An Efficient Optimal Key Based Chaos Function for

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Date of publication xxxx 00, 0000, date of current version xxxx 00, 0000. Digital Object Identifier 10.1109/ACCESS.2017.Doi Number

An Efficient Optimal Key Based Chaos Function for Medical Image Security 3

2

4

5

K. Shankar , Mohamed Elhoseny , E. Dhiravida chelvi , SK. Lakshmanaprabu , Wanqing 1,* Wu 1

CAS Key Laboratory of Human-Machine Intelligence-Synergy Systems, Shenzhen Institute of Advanced Technology-Chinese Academy ofSciences

(SIAT-CAS), Shenzhen 518055, China 2

Faculty of Computers and Information, Mansoura University, Egypt. Email: [email protected]

3

School of Computing, Kalasalingam Academy of Research and Education, Krishnankoil, India. Email: [email protected]

4

Department of Electronics and Communication Engineering, Mohamed Sathak A.J. College of Engineering, Chennai, India. Email:[email protected] 5

Department of Electronics and Instrumentation Engineering, B. S. Abdur Rahman Crescent Institute of Science and Technology, Chennai, India. E-mail: [email protected].

* Corresponding author: Wanqing Wu, [email protected]

This paragraph of the first footnote will contain support information, including sponsor and financial support acknowledgment. For example, “This work was supported in part by the U.S. Department of Commerce under Grant BS123456.”

ABSTRACT With the rapid development in the field of medical image encryption, researchers analyzed a number of encryption algorithms based on chaotic systems. But there is a difficulty lies i.e., small key space and weak security in one-dimensional chaotic cryptosystems. To overcome this difficulty, an alternative security model was proposed in this paper. The current study investigated highly secure medical images with a couple of subkeys, initially where a couple of subkeys is given by utilizing chaotic logistic and tent maps. As per the Chaotic (C - function) process, the security was investigated like diffusion as well as confusion. Based on the initial conditions, different random numbers were generated for each map from chaotic maps. Adaptive Grasshopper Optimization (AGO) algorithm with PSNR and CC fitness function was proposed to choose the optimal secret and public key of the system among the random numbers. The reason behind choosing adaptive process is to enhance high-security investigation of the current proposed model compared to existing methods. At last, the proposed strategy results were compared with existing security methods and literary works, but found to be high performing. INDEX TERMS Chaotic maps, Encryption, Grasshopper Optimization, Medical Images, Optimal key, PSNR, Security, Tent map

I. INTRODUCTION

In order to transfer the medical images safely, some security prerequisites must be met. These necessities are secrecy, legitimacy and integrity [1]. Cryptographic systems can be utilized to ensure the expressed security prerequisites by scrambling the medical image to accomplish classification, and by utilizing the computerized marks to provide validness and uprightness [2, 35]. The works exhibited in this instructional exercise demonstrate how encryption algorithms provide security to medical symbolism [3]. The fundamental target is the assurance of medical images amid transmission [33], and furthermore when such advanced information is documented. The VOLUME XX, 2017

consequent test is to guarantee that such coding withstands extreme treatment for instance, compression [4]. There are numerous security problems persist in the field of cloud computing [9] due to which protection must be considered as high priority. Since the patient's name, address and the other health records are available online [5, 6, 36], there might be a plausibility of theft, unapproved access and breaches may occur for the information. Preservation of these records must be done effectively. Outsider access to those records can be permitted by scrambling the first message with the help of cryptographic algorithms [7]. Since the chaotic phenomenon is common in time-defer frameworks [7],the enthusiasm keeps on expanding upon 1

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time-delay [8] disorderly frameworks. Chaos is an outstanding nonlinear technique which is sporadic, apparently irregular and to a great sense, to introductory conditions [9]. The chaotic framework possesses the qualities of high sensitivity for beginning conditions &control parameters and is broadly utilized as a part of image encryption field to additionally upgrade the haphazardness of the algorithm and keys [10]. The insufficient mix of chaotic elements and encryption [11, 12] structures makes the unpredictability of recouping its secret key, from a few sets of plain-writings and the relating cipher-texts, encrypted with a similar secret key, lower than that of the brutal force attack [13]. The patient's name straightforwardly being connected with the image is observed as imperative from the patient's perspective [31] and keeping that data secret [14], is vital for the consistency with image [15].

