![International Journal of Electrical and Computer Engineering (IJECE)
Vol. 10, No. 1, February 2020, pp. 188~195
ISSN: 2088-8708, DOI: 10.11591/ijece.v10i1.pp188-195 188
Journal homepage: http://ijece.iaescore.com/index.php/IJECE
Performance analysis of transformation and bogdonov chaotic
substitution based image cryptosystem
Prajwalasimha S. N., Basavaraj L.
Department of Electronics and Communication Engineering, ATME Research Centre, India
Article Info ABSTRACT
Article history:
Received Oct 2, 2018
Revised Aug 23, 2019
Accepted Aug 30, 2019
In this article, a combined Pseudo Hadamard transformation and modified
Bogdonav chaotic generator based image encryption technique is proposed.
Pixel position transformation is performed using Pseudo Hadamard
transformation and pixel value variation is made using Bogdonav chaotic
substitution. Bogdonav chaotic generator produces random sequences and it
is observed that very less correlation between the adjacent elements in
the sequence. The cipher image obtained from the transformation stage is
subjected for substitution using Bogdonav chaotic sequence to break
correlation between adjacent pixels. The cipher image is subjected for
various security tests under noisy conditions and very high degree of
similarity is observed after deciphering process between original and
decrypted images.
Keywords:
Chaotic generator
Confidentiality
Correlation
Encryption
Substitution Copyright © 2020 Institute of Advanced Engineering and Science.
All rights reserved.
Corresponding Author:
Prajwalasimha S N,
Department of Electronics and Communication Engineering,
ATME Research Centre,
Mysuru, Karnataka, India.
Email: prajwalasimha.sn1@gmail.com
1. INTRODUCTION
Images are pictorial depiction of information. Due to swift maturation in internet technology, digital
images being major class of multimedia, plays a vital role in communication systems. These images are
characterized inimitably by high inter pixel redundancy, strong correlation between adjacent pixels and bulk
data capacity [1-7].
Confidentiality is one of the dominant facets of communication system. Fortification of information
can be accomplished by adopting an efficient cryptosystem, which should encrypt and decrypt the information
without flaws. More prevalently and habitually used encryption algorithms such as Rivest, Shamir and
Adleman (RSA), Data Encryption Standard (DES), International Data Encryption Algorithm (IDEA) and
Advance Encryption Standards (AES) are inapposite for images due to their inimitable characteristics [2].
Chaotic systems found proliferate implementation in the fields of cryptography, due to their intrinsic
properties such as volatility, subtlety to the initial conditions, similar casualness and aperiodicity [3, 8].
With the help of chaotic theory, the inter pixel redundancy and strong correlation between adjacent pixels can
be effectively reduced.
In many low dimensional chaos based cryptographic algorithms, the cipher data directly depends on
chaotic orbit of a single chaotic system. Due to this, many low dimensional chaotic systems are more prone to
phase space reconstruction attacks [9]. Such kind of attacks can be reduced by using S-box (Substitution box)
in the algorithm. Complexity of cryptanalysis and brute force attacks can be further reduced by increasing
the size of S-box in the algorithm. One such technique is developed by Silva-García and et al [10].
They introduced S-boxes in Advanced Encryption Standard (AES) algorithm to increase the level of security.
Nonlinear chaotic differential equations are used to generate random numbers inside the S-box. But immunity
against noise has not been noticed in the algorithm.](https://image.slidesharecdn.com/v1830aug23aug2oct1815816editlelli-201201054811/85/Performance-analysis-of-transformation-and-bogdonov-chaotic-substitution-based-image-cryptosystem-1-320.jpg)
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Performance analysis of transformation and bogdonov chaotic substitution based … (Prajwalasimha S N)
189
A double humped logistic map has been developed by Lingfeng & et al. [11] by introducing general
parameters to the existing chaotic map to generate pseudo random key sequence for the substitution stage.
Robustness of the algorithm against Gaussian noise has been noticed but not against other kind of noises.
Better UACI values are observed for various images but considerable differences in the NPCR values are
noticed compared to ideal values. Rasul Enayatifar & et al. [12] developed combined permutation and
diffusion technique using 3-D logistic chaotic map. Better entropy is observed in the absence of noise for
many standard images but considerable difference in the values of NPCR and UACI is observed compared to
ideal values. A combined 1-D logistic map and 2-D Baker chaotic map based block wise permutation
algorithm has been developed by Lingfeng Liu & et al. [13]. Even though low dimensional chaotic maps are
considered, phase space is made large by multiple chaotic maps. Very minimum correlation between
the adjacent pixels in the cipher image has been noticed along with slightly high entropy but considerable
difference in the values of NPCR and UACI is observed compared to ideal values for few standard images.
