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International Journal of Advanced Science and Technology
Vol.130 (2019), pp.21-32
http://dx.doi.org/10.33832/ijast.2019.130.03
ISSN: 2207-6360 IJAST
Copyright ⓒ 2019 NADIA
IMPLEMENTING BINARY SEARCH TREE
CONCEPT FOR IMAGE CRYPTOGRAPHY
^
Mohammed A. F. Al-Husainy1 and Hamza A. A. Al-Sewadi2
1Department of Computer Science, Middle East University, Amman, Jordan
2Department of Communication Engineering, Iraq University College, Iraq
1mal-husainy@meu.edu.jo, 2alsewadi46@gmail.com
Abstract— So many cryptographic systems are secure and in use today, such as
AES, 3DES, Blowfish, RC4, etc., however, new ideas and innovations are still highly
required due to the ever-growing threats to data security. This paper presents a novel
idea for symmetric image encryption utilizing binary search tree mechanism for
generating the encryption/decryption key. This key consists of local and global parts
with free user controlled key length, hence, it provides good flexibility for high
security, which is manifested in the encrypted images. For every single byte of the
encrypted image, the substitution and transposition operations involve all the image
contents, fulfilling Shannon’s diffusion and confusion concept. Experimental
computations of the proposed encryption method have shown satisfactory visual and
image energy distribution histogram. Besides, the Peak Signal to Noise Ratio (PSNR)
and Normalized Mean Absolute Error (NMAE) measurement results were
comparable with the widely used cryptosystems such as DES and AES. On the other
hand, the proposed method has flexible key length and shorter execution time by 10%
or more depending on the image contents.
Keywords— Avalanche effect; security; image encryption
1. INTRODUCTION
Growing cyber security attacks are the main worry of all people around the world.
Efforts for enhancing data security measures are continuing by academics and industrial
firms paralleled with continuous digging for security breaches by hacking and criminal
actions, individuals, and groups. So many cryptography systems are in use today that are
secure enough, such as AES, 3DES, Blowfish, RC4, etc., [1, 2]. However, academic and
industrial research teams are continuously looking for new innovative techniques or
enhancing previously developed ones. These efforts are spent in order to protect the ever-
increasing torrent of sensitive personal computers, governmental, and commercial data that
either being stored in various integrated computers or being in transit over various digital
communication means.
Although data encryption/decryption techniques are the ancient solutions designed to
protect information from intruders since thousands of years, they are still the most widely
used techniques. Historically, only symmetric systems were available, where the same
secret key is used for encryption and decryption processes. However, recently since 1976,
at the age of digital computers, asymmetric systems were developed, where two or more
different but related keys are used; one for encryption and another for decryption processes.
These techniques are referred to as public-key systems [3]. Symmetric systems are
comparatively fast and more difficult to break, but they have the serious problem of key
^Received: May 23, 2019
Reviewed: August 21, 2019
Accepted: September 9, 2019
International Journal of Advanced Science and Technology
Vol.130 (2019)
22 Copyright ⓒ 2019 NADIA
distribution, while the asymmetric systems are slower and less secure, but proved
convenient for authentication and key distribution [4].
In this paper, a novel technique is suggested for symmetric image encryption using a
key generated by a binary search tree method. After this brief definition, literature review
presented in Sections 2, then, the methodology of the proposed image cryptography scheme
is described in Section 3. Section 4 lists out the experimentation, results, and discussion.
Then Section 5 concludes the work.
2. RELATED WORK
So many techniques for image cryptography algorithms have been reported and
implemented, however, only some examples will be listed here as representative of binary
tree cryptographic algorithms, that triggered the author’s current research. In 2007, Lim
and Mun [5] proposed a packet classification algorithm applying binary search on prefix
length to the area-based quad-tree. Their algorithm relies on constructing multiple disjoint
trees based on the relative hierarchical level rule, hence avoiding the pre-computation
required in the binary search on length. They also suggested two new optimization
techniques based on rule priorities. In their test, they implemented 5000 different rules and
tested the memory consumption and number of bytes per rule. They showed that the
performance of the algorithm was steady and does not depend on the table characteristics.