The primary contribution of this original research work is to highly secure the medical images by utilizing Chaos Function (C-) with optimal secure and public keys. The explanation behind choosing the optimal keys as, by and large, this chaotic security process is that the keys which are arbitrarily created at nineteenth range which remains so impractical to secure legitimately. So we utilize the AGO of key improvement process in chaos encryption procedure. The rest of the paper is described as follows: Section 2 reviews the recent articles published with various techniques for image security. The brief methodology of the proposed work is discussed under section 3 whereas further section i.e., section 4 discussed the implementation results of the security process and finally the paper is concluded.

II. LITERATURE REVIEW TABLE I LITERATURE REVIEW Author/year/ Ref No

Technique

Toughi Shahriyar et al. 2017 [16]

Elliptic curve cryptography (ECC)

A.M. Vengadapurvaj a et al. 2017 [17]

Homomorphic crypto algorithms

Shankar et al. 2017 [18]

Homomorphic encryption with Ant Lion Optimization (ALO)

Massoud Sokoutiet 2017 [19]

al.

Goldreich Goldwasser Halevi (GGH) algorithm

Hossein Nematzadeh et al. 2018 [20]

Modified genetic algorithm with Coupled map lattices

R. Parvaz et al. 2017 [21]

chaotic system

Feng-Hsiag Hsiao 2017 [22]

Chaotic with RSA algorithm

Hiba AbdelNabi et al. 2017 [23]

Partial Encryption

A.M. Vengadapurvaj a et al. 2017 [17]

Homomorphic crypto algorithms

Description Based on public shared key and altering point G, a random generation phase was created to achieve random sequences. A prominent encryption strategy was provided by utilizing AES with a distributed random variable In cloud storage, the data is stored in order to help the health care units because of its performance, availability along with security.

For the encryption process, though ECC is time-consuming, it is unique in the way of creating a random variable. Compared to plaintext computation, the cipher image computation process is slow.

For improving the security level, an algorithm called ALO was introduced. Based on ALO, the best-encrypted image was illustrated according to maximum entropy.

The time required for the optimization process is high.

In addition to this, the GGH algorithm does not enhance the size of the image and finally, the difficulty remains as simple as O(n2).

ChosenCipher Text Attack is the only known drawback

A number of secure cipher images were generated using a coupled map lattice. The generated cipher images were initialized as MGA population An encryption algorithm, named as color image encryption algorithm, was presented for the purpose of grayscale or binary images. The presented technique was based on chaotic system. Chaotic synchronization experienced demodulating data through programmers by means of people in public channel. RSA is an asymmetric encryption and its quality depends on the huge trouble of factorizing two expansive prime numbers.

In GA algorithm, the drawbacks are evaluation of fitness function, selection of encoding and the mapping process. Some mapping techniques like logistic, sine, and tent possess some drawbacks.

The disadvantages of using this algorithm are need for long execution time and slow key generation process compared to other algorithms.

To accomplish a high level of entropy in the encoded watermarked images, substitution-based and transposition-based encryption was proposed

Binding a watermark on the chosen images may reduce the robbery though this training is under question among numerous photographers and inventive experts.

In cloud storage, the data is stored in order to help the health care units because of its performance, availability along with security.

Compared to plaintext computation, the cipher image computation process is slow.

III. SECURITY METHODOLOGY

Access to health information system data may misuse the security of patients interms of their medical images which

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Drawbacks

may affect the integrity of the medical system. A number of investigations are going on to increase the security for medical image and the ultimate goal of the current work is to propose chaos theory-based optimal encryption technique which is graphically represented in Figure 1. 9



initial conditions and parameters, really match with those as in cryptography. The two fundamental properties of Cfunction are sensitivity to initial conditions and mixing property [24]. The C- function streams were created utilizing different chaotic maps. The different maps were examined and their qualities were investigated whereas a subpart of these maps is discussed in the following segment.