Based on the above considerations a combined 2-D Pseudo Hadamard chaotic transformation
(MPHT) and 2-D Bogdonav chaotic random diffusion based algorithm has been proposed in which a large
phase space is considered along with a substitution image. The paper is organized as follows: Section 2
describes the proposed scheme. Section 3 with statistical and differential analysis followed by conclusion
in Section 4.
2. RESEARCH METHOD
Three stages per round are involved in the encryption process: Transformation, Diffusion and
Substitution. Modified Pseudo Hadamard transformation is used in the first stage and random sequence
generated by Bagdonov chaotic generator is used in the substitution stage. Figure 1 illustartes the flow
diagram of the system.
2.1. Encryption algorithm
Step1: Original image of size 2 𝑛
X 2 𝑛
is transformed using modified Pseudo Hadamard transformation.
𝐻1′(𝑥, 𝑦) = 𝐻((𝑎 + 𝑏 + 𝑐) 𝑚𝑜𝑑 2 𝑛
, (𝑎 + 2𝑏 + 𝑐) 𝑚𝑜𝑑 2 𝑛
) 1 < 𝑎, 𝑏 < 2 𝑛
(1)
Where,
𝐻(𝑎, 𝑏) is the host image of size 2 𝑛
X 2 𝑛
𝐻1′
(𝑥, 𝑦) is the transformed image of size 2 𝑛
X 2 𝑛
𝑐 is the constant (𝑐 = 37)
Step2: Block truncated substitution image of size 2 𝑛
X 2 𝑛
is transformed using modified Pseudo Hadamard
transformation.
𝑆1′(𝑥, 𝑦) = 𝑆 𝑡
((𝑎′ + 𝑏′ + 𝑐) 𝑚𝑜𝑑 2 𝑛
, (𝑎′ + 2𝑏′ + 𝑐) 𝑚𝑜𝑑 2 𝑛
) 1 < 𝑎′, 𝑏′ < 2 𝑛 (2)
Where,
𝑆1′(𝑎′, 𝑏′) is the block truncated substitution image of size 2 𝑛
X 2 𝑛
𝑆 𝑡(𝑥, 𝑦) is the transformed truncated image of size 2 𝑛
X 2 𝑛
𝑐 is the constant ( 𝑐 = 37)
Step3: Both transformed images are subjected for bitwise XOR operation
𝐶1(𝑥, 𝑦) = 𝐻′(𝑥, 𝑦) ⊕ 𝑆′(𝑥, 𝑦) (3)
Step4: The cipher image from first stage is subjected for substitution with pre-defined S-box.
𝐶2(𝑥, 𝑦) = 𝐶1(𝑥, 𝑦) ⊕ S-box (4)
Step4: The cipher image from substitution stage is subjected for diffusion with random sequence generated
Bogdonov chaotic equation.
𝑥′
= (𝑥 + 𝑦′)𝑚𝑜𝑑 2 𝑛 (5)
𝑦′
= (𝑦 + 𝜀𝑦′
+ 𝐾𝑥′(𝑥′
− 1) + 𝜇𝑥′𝑦′) 𝑚𝑜𝑑 2 𝑛 (6)](https://image.slidesharecdn.com/v1830aug23aug2oct1815816editlelli-201201054811/85/Performance-analysis-of-transformation-and-bogdonov-chaotic-substitution-based-image-cryptosystem-2-320.jpg)
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Performance analysis of transformation and bogdonov chaotic substitution based … (Prajwalasimha S N)
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𝐶2′(𝑥, 𝑦) = 𝐶3′(𝑥, 𝑦) ⊕ 𝑥′ (10)
Step2: The obtained cipher image XORed with the elements of S-box used for encryption.
𝐶1′(𝑥, 𝑦) = 𝐶3′(𝑥, 𝑦) ⊕S-box (11)
Step3: The block truncated substitution image is subjected for MPHT with same constant and then XORed
with cipher image from previous stage.
𝑆1′(𝑥, 𝑦) = 𝑆 𝑡(𝑎′ + 𝑏′ + 𝑐) 𝑚𝑜𝑑 2 𝑛
, (𝑎′ + 2𝑏′ + 𝑐) 𝑚𝑜𝑑 2 𝑛 (12)
𝐻1′(𝑥, 𝑦) = 𝐶1′(𝑥, 𝑦) ⊕ 𝑆′(𝑥, 𝑦) (13)
Step4: the obtained image from previous step is subjected for inverse MPHT to get original image.