In 2010, Wie and Zang [6] proposed a Key Insertion and Splay Tree encryption
algorithm (referred to as KIST), that uses asynchronous key sequence to change the tree
dynamically and secretly. The encryption was achieved by byte XORing and swapping.
The proposed algorithm suffers several disadvantages and limitations, such as bad error
propagation, which is good for message integrity, but not useful in a noisy channel. Besides,
no resynchronizing method in the key sequence was implemented. Then, in 2012,
Saraswathi and Venkatesulu [7] proposed a naive algorithm for encrypting any multimedia
content using blocks of bits rather than bytes or pixels. It can encrypt any type of
compressed multimedia content by random substitution using Binary Tree Traversal
(BTT), row shifting and column shifting. They claimed to obtain superior performance
compared with DES algorithm, and its suitability for encrypting audio, images, video, and
text data.
For the protection of data stored in the cloud, an encryption algorithm was proposed by
Vanaga in 2014 [8], aiming to meet the security and privacy issues in cloud warehouses.
In this algorithm. message contents are converted to ASCII codes, building a binary tree
from these values and rearrange pre-order and in-order. Although it was convenient for
cloud computing application, the time complexity was a problem. Then in 2015, Sharma
and Bhatt [9] reported a binary tree concept for block cipher encryption with considerably
increased computation complexity and security. In this algorithm, any input message is first
broken into blocks of the 8 characters each, which are assigned to the leaf nodes of the
binary tree of level 3, and other nodes of the binary tree are then filled using functions that
generate some characters corresponding to the internal nodes of the binary tree. Then
another function is applied to transpose the positions of the characters in binary tree. They
claim cipher that provides high security in various applications; however, the ciphertext
size is double the plaintext size in their algorithm. Also, in 2015, Sagar [10] proposed an
encryption algorithm for text message implementing tree traversal processes. He relied on
the pre-order, in-order and post-order processes for encryption and decryption. Although,
this algorithm reflects the person's interest in the use of binary tree in cryptography, it was
too simple and trivial.
In 2017, Priya et al. [11] suggested and applied a novel encryption algorithm that focuses
on four block ciphers based complete encryption technique. It implements a binary tree
traversal for multi-bit word parallelism using substitution and a two-dimensional array to
perform a nonlinear diffusion process. Improvements were observed in the required
International Journal of Advanced Science and Technology
Vol.130 (2019)
Copyright ⓒ 2019 NADIA 23
memory size, encryption time, and CPU utilization, besides obtaining high security as
compared with existing algorithms such as AES, RC5, and RC6. Also, in the same year
Sivakumar et al. [12] included Binary Tree Traversal (BTT) process as one level in a data
encryption and decryption algorithm that also comprises of ASCII code conversion. BTT
is used to achieve permutation and ASCII codes for substitution. However, the algorithm
was simple and would be useful for limited applications only. Moreover, Amounas [13]
presented a new approach to enhance the security of Amazigh text using elliptic curve
cryptography and tree traversal technique. The Unicode representation of the Amazigh text
is scrambled first using the tree traversal method and then implemented in the elliptic curve
cryptosystem. Experimental results have shown that involving the tree traversal process
has improved the efficiency of the ECC algorithm.
This paper reports a novel idea for symmetric image encryption utilizing binary search
tree mechanism to create a strong key to be used for image encryption/decryption
processes. This key consists of local and global parts with free user controlled key length
seeking good flexibility for high security. In the following, the idea of binary search tree is
briefly outlined and how it can be implemented to be used in the rest of the paper.
3. BINARY SEARCH TREE
The shape of any generated Binary search tree depends mainly on the sequence of the
values that are inserted in the nodes in that tree. To clarify this property of the Binary search
tree, Figure 1 depicted two examples for two different binary trees with ten nodes having
the values 0…9. The node labels are arranged randomly as the sequence is of no
significance here.