FIGURE 1. Diagram for the proposed model.

An algorithm i.e. chaos-based image cryptosystem was introduced to perform both encryption and decryption on medical images. The proposed cryptosystem consists of two stages and it provides proficient security to original data. Initially, the plain image was assigned as input. Based on the chaos-based image cryptosystem, the mapping was done; further the level of security was also enhanced by Adaptive Grasshopper Optimization i.e., AGO, introduced for the purpose of the initial key selection process. A brief discussion of this secure methodology can be seen in the upcoming sections. A. CHAOS SECURITY ALGORITHM

The two phases involved in Chaos-based medical image security system are confusion and diffusion. For the assigned input images, the encryption and decryption were performed based on these two phases and the behavior of the proposed system was controlled by basic keys and control parameters. To improve the security level of chaos function (C-Function), double keys were generated for encryption and decryption processes and further, the double keys were generated by 16character byte keys [30]. B. CHAOS FUNCTION WITH MODELS

The functions involved in the Chaos are image encryption process which is related to its own characteristics and chaos that has randomness in the academic society. Commonly the encryption system is required one and the chaos function is illustrated in figure 2. During encryption process, the presented C-function was attached with XOR operation to enhance the unpredictability in cipher-image and a large key space in order to resist attacks. From the considered input plain images, the Cfunction was evaluated using map function and is described in the accompanying section. C. Chaotic maps

The chaotic maps create random sequences which are utilized at the time of the encryption process. Numerous ideas in chaos theory, for example, mixing and sensitivity to VOLUME XX, 2017

FIGURE2. Model for C- Function

1) LOGISTIC MAP

It is a straightforward, non-linear and dynamic as well as the polynomial condition of degree two with as output and input variable, one initial condition and one control parameter moreover; it can be portrayed as follows

an1   * an (1  an )

an (0,1) and n  0,1,.....,   (0,4)

In the logistic map, a semi-group was created through the operation of composition of function, as   (0,4) is a perioddoubling bifurcation process. 2) TENT MAP

Tent map is an iterated work, in the state of tent, shaping a discrete-time dynamical framework. This map of the image, point a n on the real line which also maps another point and  is maintained as constant here. for a n 1 \ 2  a (2) a n1   n for 1 / 2  a n  (1  a n ) Depending upon the constant value, the tent map predicts the chaotic function. This map in C- function converge to   1 and it is in the range of   (0,1) in input plain image a where 0 is used in secret keys. 3) CONFUSION PHASE

Confusion stage is the stage when pixel change occurs and the position of the pixels is mixed over the whole image without aggravating the estimation of the pixels and thus the image ends up unrecognizable. The motivation behind confusion is to reduce the high correlation between adjoining pixels in the plain image. For this confusion phase, security model generates random keys M  {a1 , a21,....ar*c } . Such keys are of input plain image size and it vary from 0 to 255.

9



The total one-dimensional vector O is derived using the following equation, D '  D(O)

(3)

' Here D represents the permuted image and the term O

indicates the permutation key. This procedure evades the excess digitization of chaotic qualities. As an outcome, the sensitivity to little changes of the initial condition or control parameters is expanded, as the accuracy of vast permutation is decreased. 4) DIFFUSION PHASE

The function involved in the diffusion process is, the total image again gets encrypted with various chaotic numbers. The diffusion process works on the basis of tent map and it produces the random numbers [25]. Further, it is also used to ensure the sensitivity for plain image so that a very little change in any one pixel of the plain image should spread out to almost all the pixels in the whole image. It is performed on the basis of following equation (4) U i  r  mod( Di'  U i 1  s.28 )

involved are optimal multi secret and public keys as following. 1) INITIALIZATION (KEYS INITIALIZATION)