𝐻 𝑟(𝑎, 𝑏) = 𝐻1′(5𝑥 − 4𝑦 − 𝑐) 𝑚𝑜𝑑 2 𝑛
, (y – x) mod 2n
) (14)
3. EXPERIMENTAL RESULTS
Standard test images are considered from Computer Vision Group (CVG), Dept. of Computer
Science and Artificial Intelligence, University of Granada, Spain. Matlab software is used for performance
analysis and implementation. Performance analysis is made based on various security tests. Table 1 compares
resultant Entropy, Correlation, UACI and NPCR of different encryption schemes with the proposed system.
The results indicates very less correlation between the adjacent pixels after substitution phase along with high
entropy value indicating that the pixel values are altered effectively in the cipher image.
Table 1. Comparision of entropy and correlation between standard and encrypted images
Images Entropy = 8 [14] Correlation UACI ≥ 33.4635% [14] NPCR ≥ 99.6093% [14]
Lena
5.5407 (Blow Fish) [15]
0.1500 [16]
31.00 [16] 90.21 [16]5.5438 (Two Fish) [15]
5.5439(AES 256) [15]
5.5439 (RC 4) [15]
33.4201 [19] 99.5859 [19]
7.5220 [16]
7.9972 [17]
7.9950 [18]
7.9958 [19]
0.0020
32.01 [22] 99.60 [22]7.6427 [20]
7.9971 [21]
7.9970 [22]
33.4303 99.6063
7.9973
Baboon
7.9950 [18]
-4.6636e-04
30.87 [21] 99.59 [21]
7.9947 [21]
7.9968 33.2305 99.5544
Peppers
7.9960 [18]
-0.0040
30.71 [21] 99.61 [21]
7.9954 [21]
33.3761 99.6490
7.9973
Airplane 7.9972 0.0040 33.2971 99.6231
Cameraman
7.9972 [23]
-0.0041 33.3763 99.6201
7.9975
Barche 7.9973 0.0048 33.3745 99.6017
Carnev 7.9971 -9.7275e-04 33.3590 99.5651
Donna 7.9973 1.6005e-04 33.4637 99.6460
Foto 7.9968 -0.0028 33.4974 99.5667
Galaxia 7.9972 0.0024 33.4866 99.5773
Leopard 7.9972 0.0013 33.3751 99.5911
Montage 7.9966 -0.0050 33.3403 99.6384
Clock 7.9969 0.0038 33.3330 99.6094
Vacas 7.9974 -4.2689e-04 33.3868 99.6140
Fiore 7.9972 0.0058 33.4856 99.6262
Mapasp 7.9972 0.0040 33.2827 99.6201
Soil 7.9970 0.0026 33.3852 99.6017
Mesa 7.9976 0.0077 33.3114 99.6155
Papav 7.9969 4.2616e-04 33.4553 99.6216
Tulips 7.9974 0.0058 33.4337 99.5987](https://image.slidesharecdn.com/v1830aug23aug2oct1815816editlelli-201201054811/85/Performance-analysis-of-transformation-and-bogdonov-chaotic-substitution-based-image-cryptosystem-4-320.jpg)
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Int J Elec & Comp Eng, Vol. 10, No. 1, February 2020 : 188 - 195
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3.1. Noise interference
The correlation coefficient decides the similarity between retrieved (decrypted) and original
images [24]. The performance analysis of decrypted image under noisy condition is decided by comparing
the correlation coefficient between decrypted and original images. Figure 2 illustartes retrieved and original
image under different noisy conditions and Table 2 discribes the similarity in the order of correlation between
the de-crypted and original images under noise interference. If the correlation coefficient is equal to unity,
the retrieved image is same as that of the original watermark. The cipher image is considered under
various noisy conditions and the performance analysis of the algorithm is made after decrypting the noisy
cipher image.
Figure 2. Performance analysis of retrieved and original image under noisy conditions
Table 2. Performance analysis of retrieved and original image under noisy attacks
Noise Interference Correlation
Pepper & Salt 0.8617
Gaussian 0.7062
Poisson 0.8449
Speckle 0.6527
LSB neutralization attack 0.9790
3.2. Inference
The correlation co-efficient value drops to a minimum 0.6527 with speckle (multiplicative) noise in
cipher image indicating 65% similarity between the corresponding pixels in original and retrieved images.
