverse 0.979855053 0.600528263 0.532280136 Success
Random Excursion Test 0.453358511 0.708361415 0.746906358 Success
Random Excursions Variant Test 0.824497225 0.951898892 0.609856019 Success

799
4. CONCLUSION
The Proposed work presents a partial as well as complete image encryption scheme for document
images. In the partial encryption, only the significant regions with a preset size are identified and are only
permuted. The experimental results of the partial encryption are shown in the Table 2. In large size blocks,
the pixels are scattered over a larger space and the partially encrypted document appears in less intelligent
form and has lesser number of blocks permuted. Hence larger preset block sizes results in more security with
less encryption time. For smaller block sizes the permutation takes place in smaller area and the document
image appears with more correlation among pixels in the block and hence appears as original image.
As the minimum block size is reduced the percentage of significant region increases hence it takes more
encryption time. Table 2 reveals that the partial encryption is more secure as the Peak Signal to Noise Ratio
is nearly equal to the ideal value of 8dB. Hence the proposed partial encryption scheme reduces
the computational overhead and suits to real-time applications. Further the proposed scheme is extended for
complete image encryption. The results of complete image encryption are shown in Table 3. The complete
image encryption ensures more security since the input image being the partially encrypted one. The mixed
chaotic system is used for permutation and substitution. The interdependency established between the pixels
in an image, the row wise diffusion bi-directionally and the column wise diffusion unidirectional
considerably reduces encryption time. The interdependency so established creates a non-linear relationship
between the cipher image and the key and hence provides more security. The NIST ensures that
the sequences generated by the chaotic systems are random and hence the system is more secure. The results
shows that, the larger value of NPCR and UACI, a poor Correlation in Horizontal, Vertical and Diagonal
directions, the Entropy close to ideal value, a flat Histogram and a small value of PSNR ensures that
Encryption is resistant to dynamical and statistical attacks. The lesser encryption time shows that
the algorithm is suitable for real time applications. Hence this scheme is efficient to completely encrypt
the image and provide good security when compared to the existing methods. The experimental results for
various Document images are tabulated in Table 4 and 5. The results reveals more security. The pictorial
results for partial and complete encryption on document images are shown in Figure 10.
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BIOGRAPHIES OF AUTHORS
DR C Keshavamurthy is B.E. and M.E. in Electronics and Communication Engineering and
received his Ph. D in the area of C A N. His academic interests include Computer
Communication Networks, Ad-hoc Wireless Networks and Multimedia Communication. He
has a research experience of over 20 years. Served as the Principal at YDIT, Bangalore.
Currently working as a Professor of Electronics and Communication Engineering at SRSIT,
Bangalore.
Mr. C R Revanna is a B.E. in Electronics and Communication Engineering, M.E. in
Electronics at UVCE from Bangalore University, Bangalore, India. His research interest
includes Encryption, Image Processing and Cryptography. Currently working as Assistant
Professor in Electronics and Communication Engineering at Government Engineering
College, Ramanagaram, India. He is also pursuing his Ph. D. research work at Jain University,
Bangalore, India.

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