This procedure introduces the 16-Byte multi keys for encryption and decryption process. The purpose behind choosing multi-keys is one for confusion process and another for diffusion process. It is characterized as follows: S _ Key  {s1 s2 ,....sn } and P _ Key  { p1 , p2 ,....... pn } (7) Based on this initialization, the fitness was found for both encryption and decryption of the given images and for each generated solutions, the objectives were found. 2) THE OBJECTIVE FUNCTION FOR CHAOS SECURITY

This medical image security model was considered with multi-objectives such as PSNR and CC function. It is shown in the equation below (8). Objecive  MAX ( PSNR) and MAX (CC ) (8)

Here U i and U i 1 are the values of current and previous masking pixel where  denotes XOR operation and the random code value as shown in the condition below. r  mod( floor (l n * 2 20 )255)

(5)

It’s elaborated by

 l  (U i  x) /( 255  x  y ) r 0 '   ( Di  x) /( R * C  x  y )

(6) Regarding the security purpose, the key stream r is updated for each pixel and the evaluated encrypted pixel values Di depend on beforehand-encrypted pixels and the keystream. Hence the algorithm confirms the resistance to differential attacks such as known plaintext attack, chosen-plaintext attack and known cipher image. D. SECURITY ANALYSIS 1) KEY GENERATION

Key generation is a basic step in medical image security process and here all secret and public key ranges

{s1 s2 ,....sn } and { p1 , p2 ,....... pn } and control parameters were initialized which are a0 and  ,  for choosing optimal keys in chaos security AGO algorithm.

FIGURE3. Flowchart for AGO

3) NEW KEY SOLUTION UPDATING PROCEDURE

In light of the above fitness calculation, the new Grasshopper behavior was updated for Chaos work in terms of medical image security [26]. The purpose of updating new key is to improve the keys in encryption and decryption process in here and now. The above scenario is symbolized as follows. (9) New Key _ Updating  I Sl  FGl  AWl

2) ADAPTIVE GRASSHOPPER OPTIMIZATION (AGO)

Optimization alludes towards achieving the best optimal solution in a solution space with regards to some predefined criteria. In AGO, the position of the grasshoppers in the swarm indicates a conceivable solution of a given optimization issue and the flowchart is shown in the figure 3. The position of the grasshopper is signified through social interaction, gravity force, and wind advection process. It is based on update and it finds the optimal 16-byte double secret keys for chaos security process in which the steps VOLUME XX, 2017

Elaboration of this equation in below steps Component 1: Social Interaction ( I Sl ) The components totally simulate the progress of grasshoppers, yet the major part began from grasshoppers themselves which is the social interaction depicted as follows. I Sl 

N

 I(y j 1 j l

lj

ˆ lj )y

(10)

9



y

lj Here, in theth equation the distance th (10), the term yˆindicates j ij l between and grasshopper and symbolizes a unit th th vector from l grasshopper to the j grasshopper. N is the number of grasshoppers [26]. The distance between grasshoppers ought to be mapped or standardized into the interim as per literature[1, 4]. Component 2: Gravity force ( FGl )

The Gravitational force component is designed as follows:

FGl   Fuˆ g

(11)

Component 3: Wind Advection ( AWl ) This component of grasshopper optimization which is important to update the solution and is described as follows

AWl  Auˆ w

(12) From the equation, (12) andˆ (13), g and w are gravitational u uˆ and drift constants where g , w show a unity vector towards the center of the earth. Grasshoppers have no wings and their movements are exceptionally related to the direction of the wind. After finding the updating variable, the equation got extended as follows  N  H d  Ldb Final _ Solution  o  o b 2  jj 1i 

 y j  yi I  y dj  yid  yij 

     Yˆd      (13)

d H bd indicates the upper bound in the d th dimension, l b

indicates the lower bound in the

ˆ

d th dimension, Yd

symbolizes

th

the value of d dimension in the target (best solution found so far), and the parameter o is a decreasing coefficient to shrink the comfort area, repulsion area, and attraction area. In any case, the gravity should not be assumed (no AG component) and one need to accept that the wind direction ˆ