Due to LSB neutralization attack, the correlation co-efficient of 0.9790 is observed indicating 98% similarity
between original and retrieved images. It has been observed that, an average of 81% similarity between
original and retrieved images is observed under noisy conditions. And hence the proposed algorithm gives
better results under noise attacks. Figure 3 illustrates similarity in the order of correlation between](https://image.slidesharecdn.com/v1830aug23aug2oct1815816editlelli-201201054811/85/Performance-analysis-of-transformation-and-bogdonov-chaotic-substitution-based-image-cryptosystem-5-320.jpg)
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Performance analysis of transformation and bogdonov chaotic substitution based … (Prajwalasimha S N)
193
the de-crypted and original images under different noise densities. Figure 4 Illustration of resultant images
under different stage of the crypto-process. Also very close to the ideal values of Unified Average Changing
Intensity (UACI=33.39%) but slight less and Number of Pixel Changing Rate (NPCR=99.61%) equal to
the ideal value, slightly greater than that as observed in non-Chaotic substitution [25] are noticed from
the outcome of the standard images.
Figure 3. Correlation between the retrieved and original watermarks under noise interference
Figure 4. Illustration of Host image, Substitution image and Cipher image after transformation, diffusion and
substitution stages](https://image.slidesharecdn.com/v1830aug23aug2oct1815816editlelli-201201054811/85/Performance-analysis-of-transformation-and-bogdonov-chaotic-substitution-based-image-cryptosystem-6-320.jpg)
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Int J Elec & Comp Eng, Vol. 10, No. 1, February 2020 : 188 - 195
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4. CONCLUSION
In the proposed encryption scheme, Pseudo Hadamard transformation is used in the transformation
stage to vary pixel positions and Bogdonov chaotic random sequence generator is used in the substitution
stage to vary the pixel values in an image. High redundancy and strong correlation between the adjacent
pixels are effectively reduced by the proposed technique. High degree of randomness obtained from
Bogdonav chaotic generator in the substitution stage leads to achieve better entropy in the cipher image.
Correlation between host and cipher images is very less indicating poor similarities between them. Average
values of 99.61% number of pixel changing rate (NPCR) is observed which is almost equal to the ideal value
and an average value of 33.39% unified average changing intensity (UACI) is obtained which is very close to
the ideal values, for a set of twenty standard images. Further, more number of chaotic generators can be used
to get random sequences for substitution stage of encryption to increase the level of security.
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BIOGRAPHIES OF AUTHORS
Prajwalasimha S N received Bachelor of Engineering (B.E) Degree in Electronics &
Communication from Visvesvaraya Technological University, India in 2012, Master of
Technology (M.Tech) Degree in Digital Electronics & Communication Systems from
Visvesvaraya Technological University, India in 2014 and pursuing Doctoral Degree (Ph.D) in
the field of Cryptography under Visvesvaraya Technological University, India. He has
published more than 20 research papers in International Journals, Conferences & Book
Chapters and serving as Reviewer for many International Journals and Conferences. He has
been conferred with best research contribution award from IEEE ICECCT 2017. His research
interest includes Cryptography, Steganography, Digital Image Watermarking and Image
Processing.
Dr. L Basavaraj received Bachelor of Engineering (B.E) Degree in Electrical & Electronics
Engineering from University of Mysore, India, Master of Technology (M.Tech) Degree in
Digital Electronics from Darwad University, India and Doctoral Degree (Ph.D) in the field of
Image & Signal Processing under University of Mysore, India. He has published more than 40
research papers in International Journals, Conferences & Book Chapters and currenty guiding
7 Ph.D scholars. Being senior member of IEEE, his research interest includes Image & Signal
Processing.](https://image.slidesharecdn.com/v1830aug23aug2oct1815816editlelli-201201054811/85/Performance-analysis-of-transformation-and-bogdonov-chaotic-substitution-based-image-cryptosystem-8-320.jpg)
