Secure image encryption based on improved bat optimized piecewise linear chaotic map through integrated permutation-confusion and double diffusion

Abstract

The augmented growing of visual cryptography in multimedia image transmission or data transmission over unsecured networks leads in safekeeping for confidential information. Generally two techniques are employed to afford secure transmission namely data hiding and cryptography. Cryptography is the main objective of recent research work in which the way of achieving secure transmission over the network be contingent on the interest of data encryption. This encryption process encrypts the constituent of data such as manuscript, image, audial, and audiovisual to make the data unconceivable or incomprehensible during transmission. A novel secret key generation based on Improved Bat Optimized Piecewise Linear Chaotic Map is proposed for image encryption. Our proposed secret key is intended for image encryption owing to the progression of mixing, permutation, double diffusion and confusion with the size of 128 bit to perform secure transmission. The success of our proposed method is revealed by the tentative results and comparison with the existing techniques in terms of sensitivity analysis, Information Entropy, correlation coefficient and, Encryption speed.

Keywords

Image encryption cryptography secure transmission improved bat optimized piecewise linear chaotic map permutation-confusion double diffusion

1 Introduction

Now an era’s cryptography plays a major protagonist in lifespan to share the content safely and communication with effective security has been the ultimate need of the society. Secure communication has revolved into the most critical need of the modern society and its improvements are expanding significantly. To make this secure transmission of information, cryptographic procedures can be used. The security apertures may induce the privacy of users like their integrity, authenticity and reputation. So in order to ensure the viability of the cryptography, data encryption is necessary for these kinds of concepts [1]. Data encryption is the strive of the various contents of data like manuscript, audial, image and other multimedia data which makes the data invisible or unreadable to the third party [2]. For each and every second a lot of imageries and videos are created and shared through networks. The information based on these imageries and videos can be a set apart and sensitive like a person’s personal information, medical records, secret messages, etc. So while sharing these kinds of multimedia data without a proper security may cause problems for individuals and for the organizations [3]. Prevention of the image information from its information leakage a lot of image encryptions algorithms and techniques are there, together with chaos theory, random grids, and optical transforms, DNA coding and compressed sensing [4].

For an image encryption of multimedia data, chaotic cryptosystem have good features and a heavy potential role of information security than many other traditional ciphers [5]. A Chaotic system is one of the case of nonlinear dynamics which have many significant assets of sensitive reliance on initial conditions and control parameters, non-periodic and topological transitivity, pseudorandom property [6]. The feature of a chaotic system is a great ambiguity which is responsible for the unpredictability and complexity of the chaotic dynamics. By synchronizing chaotic system can be able to give potential for the applications of chaos in secure communication schemes [7]. Generally chaos is an unbalanced motion of unpredictable random behavior, a chump change in the early condition can induce a large systematic alteration in the chaotic system [8]. The chaotic cryptosystem consist of more than one chaotic map for the drive of an image encryption so that it can able to achieve high complication and high uncertainty [9]. The chaotic map will be a more efficient alternative to pseudorandom sequences, a simple chaotic map can be used for many image encryption techniques because the chaotic map will scramble the image or subsequently hide the resulting image [10, 11].

One of the eminent one dimensional chaotic maps is the logistic map and is a humble dynamical equation with critical chaotic behavior. Mainly there are two problems with the logistic map regarding to the limitation of chaotic range as well as no uniform distribution and there are some parameters which make to have no chaotic performances for the logistic map [12]. With the intention of achieving better key spacing more than one chaotic map should be used because for one dimensional chaotic map there are some limitations like weak security and small key space. So in order to achieve better key space and resisting from various attacks multiple chaotic maps can be used [1]. Through the quantum chaotic map diffusion can be achieved by combining the features of vertically and horizontally neighboring pixels of the image and there is a heavy misperception and dissemination property in image encryption technique [5]. For quantum images some new strategies comprise efficient permutation and dissemination properties for image encryption which means it scrambles the position of pixel code and diffusion operation is performed in permutation stage based on its transformations [13].