(A component) is dependable towards an objective ( Yd ). The initial segment assumes the area of the present grasshopper with respect to different grasshoppers. The status of the considerable number of grasshoppers characterizes the area of search specialists around the objective. 4) ADAPTIVE PROCESS

In this adaptive behavior, every swarm takes the information from all swarms and then considers the best fitness key solution. It is considered by global best solutions and there is a little chance available for the model local optima from the grasshopper behavior to adopt the mutation operator and to find new keys in encryption as well as in decryption. 5) UPDATING OPTIMAL KEY

The parameter ‘h’ is updated using the following equation to reduce exploration and increase exploitation which is proportional to the number of iterations.

o  omax

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o  omin  r * max R

(14)

where omax is the maximum value, omin is the minimum value, r indicates the current iteration and R denotes the maximum number of iterations. E. OPTIMAL KEY-BASED C- FUNCTION WITH ENCRYPTION AND DECRYPTION

Steps Key generation Step 1: Generate 16-byte secret keys S1 and S 2 and public keys, Pu1 and Pu 2 and then include the size R * C of the image with structural parameters  ,  and a0 . Step 2: Optimize the above-mentioned keys, S1 and S 2 , Pu1 and Pu 2 using AGO algorithm and based on this optimization, the optimal keys are retrieved as Optimal {S1 and S 2} and Optimal{Pu1 and Pu 2} . Encryption Step 3: Set optimal secret keys i.e., Optimal {S1 and S 2}

p

0 with fixed parameters like and plain medical images  ,  in (0,1) and (3.5,4) respectively.

Step 3: Continue the iteration until 100> ties in the logistic map using chaos function from the logistic map (refer

a

equation (1)) to find the decimal fraction as 100 . Step 4: Continue the logistic map for plain image dimension R * C times to take M  {a1 , a2,....ar*c } Step 5: If the fraction is more than 100, then it denotes that next step 6 to be proceeded or otherwise the encryption process has to be processed to step 7. Step 6: If the fraction value is more than 100, then the chaos function is iterated for three times and the particular value is divided into 15 digits with five integers of each image pixel value 256. Step 7: Then this encryption process sorts the confusion matrix variables using first optimal secret key i.e., S1 . Step 8: Provide D0 and other structural parameters to evaluate the diffusion function equation (6). Step 9: Do the tent map function for M times using the equation (2) to get random code variable. Step 10: Based on random code, encrypt the plain image to cipher the image i.e., i=1,it is an XOR operation in the equations (4 and 5). Step11: These all steps should be repeated in R * C length of the image. Decryption Step: 12: Perform the step 1 to and decrypt the ciphered medical image into a plain image using optimal keys i.e., Optimal{Pu1 and Pu 2} . 1) ENCRYPTION

In encryption, chaotic systems were utilized as in previously mentioned confusion as well as diffusion stages. Additionally, difficult chaotic maps were selected as opposed to the basic ones in order to additionally upgrade the multifaceted nature 9



of the calculation and in this manner the security can be enhanced. This security strategy encoded the medical image and chose the parameters from acquired AGO-based optimal key which was assigned to the computerized color image encryption due to high secret high-dimension chaotic system by utilizing 16-byte mystery key 1 with confusion process. At this point, a second process utilizing the 16-byte mystery key 2 Optimal{S1, S 2} with diffusion process, encrypted the rearranged image by changing its pixel values in light of three high-dimensional chaotic frameworks. In view of the optimal two keys, the plain medical image was changed to cipher image and this C-work function decoding is illustrated in the figures 4 and 5.

high-dimensional maps and sufficiently complex. The underlying conditions and control parameters for producing chaos-sequence were utilized as the confusion key Optimal { pu1, pu 2} . Thus, in the decryption procedure, the same chaotic frameworks with the same confusion key were utilized to get the initial position of the image. V. RESULT AND DISCUSSION

The proposed medical image security model was implemented in MATLAB 2016a with i5 processor and 4GB RAM. The simulation security results of optimal chaotic encryption were compared to other existing security algorithms with different measures. 1) DATABASE DESCRIPTION

The medical images such as Brian, Lung EEG images and other images [27, 28, 29] were collected from website for security analysis. The sample images are shown in the figure 6 below.