Performance analysis of transformation and bogdonov chaotic substitution based image cryptosystem
- 1. International Journal of Electrical and Computer Engineering (IJECE) Vol. 10, No. 1, February 2020, pp. 188~195 ISSN: 2088-8708, DOI: 10.11591/ijece.v10i1.pp188-195 188 Journal homepage: http://ijece.iaescore.com/index.php/IJECE Performance analysis of transformation and bogdonov chaotic substitution based image cryptosystem Prajwalasimha S. N., Basavaraj L. Department of Electronics and Communication Engineering, ATME Research Centre, India Article Info ABSTRACT Article history: Received Oct 2, 2018 Revised Aug 23, 2019 Accepted Aug 30, 2019 In this article, a combined Pseudo Hadamard transformation and modified Bogdonav chaotic generator based image encryption technique is proposed. Pixel position transformation is performed using Pseudo Hadamard transformation and pixel value variation is made using Bogdonav chaotic substitution. Bogdonav chaotic generator produces random sequences and it is observed that very less correlation between the adjacent elements in the sequence. The cipher image obtained from the transformation stage is subjected for substitution using Bogdonav chaotic sequence to break correlation between adjacent pixels. The cipher image is subjected for various security tests under noisy conditions and very high degree of similarity is observed after deciphering process between original and decrypted images. Keywords: Chaotic generator Confidentiality Correlation Encryption Substitution Copyright © 2020 Institute of Advanced Engineering and Science. All rights reserved. Corresponding Author: Prajwalasimha S N, Department of Electronics and Communication Engineering, ATME Research Centre, Mysuru, Karnataka, India. Email: [email protected] 1. INTRODUCTION Images are pictorial depiction of information. Due to swift maturation in internet technology, digital images being major class of multimedia, plays a vital role in communication systems. These images are characterized inimitably by high inter pixel redundancy, strong correlation between adjacent pixels and bulk data capacity [1-7]. Confidentiality is one of the dominant facets of communication system. Fortification of information can be accomplished by adopting an efficient cryptosystem, which should encrypt and decrypt the information without flaws. More prevalently and habitually used encryption algorithms such as Rivest, Shamir and Adleman (RSA), Data Encryption Standard (DES), International Data Encryption Algorithm (IDEA) and Advance Encryption Standards (AES) are inapposite for images due to their inimitable characteristics [2]. Chaotic systems found proliferate implementation in the fields of cryptography, due to their intrinsic properties such as volatility, subtlety to the initial conditions, similar casualness and aperiodicity [3, 8]. With the help of chaotic theory, the inter pixel redundancy and strong correlation between adjacent pixels can be effectively reduced. In many low dimensional chaos based cryptographic algorithms, the cipher data directly depends on chaotic orbit of a single chaotic system. Due to this, many low dimensional chaotic systems are more prone to phase space reconstruction attacks [9]. Such kind of attacks can be reduced by using S-box (Substitution box) in the algorithm. Complexity of cryptanalysis and brute force attacks can be further reduced by increasing the size of S-box in the algorithm. One such technique is developed by Silva-García and et al [10]. They introduced S-boxes in Advanced Encryption Standard (AES) algorithm to increase the level of security. Nonlinear chaotic differential equations are used to generate random numbers inside the S-box. But immunity against noise has not been noticed in the algorithm.