For chaotic encryption, synchronization is one of the main approaches by the use of nonlinear backstopping control, we can control the synchronization and several categories like time delayed systems, observer systems, unidirectional and bidirectional coupling, feedback control, active control etc. [14]. Recent advances in chaos encryption have prompted numerous security concepts much more by channels, observers and controllers which will decrease the insecurity during the transmission. Usage of channels and observers, we can control the chaotic system. The classical observers are not attractive because of higher order systems and non-attractive system. For a secure chaotic communication, a variation of the information signal and an effective harmonization is necessary [15].

To combat with the above challenges in image encryption, this paper proposed a novel Improved Bat Optimized Piecewise Linear Chaotic Map technique to engender the secret key for image encryption. The main aid of this paper highlights the secure image encryption to maintain the confidentiality and security in the time of image transmission over the network. The rest of this paper is prearranged as follows. The works related to visual cryptography in terms of image encryption and chaotic map is explained in section 2. Our proposed method is enlightened in section 3. In section 4 the results and discussion is given and trailed by conclusion in section 5.

2 Related works

The contextual of literature related to image encryption for the visual cryptosystem is documented below

Norouziet al. [16] had introduced a novel image encryption algorithm centered on the hyper-chaotic systems. For encrypting each pixel they use, a sum of pixels which was placed afterward pixel and it used dissimilar summation for encrypting dissimilar input image to further improve the conflict of cryptosystem contrary to known or chosen-plaintext and discrepancy attacks. During encryption the key stream depends on both initial keys and plain image. The proposed key possessed high key sensitivity and had a better capability against statistical attack. The proposed method reveals that an immediate change in the original image and a key results a significant change in the ciphered image and it cannot obtain the correct plain-image. The proposed method was so beneficial for high security level, high plain text sensitivity, high key sensitivity, etc. and the method was very secure and definitive with high potential of secure communication.

Zengqiang Chen et al. [17] had introduced a new method of hyper chaotic algorithm for an encryption of an image based on the matrix of total image scuffling to scuffle the spots of each image pixel of the plain image. The main process of the hyper chaotic system was to distract the association between the plain-image and the cipher-image. The combination of different states of hyper chaotic method was that it differ the grey values of the scuffled image. In order to obscure the high correlation among the pixels, an image total scuffling matrix was used to scuffle the locus of the plain-image. A proper and perfect encryption should combat with all varieties of known attacks because it was subtle to the secret keys and the space between the keys must be far to make brute-force attacks infeasible. The resultant proposed algorithm had a high advantage against high security and key space.

Lintao Liu et al. [18] had introduced a new scheme based on the hybrid chaotic maps and dynamic random growth technique for a block image encryption. This hybrid chaotic map dealt with the concept of cat map with the architecture of arrangement and dissemination. An Arnold cat map and dynamic random growth technique is used in the permutation process to disturb the original image and neglects its fatal drawback. Different methods like sensitivity analysis, computational performance analysis statistical analysis, and analyzing key space are used for the security. Based on this proposed concept they combat all statistical attack, brute-force attack, and differential attack. So it is very beneficial for the transmission of image through internet.

Haiqing Zhao et al. [19] had implemented a SHA-3 hash function for proficient and secure image encryption. In this scheme permutation and diffusion is employed for the structural design of classical encryption. To avoid the greater time consumption, random direction of shuffling is done based on the method of wave-line confusion. Generated key stream by Arnold map is used for horizontal and vertical circular confusions which is adopted by the hash value use of chaotic matrix produced from plain image. This proposed technique combats the attack of plaintext while comparing with the previous encryption method. Here they design a block method with the output of hash value in the permuted image and this current block technique will combat well with the chosen plaintext. This encryption method has a heavy and better security for digital image communication.

Narendra K. Pareek et al. [21] suggested the diffusion-substitution by using gray image encryption. They utilized the size of 128 bit secret key for dynamic blocks. The diffusion and substitution process uses these dynamic blocks which are key dependent. Here high level of security is done by growing the size of secret key and by executing it with higher number of iteration. By increasing the size of the secret key in proposed algorithm the sturdiness against brute-force attacks will be improved. The results have been given to validate the high security features and effectiveness of their system.