FIGURE6. Sample images

2) EXPERIMENTAL RESULTS

FIGURE4. Proposed Encryption Model

In this paper, a few medical images (Brian, Lung, and so forth) were taken along with their encoded images. Table 2 demonstrates the first encrypted and decrypted images of the proposed security model. The proposed algorithm encoded the image totally or there is no piece of the image which isn't legitimately encrypted. TABLE II IMAGE SECURITY RESULTS FOR PROPOSED MODEL Image ID I1

Original Medical image

Encrypted Image

Decrypted Image

I2

FIGURE5. Proposed Decryption Model

I3

2) DECRYPTION

In the decryption process, the pixel value diffusion was evaluated using one chaotic system among the three functions. Then, to retrieve the original pixel values for a second time, one of the chaotic systems was introduced in the primary stage of decryption. The main phase of the decryption process utilized three-dimensional sequence produced by any of the chaotic frameworks. It was a sort of VOLUME XX, 2017

I4

9



I5

approximately 70% in terms of the measurement condition was considered for encoding the sensitive data. TABLE III PERFORMANCE MEASURE EVALUATION

I6

I7

Image ID

PSNR (dB)

I1 I2

CC

Entropy

NPCR (%)

UACI (%)

51.2

1

7.45

95.22

42.22

53.5

0.95

6.18

85.55

38.45

I3

56.22

0.95

6.21

82.22

39.5

I4

49.45

1

7.85

81.16

52.22

I5

62.22

0.95

7.8

82.78

48.22

I6

57.45

0.98

8

7922

45.45

I7

52.33

1

6.59

92.22

36.22

3) PERFORMANCE MEASURES

Peak Signal to Noise Ratio:

 255 2   PSNR  10 log   MSE  Correlation Coefficient (CC): N

CC 

 (l i 1

N

 (l i 1

i

i

(15)

 d (l ))  (mi  d (m))  d (l )) 2  (mi  d (m)) 2

(16)

Entropy: Entr 

2 N 1

 P log1 / K  i 0

i

i

(17) FIGURE7. Images Vs key sensitivity analysis

Number of Pixels Change Rate (NPCR): D(i, j )  i, j NPCR  *100% M *N Unified Average Changing Intensit UACI:

(18)

1  e1(i, j )  e2(i, j )  *100  255  M *N 

(19)

UACI 

In the equations above, the parameters are Pi  Probability of i th gray level image, Di  Difference between cipher images and M*N as size of the encrypted image. Finally e1 and e2 are the two ciphered images and their corresponding original images have only one pixel difference. The applied security algorithm can change all the pixels and by changing only one pixel, all of the pixels in the encrypted image can be changed [34]. The attained values of CC and PSNR for various directions of scanning patterns are tabulated in table 3. The adjacent pixels’ relevance of the improved algorithm is superior to the original algorithm. From the table, for I3 image, the PSNR value of Share 1 is 56.22 whereas forI4, it is 49.56. The PSNR was calculated using the equation discussed earlier. The image I3has a CC value of 0.945 whereas the CC value is 0.99 in case of I6. Further, the method with higher entropy value or

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TABLE IV MAP-BASED RESULTS FOR ENCRYPTED IMAGES Logistic map Tent map Image ID PSNR CC PSNR CC I1 55.26 -0.0012 49.22 0.0025 I2