- 2. Int J Elec & Comp Eng ISSN: 2088-8708 Performance analysis of transformation and bogdonov chaotic substitution based … (Prajwalasimha S N) 189 A double humped logistic map has been developed by Lingfeng & et al. [11] by introducing general parameters to the existing chaotic map to generate pseudo random key sequence for the substitution stage. Robustness of the algorithm against Gaussian noise has been noticed but not against other kind of noises. Better UACI values are observed for various images but considerable differences in the NPCR values are noticed compared to ideal values. Rasul Enayatifar & et al. [12] developed combined permutation and diffusion technique using 3-D logistic chaotic map. Better entropy is observed in the absence of noise for many standard images but considerable difference in the values of NPCR and UACI is observed compared to ideal values. A combined 1-D logistic map and 2-D Baker chaotic map based block wise permutation algorithm has been developed by Lingfeng Liu & et al. [13]. Even though low dimensional chaotic maps are considered, phase space is made large by multiple chaotic maps. Very minimum correlation between the adjacent pixels in the cipher image has been noticed along with slightly high entropy but considerable difference in the values of NPCR and UACI is observed compared to ideal values for few standard images. Based on the above considerations a combined 2-D Pseudo Hadamard chaotic transformation (MPHT) and 2-D Bogdonav chaotic random diffusion based algorithm has been proposed in which a large phase space is considered along with a substitution image. The paper is organized as follows: Section 2 describes the proposed scheme. Section 3 with statistical and differential analysis followed by conclusion in Section 4. 2. RESEARCH METHOD Three stages per round are involved in the encryption process: Transformation, Diffusion and Substitution. Modified Pseudo Hadamard transformation is used in the first stage and random sequence generated by Bagdonov chaotic generator is used in the substitution stage. Figure 1 illustartes the flow diagram of the system. 2.1. Encryption algorithm Step1: Original image of size 2 𝑛 X 2 𝑛 is transformed using modified Pseudo Hadamard transformation. 𝐻1′(𝑥, 𝑦) = 𝐻((𝑎 + 𝑏 + 𝑐) 𝑚𝑜𝑑 2 𝑛 , (𝑎 + 2𝑏 + 𝑐) 𝑚𝑜𝑑 2 𝑛 ) 1 < 𝑎, 𝑏 < 2 𝑛 (1) Where, 𝐻(𝑎, 𝑏) is the host image of size 2 𝑛 X 2 𝑛 𝐻1′ (𝑥, 𝑦) is the transformed image of size 2 𝑛 X 2 𝑛 𝑐 is the constant (𝑐 = 37) Step2: Block truncated substitution image of size 2 𝑛 X 2 𝑛 is transformed using modified Pseudo Hadamard transformation. 𝑆1′(𝑥, 𝑦) = 𝑆 𝑡 ((𝑎′ + 𝑏′ + 𝑐) 𝑚𝑜𝑑 2 𝑛 , (𝑎′ + 2𝑏′ + 𝑐) 𝑚𝑜𝑑 2 𝑛 ) 1 < 𝑎′, 𝑏′ < 2 𝑛 (2) Where, 𝑆1′(𝑎′, 𝑏′) is the block truncated substitution image of size 2 𝑛 X 2 𝑛 𝑆 𝑡(𝑥, 𝑦) is the transformed truncated image of size 2 𝑛 X 2 𝑛 𝑐 is the constant ( 𝑐 = 37) Step3: Both transformed images are subjected for bitwise XOR operation 𝐶1(𝑥, 𝑦) = 𝐻′(𝑥, 𝑦) ⊕ 𝑆′(𝑥, 𝑦) (3) Step4: The cipher image from first stage is subjected for substitution with pre-defined S-box. 𝐶2(𝑥, 𝑦) = 𝐶1(𝑥, 𝑦) ⊕ S-box (4) Step4: The cipher image from substitution stage is subjected for diffusion with random sequence generated Bogdonov chaotic equation. 𝑥′ = (𝑥 + 𝑦′)𝑚𝑜𝑑 2 𝑛 (5) 𝑦′ = (𝑦 + 𝜀𝑦′ + 𝐾𝑥′(𝑥′ − 1) + 𝜇𝑥′𝑦′) 𝑚𝑜𝑑 2 𝑛 (6)
- 3. ISSN: 2088-8708 Int J Elec & Comp Eng, Vol. 10, No. 1, February 2020 : 188 - 195 190 Where, ε = 7(d)2 K = 9(d)2 μ = 3(d) d = ∑ ∑ 𝐻(𝑎, 𝑏)256 1 256 1 𝐶3(𝑥, 𝑦) = 𝐶2(𝑥, 𝑦) ⊕ 𝑥′ (7) Where, 𝐶3(𝑥, 𝑦) is the cipher image after diffusion of size 2 𝑛 X 2 𝑛 Step5: The number of execution rounds (d) is placed in the four extreme corners of the cipher image along with the respective pixel values. Figure 1. Flow diagram of proposed cryptosystem 2.2. Decryption algorithm The number of rounds for decryption stage (d) is taken from the pixel values in the four extreme corners of the cipher image. Step1: The cipher image is then subjected for XOR operation with random sequence generated Bogdonav chaotic equation with the same constant co-efficient. 𝑥′ = (𝑥 + 𝑦′)𝑚𝑜𝑑 2 𝑛 (8) 𝑦′ = (𝑦 + 𝜀𝑦′ + 𝐾𝑥′(𝑥′ − 1) + 𝜇𝑥′𝑦′) 𝑚𝑜𝑑 2 𝑛 (9) Where, ε = 7(d)2 K = 9(d)2 μ = 3(d)
- 4. Int J Elec & Comp Eng ISSN: 2088-8708 Performance analysis of transformation and bogdonov chaotic substitution based … (Prajwalasimha S N) 191 𝐶2′(𝑥, 𝑦) = 𝐶3′(𝑥, 𝑦) ⊕ 𝑥′ (10) Step2: The obtained cipher image XORed with the elements of S-box used for encryption. 𝐶1′(𝑥, 𝑦) = 𝐶3′(𝑥, 𝑦) ⊕S-box (11) Step3: The block truncated substitution image is subjected for MPHT with same constant and then XORed with cipher image from previous stage. 𝑆1′(𝑥, 𝑦) = 𝑆 𝑡(𝑎′ + 𝑏′ + 𝑐) 𝑚𝑜𝑑 2 𝑛 , (𝑎′ + 2𝑏′ + 𝑐) 𝑚𝑜𝑑 2 𝑛 (12) 𝐻1′(𝑥, 𝑦) = 𝐶1′(𝑥, 𝑦) ⊕ 𝑆′(𝑥, 𝑦) (13) Step4: the obtained image from previous step is subjected for inverse MPHT to get original image. 