3 Improved bat optimized piecewise linear chaotic map based visual cryptography

Nowadays transmitting number of imageries and videos through the internet is increasing rapidly and which also becomes very popular. Moreover security is very mandatory while sharing some secret information through the network. During the transmission of data through internet, it may leads to security issue due to interference, interruption, etc. In order to afford secure transmission of images, image encryption is utilized so that the information based on the image can be prevented. This can be done by various techniques and algorithms like chaos theory, gray code, elliptical curve, ElGamal, p-Fibonacci Transform etc. Among these chaotic cryptosystem acting a foremost part in image security during transmission and shows the best result for redundancy. However there remains a gap in security because of the inflexible nature of the existing chaotic cryptosystems. Hence we aimed to design a highly efficient secure image encryption technique based on logistic mapping in this paper. The style of the proposed framework is illustrated as follows.

Initially the input image is extracted from the database be a multimedia image (gray-scale image). Then the secret key for encryption is generated based on a unique key generation method called Improved Bat Optimized Piecewise Linear Chaotic Map. This process will generate a secret key that is further mixed up with the input image using XOR operation in the mixing process. After the collaborating process bit level permutation is employed in which the bits in each pixel taken from the mixed image are permuted with the secret key chosen. The permuted image then undergoes a double diffusion process, here the scrambling of the image is done based on zigzag scanning pattern and also with the spiral pattern. Finally, in the misperception stage pixel swapping is employed which will generate a final cipher image with high level of security. The process involved in the proposed image encryption standard is briefly explained in the subsequent sections.

3.1 Methodology

Numerous datasets have been proposed for considering the issue of producing image descriptions. Be that as it may, there is some reasonable dataset is decided for the proposed work to enhance the execution of the proposed work. In proposed work the images are taken from the standard test image dataset (www.imageprocessingplace.com). This image dataset contains the gray scale images (Lena, peppers, cameraman, lake, etc.) all in uncompressed tiff format, and of the same 512×512 size. Initially the mixing process should be done for the input image g_n by using the secret key and produce the mixed image as M_n. Then M_n is fed into the permutation stage to produce the permuted image as P_n, afterwards P_n is forward to the double diffusion stage where zigzag and spiral diffusion operations are performed sequentially. The above zigzag and spiral diffusions are represented as z_n andsp_n respectively. The processed image sp_n from the above step is delivered to the confusion stage to produce the encrypted image E_n with the help of generated secret key. The below sections illustrated the process which is to be carried out for secret key generation for the encryption operation given in Fig.1.

Fig.1

Process Flow of Proposed Method

3.2 Secret Key generation by improved bat optimized Piecewise Linear Chaotic Map

To guarantee the security of the visual cryptosystem, the proposed methodology generates the secret key for the image encryption and a good visual cryptosystem should be subtle to the secret key. Piecewise Linear Chaotic Map (PWLCM) is used to engender the secret key, then the improved bat optimization algorithm is employed to find the optimal secret key with length of 128 bit for mixing and integrated permutation-Confusion, double diffusion stages.

3.2.1 Piecewise Linear Chaotic Map (PWLCM)

Initially the input grayscale image taken from the dataset with resized image as 256×256, if the image is in the size of 512×512. The gray scale image g_n is in the form of decimal numbers from 0 to 255. Suppose the input image has length of M×N by utilizing the PWLCM as the following expression (1) mapping operation is performed in the input image [4]. $\begin{matrix} g_{i} = {\begin{matrix} g_{i - 1} / - η, 0 < g_{i - 1} < η \\ (g_{i - 1} - η) / - (0.5 - η), η \leq g_{i - 1} < 0.5 \end{matrix} \end{matrix}$ (1)

Where the positive control parameter η in the range of (0, 0.5). The chaotic sequence has MN elements, G={g₁, g₂, …g_MN} and each element is converted to the integer sequence S(i) as defined by [4] $S (i) = mod (floor (G (i) \times 10^{14}), 256)$ (2)

Where the element in S(i) range from 0 to 255. This secret key with length of 256 bit is generated using the mapping of input g_n image. From the generated secret key S the Improved Bat Optimization algorithm is applied to produce the optimal secret key, which is described as below section.