Fig. 1 Two different Binary trees generated from two different sequences of values (a) 9,
3, 6, 1, 5, 7, 0, 4, 2, 8 and (b) 5, 2, 3, 7, 1, 6, 8, 0, 9, 4.
In Figure 1, the path from each node in the tree to the root contains different number of
nodes that contained different values. Table I contains the list of the node values in the path
from each node to the root (exclude the node itself).
International Journal of Advanced Science and Technology
Vol.130 (2019)
24 Copyright ⓒ 2019 NADIA
Table I. List of Values in the Path from each Node to the Root (Exclude the Node Itself)
Node
List of values in the path of the node
in tree (a)
in tree (b)
N0
1, 3, 9
1, 2, 5
N1
3, 9
2, 5
N2
1, 3, 9
5
N3
9
2, 5
N4
5, 6, 3, 9
3, 2, 5
N5
6, 3, 9
-
N6
3, 9
7, 5
N7
6, 3, 9
5
N8
7, 6, 3, 9
7, 5
N9
-
8, 7, 5
4. THE PROPOSED IMAGE ENCRYPTION METHOD
The main idea of the proposed encryption method is to focus on utilizing the structure
of the Binary search tree as sub keys that are constructed from the input key for image
encryption and decryption processes.
In the encryption phase, the inputs are the source image S and the secret key K, which
might be any type of digital files, and produces the encrypted image E as output. Both S
and K are treated as files of bytes. Where SLength and KLength represent the length in bytes of
S and K respectively. Four main processes are conducted through the encryption phase: 1)
Initial Key Generation, 2) Global Image Processing, 3) Local Image Processing, and 4)
Construct an Encrypted Image E. Each process consists of a set of operations as detailed in
the following
4.1. INITIAL KEY GENERATION
Read the contents (bytes) of the secret key K and implement equation 1 to generate the
specific key used by the proposed encryption method.
(1)
Where represents the XOR operation and i and j represent the ith and jth bytes in the
secret key K respectively.
4.2. GLOBAL IMAGE PROCESSING
In this step, a set of operations are implemented on the image and key, each of the source
image S and the key K are treated as one block (without splitting S or K into blocks).
4.2.1 PREPARATION OPERATION
The following steps are followed in order to re-represent the secret key K to construct
a new key K'.
1. Equation 2 is used to calculate the minimum number of bits N that are needed to
represent the index of each byte in the source image S. The indices of the byte in the
source image S are from 0 to SLength -1.
(2)
2. Represent the secret key K as a list of bits KB by converting each byte of K into its
equivalent bits. The length of KB is calculated using equation 3.
(3)
International Journal of Advanced Science and Technology
Vol.130 (2019)
Copyright ⓒ 2019 NADIA 25
3. Construct a new key K' by sequentially reading N bits from KB, converting them to
their equivalent decimal values, then store these values in K'. Ignore any remaining
number of bits less than N at the end of KB.
4. Implement equation 4 on each value in K' to create new values that are limited in the
range 0 to SLength -1.
(4)
Where j represents the index of K' and j: 0…K'Length -1.
4.2.2 GLOBAL KEY GENERATION (BINARY SEARCH TREE): After
completing the previous preparation operation, the following steps are implemented to
generate the Binary search tree (in (1)) that will be used (in (2)) to extract the necessary
lists to be used later in the next operations.
1. Read sequentially the distinct values of K', without repetition, then generate the
corresponding Binary search tree from them. The generated Binary search tree must
contain SLength nodes; each node contains one value in the range 0 to SLength. If some
values haven't been found in K', then these missed values must be inserted to the
Binary search tree after finishing the read operation of the K' values.
2. Extract the lists L0 to LSLength of values in the path of each node from N0 to NSLength,
respectively in the generated Binary search tree in (1) [where Ni is the number of bits
in K' and Li are the list of values in Ni].
4.2.3 TRANSPOSITION OPERATION: For each byte at the index Sj in the source
image S, where j: 0…SLength. Successively exchange the location of Sj with the bytes in S
at the indices recoded in the list Lj. After completing this operation, the original byte at the
index Sj is transposed to a new location in the source image S.