𝐻 𝑟(𝑎, 𝑏) = 𝐻1′(5𝑥 − 4𝑦 − 𝑐) 𝑚𝑜𝑑 2 𝑛 , (y – x) mod 2n ) (14) 3. EXPERIMENTAL RESULTS Standard test images are considered from Computer Vision Group (CVG), Dept. of Computer Science and Artificial Intelligence, University of Granada, Spain. Matlab software is used for performance analysis and implementation. Performance analysis is made based on various security tests. Table 1 compares resultant Entropy, Correlation, UACI and NPCR of different encryption schemes with the proposed system. The results indicates very less correlation between the adjacent pixels after substitution phase along with high entropy value indicating that the pixel values are altered effectively in the cipher image. Table 1. Comparision of entropy and correlation between standard and encrypted images Images Entropy = 8 [14] Correlation UACI ≥ 33.4635% [14] NPCR ≥ 99.6093% [14] Lena 5.5407 (Blow Fish) [15] 0.1500 [16] 31.00 [16] 90.21 [16]5.5438 (Two Fish) [15] 5.5439(AES 256) [15] 5.5439 (RC 4) [15] 33.4201 [19] 99.5859 [19] 7.5220 [16] 7.9972 [17] 7.9950 [18] 7.9958 [19] 0.0020 32.01 [22] 99.60 [22]7.6427 [20] 7.9971 [21] 7.9970 [22] 33.4303 99.6063 7.9973 Baboon 7.9950 [18] -4.6636e-04 30.87 [21] 99.59 [21] 7.9947 [21] 7.9968 33.2305 99.5544 Peppers 7.9960 [18] -0.0040 30.71 [21] 99.61 [21] 7.9954 [21] 33.3761 99.6490 7.9973 Airplane 7.9972 0.0040 33.2971 99.6231 Cameraman 7.9972 [23] -0.0041 33.3763 99.6201 7.9975 Barche 7.9973 0.0048 33.3745 99.6017 Carnev 7.9971 -9.7275e-04 33.3590 99.5651 Donna 7.9973 1.6005e-04 33.4637 99.6460 Foto 7.9968 -0.0028 33.4974 99.5667 Galaxia 7.9972 0.0024 33.4866 99.5773 Leopard 7.9972 0.0013 33.3751 99.5911 Montage 7.9966 -0.0050 33.3403 99.6384 Clock 7.9969 0.0038 33.3330 99.6094 Vacas 7.9974 -4.2689e-04 33.3868 99.6140 Fiore 7.9972 0.0058 33.4856 99.6262 Mapasp 7.9972 0.0040 33.2827 99.6201 Soil 7.9970 0.0026 33.3852 99.6017 Mesa 7.9976 0.0077 33.3114 99.6155 Papav 7.9969 4.2616e-04 33.4553 99.6216 Tulips 7.9974 0.0058 33.4337 99.5987
- 5. ISSN: 2088-8708 Int J Elec & Comp Eng, Vol. 10, No. 1, February 2020 : 188 - 195 192 3.1. Noise interference The correlation coefficient decides the similarity between retrieved (decrypted) and original images [24]. The performance analysis of decrypted image under noisy condition is decided by comparing the correlation coefficient between decrypted and original images. Figure 2 illustartes retrieved and original image under different noisy conditions and Table 2 discribes the similarity in the order of correlation between the de-crypted and original images under noise interference. If the correlation coefficient is equal to unity, the retrieved image is same as that of the original watermark. The cipher image is considered under various noisy conditions and the performance analysis of the algorithm is made after decrypting the noisy cipher image. Figure 2. Performance analysis of retrieved and original image under noisy conditions Table 2. Performance analysis of retrieved and original image under noisy attacks Noise Interference Correlation Pepper & Salt 0.8617 Gaussian 0.7062 Poisson 0.8449 Speckle 0.6527 LSB neutralization attack 0.9790 3.2. Inference The correlation co-efficient value drops to a minimum 0.6527 with speckle (multiplicative) noise in cipher image indicating 65% similarity between the corresponding pixels in original and retrieved images. Due to LSB neutralization attack, the correlation co-efficient of 0.9790 is observed indicating 98% similarity between original and retrieved images. It has been observed that, an average of 81% similarity between original and retrieved images is observed under noisy conditions. And hence the proposed algorithm gives better results under noise attacks. Figure 3 illustrates similarity in the order of correlation between
- 6. Int J Elec & Comp Eng ISSN: 2088-8708 Performance analysis of transformation and bogdonov chaotic substitution based … (Prajwalasimha S N) 193 the de-crypted and original images under different noise densities. Figure 4 Illustration of resultant images under different stage of the crypto-process. Also very close to the ideal values of Unified Average Changing Intensity (UACI=33.39%) but slight less and Number of Pixel Changing Rate (NPCR=99.61%) equal to the ideal value, slightly greater than that as observed in non-Chaotic substitution [25] are noticed from the outcome of the standard images. Figure 3. Correlation between the retrieved and original watermarks under noise interference Figure 4. Illustration of Host image, Substitution image and Cipher image after transformation, diffusion and substitution stages