3.2.2 Improved bat optimization

The optimization of the secret key generated randomly through the above process is done with the aid of the optimization technique called Improved Bat optimization algorithm. In this framework, from the 256-bit length key is optimized into 128 bit length owing to the optimization algorithm. Various changes were acknowledged over current Bat Algorithm (BA) to produces much nearer values to optimum values of benchmark functions and also to evade local optimum tuning up the convergence speed iteratively. The new mathematical formulation as $Pulse emission rate u_{i}^{t + 1} = u_{i}^{0} - u_{i}^{0} e^{- γ t}$ (3) $Loudness L_{i}^{t + 1} = α L_{i}^{t}$ (4) Local search solution as $NewSol = BestSol + (T_{max} + t) \times \frac{NewVelocity}{T_{max}}$ (5)

Where γ, α,t is current iteration, T_max is Maximum Iteration. Every bat of the swarm moves by updating its velocity and position for each generation. To make this movement, the following equations are used: $y_{i} = y_{min} (1 + λ) - λ y_{max}$ (6) $v_{i}^{t} = v_{i}^{t - 1} y_{i} + [x_{i}^{t - 1} - x_{*}]$ (7) $x_{i}^{t} = x_{i}^{t - 1} + v_{i}^{t}$ (8)

Where the parameter λ is a randomly generated number in the [0, 1] interval. Additionally, x_* denotes the current best solution in the bat, and $v_{i}^{t}$ and $x_{i}^{t}$ represent the velocity and position of a bat i at time stept. The principle goal of this optimization algorithm for proposed framework is choosing the 128 bit length from 256 bit with low sum value and objective function for this intention is expressed using (6) and the algorithm is interpreted in below: (9)

IBAO Algorithm
Define the objective function using (6) Initialize the bat population
for each bat in the population do
Initialize pulse rate, loudness and velocity
using (3), (4) and (7)
end
repeat
for each bat in the population do
Generate new solution using (5)
Select one solution among the best one;
End
Until termination criterion not reached
Rank the bats and return the current best bat of the population.

The above algorithm bring about the optimal secret key with 128 bit length and for the upcoming section the secret key is utilized as both session key and sub pair key for the encryption. The procedure for the encryption is illustrated as below.

3.3 Image encryption by integrated permutation-confusion and double diffusion

Encryption is the most effective way to achieve data security for the visual cryptosystem in behalf of the mixing, permutation, confusion and double diffusion. Session key is reformed into ASCII values to apply for mixing and double diffusion process. Then the sub pair key is converted into hexadecimal values to apply for the permutation process. The following notations are describe the session key and sub pair key

k = k₁k₂k₃...k₃₂ (in hexadecimal),

K = K₁K₂K₃... K₁₆ (in ASCII),

Here, k_i ’s (referred to as sub-keys) are hexadecimal digits (0–9 and A–F) and K_i ’s represent session keys and the processes for the encryption is discussed detail in consequent sections.

3.3.1 Mixing process

The session key is used for mixing process in which each pixel of an image g_n is replaced by the new pixel which is acquired by the XOR operation between the current pixel and previous pixel as well as session key. For first pixel, since there will be no previous pixel so in place of previous pixel we use zero. If g_n is an image having the pixels from x₁₁, x₁₂, …x_MN, then the mixing process is explained as below:

Steps for mixing process:

Image g_n having the size of M×N

i← position of first session key

for x=1:M_{//M-Numberofrows}

for y=1:N_{//N-Numberofcolumns}

M_xy=M_xy⊕M_xy-1⊕k_i

i← next session key position ((i mod 16)+1)

end for

From the above algorithm the mixed image M_n having replacement of pixels with M₁₁, M₁₂, …M_xy. The resultant mixed image is conceive to the permutation procedure it is discussed in the forthcoming section.

3.3.2 Permutation process

The mixed image M_n is imminent for the permutation process in which altering the pixel values of image M_n with one of their surroundings pixels from the eight possible adjacent locations such as East(E), North (N),North East (NE),,North West (NW), West (W), South (S), South West (SW),, South East (SE) as shown Fig.2. The permutation is fulfilled with the sub pair key and the neighboring pixel are picking depends on the key k_i as shown in Table 1.