4.3. LOCAL BLOCK PROCESSING
To achieve a high level of confusion and diffusion in the image pixels, the source image
S and the key K are split into a set of blocks and a set of operations are implemented on
each block separately.
4.3.1. PREPARATION OPERATION: Split the source image S into a set of sub-lists
of length 256 bytes. Similarly, split the secret key K into the same number of sub-lists of
length 256 bytes, too. Where Si and Ki are the ith sub-list of the source image S and the
secret key K, respectively. It is necessary to be mentioned here that if the number of bytes
in the secret key file K is less than the number of bytes in the source image S, then the bytes
in the secret key file are repeated to match the number of bytes in S. Figure 2 shows an
example of Si and Ki sub-lists.
Fig. 2 Examples of Si and Ki sub-lists.
International Journal of Advanced Science and Technology
Vol.130 (2019)
26 Copyright ⓒ 2019 NADIA
4.3.2. LOCAL KEY GENERATION (BINARY SEARCH TREE)
After completing the previous preparation operation, the following steps are
implemented (on each block of K) to generate the Binary search tree (in (1)) that will be
used (in (2)) to extract the necessary lists to be used later in the next operations.
1. Read sequentially the distinct byte values (i.e., without repetition) in Ki. And generate
the corresponding Binary search tree from them. The generated Binary search tree
must contain 256 nodes; each node contains one value in the range 0 to 255. If some
bytes haven't been found in Ki, then these missed values will be inserted into the
Binary search tree after finishing the read operation of the byte values in Ki.
2. Extract the list L0 to L255 of values in the path of each node from N0 to N255 in the
generated Binary search tree in (1) above.
4.3.3. SUBSTITUTION OPERATION: For each byte Bj or the index j of the sub-list Si,
where j: 0...255, implement an XOR operation using equation 5 for Bj with all the bytes
values in the Lj.
(5)
Where represents the XOR operation and k represents the values in the list Lj.
The resulting value of Bj replaces the corresponding byte Bj in the original image. At the
completion of this substitution phase, the encrypted image proceeds next to the
transposition phase.
4.3.4. TRANSPOSITION OPERATION: For each byte Bj at the index j in the sub-list Si,
where j: 0...255, successively exchange the location of Bj with the bytes in Si at the indices
stored in the list Lj. Hence, the original byte at the index Bj is shifted to a new location in
the sub-list Si.
4.4. CONSTRUCT ENCRYPTED IMAGE E
The resulted sub-lists obtained after the transposition phase are merged together in order
to construct the encrypted output image E, which will be either stored for later use or
transmitted over any insecure channel to the intended recipient.
As the decryption process is the inverse of the encryption process, hence, having the
encrypted image E as input, and the secret key K, the source image S can be produced as
the output. Both E and K are treated as files of bytes. The same main operations described
in the encryption phase are implemented during the decryption phase with the exception
that the substitution and transposition operations are performed in reverse order. Therefore,
no need for repeating these processes here.
5. RESULTS & DISCUSSION
To evaluate the proposed encryption method, hundreds of images have been encrypted
using different keys. Images of various sizes, contents, and types have been used for testing
purposes in order to check the performance of the proposed encryption and decryption
processes, looking for advantages, drawbacks, and discrepancies. However, different
binary search trees were also experimented with. However, three different source images
were selected to be listed in this paper as examples, namely a snappy girl photo (size:
166×256), a bus (size: 533×300), and a camera (size: 455×256). Figure 3 illustrates these
selected images.
International Journal of Advanced Science and Technology
Vol.130 (2019)
Copyright ⓒ 2019 NADIA 27
Fig. 3 Selected source images used in the experiments.
The performance observation of the proposed encryption method included Visual and
Statistical Tests, Avalanche Effect, Comparison with other Methods, and the key size used.
These observations are presented and discussed in the following.