49.45

0.0014

52.22

-0.0045

I3

52.22

0.0045

51.22

0.000278

I4

48.22

-0.00058

55

-0.0071

I5

52.11

-0.0014

49.2

-0.011

I6

53.22

0.0782

48

0.0145

I7

55.26

-0.0012

49.22

0.0025

Image key encryption and decryption procedure is an essential one due to which the work primarily focused on key-based optimization utilizing C-function security analysis and investigated the optimal key sensitivity. It suggests that a little change in the secret key should create a completely unique encrypted image. It implies that a slight change in the key should cause some huge changes in the ciphered image. The level of public and secret key accomplished in AGO was 85.12% to 85.69% compared to ordinary techniques. It proves the robustness of the proposed scheme, sensitivity analysis with respect to key is performed. High key sensitivity is necessary from secure image cryptosystems 9



which implies that the cipher image cannot be decrypted effectively regardless of the size of distinction between the encryption and decryption keys. Table 4 tabulates the chaotic capacity, map-based PSNR and CC outcomes for encrypted images. PSNR and CC values of strategic and tent map functions had a distinction of 0.56% for I4 image. Notwithstanding the chaotic highlights of mixing, flighty, and outrageous, the images were found to be sensitive to introductory seeds through various chaotic maps and orbits hopping systems.

FIGURE 10. Comparative analysis - PSNR.

FIGURE 8. PSNR - Attack Vs Without attack.

FIGURE 11. Comparative analysis - CC.

FIGURE 9. CC - Attack Vs Without attack.

The attack changed the image data [32]. However the proposed strategy recovered the image with limited noise and its PSNR value i.e., 72% was recovered. So maximum data was recovered with minimum distortion. For the most part, the proposed C-work i.e., Chaos work had some attack due to which an investigation was performed in this exhibition which is illustrated in the figure 8and 9. For I5, the attack minimized PSNR value to be 32.3% of the proposed work and the CC esteem additionally was limited up to -0.56%. Then the performance parameters were kept minimum for attack assigned for the image contrasted with the proposed work.

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FIGURE 12. Comparative analysis - Entropy.

Figure 10-13 describes the proposed model versus existing security algorithms that have similar model. Here the study considered existing security procedures such as ECC [16], Homomorphic Encryption [17], Homomorphic encryption with ALO [18], chaotic SYSTEM [21] lastly chaotic function with GO calculation for all execution measures. In I3, the PSNR value was found to be 56.22 and when compared with other procedures, the distinction value is 6.23 to 8.89% and 9



comparable distinction was found in different images with everything being equal. Likewise, the correlation between the simulation times required at the permutation stage demonstrates that the computational time required in the proposed model is three times lesser than that of the existing algorithms.

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[2]

[3]

[4]

[5]

[6]

[7]

FIGURE 13. Comparative analysis - NPCR and UACI.

[8]

VI. CONCLUSION

In this paper, an innovative and secure encryption algorithm was proposed for the security purposes of medical images. To conquer the downsides of chaos work, the optimal keys were selected randomly. In chaotic cryptosystems, its structural parameters and the initial value were utilized as encryption keys. The chaotic maps are found to be computationally economical as well as fast. The optimal key determination was performed by the proposed AGO algorithm and furthermore the performance was analyzed and discussed in section 4. For optimization too, the current study took the fitness as PSNR and the CC values of the encrypted images. The test investigation results inferred that the image encryption in light of PSNR, CC, entropy etc., demonstrate the benefits of vast key space and high-level security while maintaining efficiency at satisfactory levels. Accordingly, one round of encryption with the proposed algorithm is sufficient to oppose an exhaustive attack, differential attack, and statistical attack. In addition, the same size encrypted and decrypted image confirms the slightest distortion in the image.

[9]

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[11]

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[17]

ACKOWNLEDGEMENTS

This research is supported in part by the Shenzhen Governmental Basic Research Grant (JCYJ20160331185848286, JCYJ20170413170301569), the National Natural Science Foundation of China (61873349), Guangdong Province Natural Science Fund (2016A030310129), the Guangzhou Science and Technology Planning Project (201704020079, 201803010093), CAS President’s International Fellowship for Visiting Scientists (2017VTA0011)

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[18]

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VOLUME XX, 2017

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An Efficient Optimal Key Based Chaos Function for

An Efficient Optimal Key Based Chaos Function for

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