Table 1
Location of neighboring surrounding pixels to pixel

Sub key Value (k_i) Direction of adjacent pixel Location of surrounding pixel P_x,yw.r.t current pixel P_i,j

0/F East P(i, j+1)

1/E North East P(i-1, j+1)

2/D North P(i-1, j)

3/C North West P(i-1, j-1)

4/B West P(i, j-1)

5/A South West P(i+, j-1)

6/9 South P(i+1, j)

7/8 South East P(i+1, j+1)

Sub key Value (k_i)	Direction of adjacent pixel	Location of surrounding pixel P_x,yw.r.t current pixel P_i,j
0/F	East	P(i, j+1)
1/E	North East	P(i-1, j+1)
2/D	North	P(i-1, j)
3/C	North West	P(i-1, j-1)
4/B	West	P(i, j-1)
5/A	South West	P(i+, j-1)
6/9	South	P(i+1, j)
7/8	South East	P(i+1, j+1)

Fig.2

Locations of pixels around a pixel.

To change the property of the first pixel first sub key is used and vice versa, if all the keys are exhausted means again the first sub key is used. After the adjacent pixels are selected then the altering of pixels obtained by the XOR operation between the adjacent pixel and current pixel. The resultant permuted image P_n is allowing to the double diffusion stage

3.3.3 Double diffusion

The permuted image P_n is fed into the double diffusion stage in this case as both zigzag and spiral diffusions are performed simultaneously. Initially the image P_n is alienated into blocks consistent with the session key for that calculate K_i mod 10 then choose as in the following Table 2:

Table 2
Block size deciding table

_kMod10 0 1 2 3 4 5 6 7 8 9

Block size 16 24 32 40 48 56 64 72 80 96

_kMod10	0	1	2	3	4	5	6	7	8	9
Block size	16	24	32	40	48	56	64	72	80	96

In the zigzag dissemination stage pixels of each block are reshuffled within the same block by a zigzag path as shown in Fig.3. The pixels happenstance in the pathway is organized consecutively row by row and column by column in the same block. This is the methodology for reshuffle the pixel location in the zigzag manner and the zigzag image z_n is given to the spiral diffusion stage. Table 3 shows the original position of pixel and changing the position by zigzag diffusion.

Fig.3

Zigzag diffusion.

Table 3

Original pixels locality and their modified position location are shown on left and right respectively

1	2	3	4	16	1	6	3
5	6	7	8	2	9	4	11
9	10	11	12	5	7	14	8
13	14	15	16	10	13	12	15

In spiral diffusion stage the scrambling of the image is done based on spiral scanning pattern. The scrambling is done in key dependent manner. The sub-key pairs are formed as (k1, k2), (k3, k4), (k5, k6),... and the first pair is used to select the starting location in the current block in the first round of scrambling and the next pair for the next block. The spiral diffusion image sp_n is allowing to the confusion process to improve the encryption quality of an image.

3.3.4 Confusion process

In confusion process, swapping the pixels can be finished by without modifying the values of diffused image sp_n as shown in Fig.5. For instance replacement of current pixel in the position (i, j) is substituted by (i, j+1). The resultant image c_n from the confusion process is given to the encryption stage. The engendered secret key is embedded with the confusion image to produce the cipher image E_n. The encrypted image is passing out to the decryption process to yielding the decrypted image $g_{n}^{'}$ .

Fig.4

Spiral diffusion.

Fig.5

Confusion process.

3.4 Image decryption

The converse process of encryption procedure is known as Decryption and the input for the decryption is encrypted image E_n and the key with length of 128 bit. The encrypted image is allowing to the double diffusion stage to perform the reverse operation of both spiral and zigzag scrambling. Afterwards the result of the previous stage is passing to the permutation process to perform the inverse operation of permutation, then the inverse permuted image is granting to the mixing stage. The production of the consequential image is decrypted image as $g_{n}^{'}$ . The following section shows the outcome of the proposed framework and comparison analysis of existing methods.

4 Experimental results

The investigational results for the proposed method expose the visual cryptosystem process of different gray scale image from the standard test image dataset.

4.1 Experimental setup

The proposed technique is implemented in MATLAB and the system requirements of the proposed method are shown in below.

System Specification

Operating System: Windows 7,64 bit

Processor: Intel Pentium

RAM: 4GB

Platform: MATLAB

4.2 Results of proposed system

As per the proposed method the image is chosen from the image dataset. For the input image the secret key will be spawned using the improved bat optimized with PWLCM. The generated secret key it will be considered as the session key and sub pair key consistent with the ASCII and hexadecimal conversion of secret key. The results obtained from the proposed are illustrated in Fig.5.