5.1. VISUAL AND STATISTICAL TESTS
One of the main factors of the performance for any image encryption method is the
distortion ratio of the encrypted images that is generated by the ciphering process. This
distortion is clearly noticed for all considered encrypted images. As an example of this
factor, Figure 4 shows illustrations for the obtained distortion in the selected images of
Figure 3. It is visually clear that the proposed method was successful in producing highly
distorted (garbage) encrypted image from the input source image.
Fig. 4 Corresponding encrypted images for the source images in Fig. 3
Another important factor in the efficiency of any image encryption method is its ability
to produce flatness in the histogram of the colors (byte intensity distribution) in the
encrypted image compared with a histogram of the colors (byte intensity distribution) in
the source image. Figure 5 depicts the bytes intensity distribution histogram for the source
and encrypted images of the examples under consideration.
International Journal of Advanced Science and Technology
Vol.130 (2019)
28 Copyright ⓒ 2019 NADIA
Fig. 5 Histogram of the colors (bytes) of source and encrypted images
Comparing the histograms for the source and encrypted images shows clearly that the
histogram of the encrypted images has been widened in such a way that indicate the even
distribution of the produced distortion by the proposed method over the whole color range.
5.2. AVALANCHE EFFECT
The construction of an encryption technique should take into consideration the
avalanche effect as one of the main design objectives. Therefore, it represents one of the
desirable properties in any cryptographic algorithm. Avalanche effect reflects the
sensitivity of the encryption method even to tiny variations in the parameters; hence it
means that when a small change in an input (either in the key or the plaintext) this should
cause a tremendous/big change in the cipher text. Any encryption method's success in
achieving this property makes it a high-quality encryption method. The following two sub-
sections present the effect of changing bits in the key on the number of bits that will be
changed in the generated encrypted image and the recovered source image respectively.
5.2.1. NUMBER OF BITS CHANGED IN THE ENCRYPTED IMAGE: To test the
quality of the proposed encryption method and the strength of the used encryption key of
avalanche effect, a few bits in the used key are changed during the experiments, then the
number of change bits resulted in the encrypted image were calculated according to
equation 6. Table II lists the avalanche effect test results that have been recorded during
the experiments for different number of changed bits in the encryption key. Although, this
International Journal of Advanced Science and Technology
Vol.130 (2019)
Copyright ⓒ 2019 NADIA 29
test is performed for many images, only the results for the Snappy girl image is listed here
as an example.
(6)
Table II. Avalanche Test Recorded Results of the Snappy Girl Image.
Number of bits changed
in the encryption key
Avalanche Test Value
(%)
1
49.733
6
50.666
20
49.957
30
49.671
To highlight the efficiency of the proposed encryption method compared with the other
well-known encryption methods, Table III shows the average values of the avalanche effect
test that are computed by equation 6 for the experiments on various color images using the
proposed method compared with those calculations for DES and AES encryption methods
Table III. Average of Avalanche Test Values for the Proposed, DES and AES Encryption
Methods
Encryption
Method
Average of the Avalanche Test
Values (%)
Proposed
51.122
DES
50.057
AES
49.970
It can be seen from Tables II and III that the average avalanche effect of the proposed
method is acceptable and slightly better as compared with those for DES and AES
algorithms.
5.2.2. RECOVERED SOURCE IMAGE: Another way of looking at the avalanche
effect by testing the sensitivity of any changes in the key used in the proposed method
against any changes in its bits of the decryption key. The avalanche test has been applied
to the key, by changing some bits in the decryption key and use it to decrypt the encrypted
image. Figure 6 shows the decrypted image after changing a number of bits are in the key.
It is clear that when some bits change in the key, the original source image cannot be
recovered from the encrypted image. This means that the key used in the proposed method
has inherent resistance against the avalanche effect.