- 7. ISSN: 2088-8708 Int J Elec & Comp Eng, Vol. 10, No. 1, February 2020 : 188 - 195 194 4. CONCLUSION In the proposed encryption scheme, Pseudo Hadamard transformation is used in the transformation stage to vary pixel positions and Bogdonov chaotic random sequence generator is used in the substitution stage to vary the pixel values in an image. High redundancy and strong correlation between the adjacent pixels are effectively reduced by the proposed technique. High degree of randomness obtained from Bogdonav chaotic generator in the substitution stage leads to achieve better entropy in the cipher image. Correlation between host and cipher images is very less indicating poor similarities between them. Average values of 99.61% number of pixel changing rate (NPCR) is observed which is almost equal to the ideal value and an average value of 33.39% unified average changing intensity (UACI) is obtained which is very close to the ideal values, for a set of twenty standard images. Further, more number of chaotic generators can be used to get random sequences for substitution stage of encryption to increase the level of security. REFERENCES [1] Leo Yu Zhang, et al., “On the Security of a Class of Diffusion Mechanisms for Image Encryption,” IEEE Transactions on Cybernetics, vol. 48, no. 4, pp. 1163-1175, 2018. [2] Alireza Jolfaei, et al., “On the Security of Permutation-Only Image Encryption Schemes,” IEEE Transactions on Information Forensics and Security, vol. 11, no. 2, pp. 235-246, 2016. [3] Yue Wu, et al., “Discrete Wheel-Switching Chaotic System and Applications,” IEEE Transactions on Circuits and Systems, vol. 61, no. 12, pp. 3469-3476, 2014. 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- 8. Int J Elec & Comp Eng ISSN: 2088-8708 Performance analysis of transformation and bogdonov chaotic substitution based … (Prajwalasimha S N) 195 [21] Nabil Ben Slimane, et al., “Nested chaotic image encryption scheme using two-diffusion process and the Secure Hash Algorithm SHA-1,” Proc.of 4th International Conference on Control Engineering & Information Technology, 2016. [22] Prajwalasimha S N and S. R. Bhagyashree, “Image Encryption using Discrete Radon Transformationand Non chaotic Substitution,” Proc. 2nd IEEE International Conference on Electrical, Computer and Communication Technologies, pp. 842-846, 2017. [23] Prajwalasimha S N, Kavya S R and Tanaaz Zeba Ahmed, “Design and Analysis of Pseudo Hadamard Transformation and non-Chaotic Substitution based Image Encryption Scheme,” Indonesian Journal of Electrical Engineering and Computer Science (IJEECS), vol. 15, no. 3, 2019. [24] Shetter A., et al., “Image de-noising algorithm based on filtering and histogram equalization,” Proceedings of the International Conference on I-SMAC (IoT in Social, Mobile, Analytics and Cloud), I-SMAC, pp 325-328, 2018. [25] Prajwalasimha S N and Basavaraj L, “Design and Implementation of Transformation and non-Chaotic Substitution based Image Cryptosystem,” International Journal of Engineering and Advanced Technology, vol. 8, no. 6, pp. 1079-1083, 2019. BIOGRAPHIES OF AUTHORS Prajwalasimha S N received Bachelor of Engineering (B.E) Degree in Electronics & Communication from Visvesvaraya Technological University, India in 2012, Master of Technology (M.Tech) Degree in Digital Electronics & Communication Systems from Visvesvaraya Technological University, India in 2014 and pursuing Doctoral Degree (Ph.D) in the field of Cryptography under Visvesvaraya Technological University, India. He has published more than 20 research papers in International Journals, Conferences & Book Chapters and serving as Reviewer for many International Journals and Conferences. He has been conferred with best research contribution award from IEEE ICECCT 2017. His research interest includes Cryptography, Steganography, Digital Image Watermarking and Image Processing. Dr. L Basavaraj received Bachelor of Engineering (B.E) Degree in Electrical & Electronics Engineering from University of Mysore, India, Master of Technology (M.Tech) Degree in Digital Electronics from Darwad University, India and Doctoral Degree (Ph.D) in the field of Image & Signal Processing under University of Mysore, India. He has published more than 40 research papers in International Journals, Conferences & Book Chapters and currenty guiding 7 Ph.D scholars. Being senior member of IEEE, his research interest includes Image & Signal Processing.