The mixing process uses the session key and the mixed image is passed to the process of permutation stage. The permutation can be done with the help of sub pair key and is allowing to the double diffusion stage to perform both zigzag and spiral scrambling. The permuted image is delivering to the misperception stage to produce the cipher image with generated secret key hiding process. The performance assessment of the proposed method is explained in the subsequent section.

4.3 Performance evaluation

The performance of our proposed method is evaluated in terms of correlation coefficient, Entropy and sensitivity analysis. These measuring terms are calculated by the following formulas;

4.3.1 Correlation Coefficient (CC)

A worthy encryption algorithm must produce a very low correlation coefficient between the original image and encoded image. i.e. the features of encoded image must be independent on original image. So far measuring the encryption quality of an image by processing the relationship coefficient (CC) in the accompanying mode $C_{xy} = \frac{cov (x, y)}{\sqrt{d (x)} \sqrt{d (y)}}$ (10) $cov (x, y) = \frac{1}{N} \sum_{i = 1}^{N} (x_{i} - E (x)) (y_{i} - E (y))$ (11) $E (x) = \frac{1}{N} \sum_{i = 1}^{N} x_{i}$ (12) $d (x) = \frac{1}{N} \sum_{i = 1}^{N} (x_{i} - E (x))^{2}$ (13)

Where x and y are the two adjacent pixels grey-scale values in the image, N is the number of pixels in an image.

4.3.2 Information entropy

Information Entropy is used to measure the texture of the input image. It expresses the degree of indecisions in the system and express by the following equation $H (c) = \sum_{i = 0}^{2^{L} - 1} P (c_{i}) {log}_{2} \frac{1}{P (c_{i})}$ (14)

Table 4

Comparative analysis

Parameters
Methods	CC	Entropy	Sensitivity analysis		Encryption speed (s)
			NPCR (%)	UACI (%)
Proposed	0.227	7.975	0.9231	0.3921	0.33
Hyper chaotic	0.2303	7.461	0.706	0.3347	0.43
Cat map	0.24	7.96	0.6622	0.3325	0.58
SHA-3	0.28	7.931	0.688	0.3339	0.38

Where L is the pixel length value in binary number (for a gray image, L=8), P(c_i) is the probability of c_i. For a true random source making 2^L symbols, the entropy should be L. For 256-gray – scale image the pixel data have 2⁸ conceivable values, the entropy of a true random image must be 8. The competent cryptosystem produce the encrypted image with nearer entropy value then this infers information leakage in the encryption procedure is irrelevant.

4.3.3 Sensitivity analysis

It is used to analyze the inspiration of trivial change in one pixel even just one-bit in the plain-image in general cipher-image, in other words the attacker will try to perceive the change in the encrypted image by altering some pixel values in the original image There are two dealings are used to detect the impact of the single pixel value on the whole encrypted image The measures are(a) NPCR (number of pixel change rate) and(b) UACI (unified averaged changing intensity), and the calculation of these measures defined in subsequent Equations (15) and (16). $NPCR = \frac{\sum_{xy} D (x, y)}{M \times N} \times 100$ (15) $UACI = \frac{1}{M \times N} [\sum_{x, y} \frac{| c_{1} (x, y) - c_{2} (x, y) |}{255}] \times 100 {%$ (16) Where c₁ and c₂ are two cipher-images whose equivalent plain images have just only-one pixel difference. If c₁(x, y)=c₂(x, y) then D(x, y)=0; otherwise D(x, y)=1. The measures given in Equations (12) and (13) should also be maximum to avoid the security attack.

4.3.4 Encryption speed

Encryption speed is extremely reliant on on the image encryption algorithm used and also CPU structure, operating system platform, RAM size, the programming language and also on the compiler options. On the other hand it is an important index of, especially in the area of high necessities of real-time. These above parameters are compared between existing and the proposed method will be conferred in the succeeding section.

4.4 Comparative analysis

The comparative analysis is discussed between the existing and the proposed method by the parameters as Correlation Coefficient, Entropy, NBCR and UACI in Table 4. The proposed method shows better results than the existing methods.