Fig. 6 The recovered source images (of the Snappy girl image) after changing bits in the
key
International Journal of Advanced Science and Technology
Vol.130 (2019)
30 Copyright ⓒ 2019 NADIA
5.3. NMAE AND PSNR COMPARISON
In order to have a more rigorous vision about the performance of any encryption method,
a set of metrics such as Normalized Mean Absolute Error (NMAE), Peak Signal to Noise
Ratio (PSNR), and Encryption Time (ET) should be computed and compared with the
established and widely used methods. Hence, NMAE and PSNR for the proposed
Encryption method have been computed using equation 7 and 8 respectively. The obtained
results are compared with those for DES and AES algorithms, and are listed in Table IV
and Table V. Moreover, the execution time for the encryption process of the proposed
method is recorded and compared with its values when executing DES and AES, and the
results are listed in Table VI. In order to have a more realistic comparison, all calculation
for the three methods were done on the same computing environment.
(7)
(8)
Where MaxS is the maximum possible pixel value of the image S.
Table IV. Normalized Mean Absolute Error Values (in %)
Image
Method
Proposed
DES
AES
Snappy Girl
45.40
46.03
45.89
Bus
90.07
90.38
89.98
Camera
93.00
93.05
93.25
Table V. Peak Signal to Noise Ratio Values (in decibel dB)
Image
Method
Proposed
DES
AES
Snappy Girl
7.67
7.60
7.62
Bus
6.27
6.29
6.31
Camera
6.86
6.86
6.85
Table VI. Encryption Time values (in msec.)
Image
Method
Proposed
DES
AES
Snappy Girl
360
516
454
Bus
288
1276
1636
Camera
929
854
1222
From Table IV and Table V, it can be seen, that the NMAE and PSNR measurements
for the proposed encryption method is comparable with those for DES and AES algorithms.
This result can be considered as an encouraging sign for the success of the proposed
method. Furthermore, the execution time for the proposed method shows remarkable
improvement for most images, however, for some images it was much faster than AES but
slightly less for DES. These observations can be explained as they are attributed to the
image contents or quality of the source image. However, on the average, there is a
noticeable improvement in the execution speed of the proposed method.
5.4. KEY SIZE USED
The size of the encryption key used in any cryptographic methods plays the major factor
in algorithm immunity and the level of difficulty faced by attackers. For the proposed image
encryption method, two keys are used, one is used in the global operation and another one
International Journal of Advanced Science and Technology
Vol.130 (2019)
Copyright ⓒ 2019 NADIA 31
is used in the local operations. The number of bits in the global key KG and those in the
local operation KL are calculated using equation 9 and 10.
(9)
(10)
The key size that has to be breached by the attacker is the total number of bits in both
keys (i.e., Their summation KG + KL ). This key is proportional to the size of the input key
selected by the user, and since the user can select a file of any size as the key, obviously, a
large enough key will be selected to make life extremely difficult for attackers. Table VII
gives a comparison for key size expected for the proposed method with those used by other
encryption methods [14].
Table VII. Encryption Key Size Comparison [14]
Algorithm
Used Key Size (in bit)
3DES
56, 112, 168
AES
128,192, or 256
Twofish
128, 192, or 256
Blowfish
32 to 448
RC4
40 to 2048
Proposed Method
> 2048
6. CONCLUSIONS
The novel algorithm presented in this paper utilizes the binary search tree as a mean for
producing a strong secret encryption key. This key is practically a very long, having two
parts; local and global free user-controlled length, hence it has resulted in a key space much
larger than globally used algorithms, such as AES and 3DES.
Visually observed encrypted images and histogram energy distribution were satisfactory
due to the even distribution of the energy over the color intensity range from 0 to 256.
Moreover, comparison of the measured normalized mean square error, and peak signal
to noise ratios for the proposed algorithm were to in good agreements with those for AES
and DES, and hence, great promises on the expected usability of this cryptography
technique can be anticipated. Besides, a remarkable improvement in the algorithm runs
time execution speed.
ACKNOWLEDGEMENTS
Mohammed A. F. Al-Husainy and Hamza A. A. Al-Sewadi are grateful to the Middle
East University Amman (Jordan) for the financial support granted to cover the publication
fee of this research article.
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