Figures 7–11 shows the graphical representation of comparison between our proposed methods with some existing methods based on Table 4. The Fig.7 shows the correlation coefficient parameter evaluation between the existing method and proposed method. We obtain the CC value as 0.227 which is smaller than the CC value attained by the existing method.

Fig.6

Results of proposed system (a) Resized image (b)Mixed Image (c) permuted image (d) zigzag diffusion (e) spiral diffusion (f) confusion image (g) Encrypted Image (h)Decrypted Image.

Fig.7

Comparison in terms of correlation coefficient.

Fig.8

Comparison in terms of Information entropy.

Fig.9

Comparison in terms of NPCR.

Fig.10

Comparison in terms of UACI.

Fig.11

Comparison in terms of Encryption speed.

The Fig.8 shows the information entropy parameter evaluation between the existing method and proposed method. The entropy value of the proposed framework is 7.97 which are closer to the entropy value of a true random image. The existing entropy value is less than the proposed method.

The NPCR value of the proposed method is better than existing method and for the visual crypto system the NPCR value is ranges from 0 to 1 and the graph is shown in Fig.9. NPCR is used to perceive the modification of the changes in the cipher image to detect the sensitivity of the crypto system.

The UACI parameter also used to quantity the sensitivity investigation of the cryptosystem and for the proposed method produce the better result than the existing method. This measurement also used to detect the changes of pixels of different cipher images. The proposed method produces the value as 0.3921 which is better than the existing method.

The encryption speed parameter also used to measure the time of encryption process of the cryptosystem and for the proposed method produce the minimum time consumption than the existing method. This measurement is specified in the seconds.

The comparison graphs differentiate the three different techniques for image encryption with the proposed framework and the performances also give the better results. The entropy value of the proposed framework is 7.97 which are closer to the entropy value of a true random image. The other parameters correlation coefficient, NPCR, UACI and the encryption speed also produces the enhanced result than the existing parameters.

4.5 Discussion

Improved bat optimized with piecewise linear chaotic system for image encryption is implemented in this manuscript. The existing researches included are hyper-chaotic, cat map, SHA-3 which is the viable methodologies for secret key generation in the past decades. When we compare our implemented research and the previous encryption strategies in the literature the proposed framework has the better result. The above execution assessment and comparison in Table 4 shows that the our proposed technique is superior to the existing strategies in terms of correlation coefficient, information entropy, NBCR,UACI and encryption speed. Thus the proposed method works quicker than different existing methods. So we can say that our proposed method produces the secure image encryption for the given image in effective manner.

5 Conclusion

In this research work we introduced an Improved Bat Optimized Piecewise Linear Chaotic Map for the secret key generation with secure image encryption due to the practice of mixing, permutation, double diffusion and confusion. In keeping with the generated secret key the encryption process of an image produces the cipher image. In mixing process replacement of current pixels is done by XOR operation and the permutation process changes the pixel values through the adjacent pixels from the direction of current pixel. In double diffusion stage the permuted image is passed to zigzag and spiral stage using image block division which is done with the key. After that confusion process is done by means of swapping the pixel positions without modifying the values. The corresponding experimental results demonstrate that the proposed strategy produces the efficient encryption results over the parameter evaluation such as Information Entropy, Correlation Coefficient, Sensitivity analysis and encryption speed. Thus the outcome of proposed framework brings out the secure image encryption over the networks while image transmission.

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Secure image encryption based on improved bat optimized piecewise linear chaotic map through integrated permutation-confusion and double diffusion

Abstract

Keywords

1 Introduction

2 Related works

3 Improved bat optimized piecewise linear chaotic map based visual cryptography

3.1 Methodology

3.2.1 Piecewise Linear Chaotic Map (PWLCM)

3.3.1 Mixing process

3.3.2 Permutation process

Table 2 Block size deciding table kMod10 0 1 2 3 4 5 6 7 8 9 Block size 16 24 32 40 48 56 64 72 80 96

4 Experimental results

4.1 Experimental setup

4.2 Results of proposed system

4.3 Performance evaluation

4.3.1 Correlation Coefficient (CC)

4.4 Comparative analysis

5 Conclusion

References

Table 2
Block size deciding table

_kMod10 0 1 2 3 4 5 6 7 8 9

Block size 16 24 32 40 48 56 64 72 80 96