Performance Evaluation of Symmetrical Encryption Algorithms with Wavelet Based Compression Technique

To overcome the different issues connected with security and limited bandwidth during transmission of images, compression and encryption play an important role. To measure the effect on the performance of compression technique followed by encryption techniques is a challenging task. In this paper, biorthogonal discrete wavelet transform (DWT) technique is proposed for compression which is followed by advanced encryption standard (AES) and data encryption standard (DES) technologies to achieve secure transmission of data. The performances of DWT-AES and DWT-DES Compression-encryption (CE) algorithms are analyzed based on statistical and differential parameters. We illustrate the authentication of results by applying the proposed CE algorithms over five standard test images and also by comparing with different state of the art methods. The results show that combination of DWT-DES CE methodology provides high quality of reconstructed image with robustness against different attacks.


Introduction
As the use of internet to transmit the information from sender to receiver is increasing in our daily lives.Security and bandwidth are the two important parameters during transmission of information.The large size information needs compression of data so that it can be transmit with limited bandwidth and minimal transmission time [1].Every sender also wants to secure the information from various unethical attacks during transmission.To provide the security to transmitting data during transmission, encryption is performed [2].So, compression and encryption are the two important methods during transmission of data where compression reduces the need of higher transmission bandwidth by minimizing the redundancy of data and encryption provides security to information against different attacks [3] [4].Compression and encryption, both processes are having key importance for secure transmission of images over minimal bandwidth.Compression and encryption processes can be used in either order i.e. compression prior to encryption or compression after the encryption.The advantages of using compression algorithm before applying encryption algorithms are as follows [5]: A. It reduces the possibility of decoding of encrypted image by hackers.B. It reduces the encryption/decryption algorithms execution time.C. It reduces the misuse of cryptanalysis.On the basis of redundancy removal methodology, the compression techniques are classified in two categories as Lossless and Lossy compression.Lossless compression methods, like Arithmetic coding, LempelZiv algorithm, Entropy Encoding, Run Length coding, and Huffman coding, produce original image from compressed image during reconstruction without any loss of information [6].The lossless compression removes minimum amount of redundancy from the original image and by this it has low compression ratio [7].On the other hand, however lossy compression methods, like discrete cosine transform, discrete wavelet transform, fractal algorithm, Block Truncation coding etc., allows the reconstruction of original image from compressed image but the quality of reconstructed image will be degraded based upon the threshold used but with higher compression ratio [5].If a system needs compression of image data up to a great extent with little compromise in image quality at receiver end then the lossy compression methods are advantageous.The wavelet transform is used to find the better compression ratio by transforming the image data from time space domain to time frequency domain [8] [9].Multi resolution image analysis can be performed by using wavelet transform.In this paper, discrete wavelet transform (DWT) is used for compression of image because it decomposes an image into lower resolutions and works on the principle of thresholding [10].DWT also offers timefrequency localization through which error occurring due to thresholding can be minimized.In DWT the transformation is performed on entire image so that at low bit rate correlation can not be lost between subbands [11].In this paper, the combination of compression and encryption is used to remove redundant data and to provide security to the image during transmission.The main contributions of this paper are as follows:

Literature review
As the need of secure transmission of information over communication channel with minimum use of bandwidth is growing rapidly, a variety of research in the field of compression and encryption of information is taking place.In 2015 Wang et al. [12] have proposed DWT transformation on input image using Bior 2.2 wavelet filters with 3 level of decomposition.Resulted sub bands LL and (LH, HL, HH) are encrypted using stream cipher and permutation method respectively.Results show that compression ratio is 4.461 and PSNR is the range of 30-35 dB for different 512x512 pixel size test images.In 2016 Tong et al. [13] have proposed a compression-encryption technique by combining lifting wavelet transform (LWT) and set partitioning hierarchical tree (SPIHT) followed by chaotic sequence generation symmetrical encryption scheme.Authors have shown that proposed technique is highly sensitive to plain text and have excellent key sensitivity.Entropy value of five test images are in range of 7.5 to 7.99 and compression ratio is 50%.In 2017 S. Gonge et al. [14] have also proposed a watermarking technique for digital 2D images using combination of discrete wavelet transform and advanced encryption standard.In 2017 ahmad et al. [15] have proposed a image encryption algorithm based on orthogonal matrices and chaos theory.Authors have recovered original image from AWGN interrupted received image.The PSNR is about 40dB, NPCR is 99.1% and UACI is 15.4%.Here the PSNR is having moderate value so quality of decompressed image is average but since UACI is lower than the threshold value that is 33%, then proposed algorithm is lacking in security during transmission.In 2017 E. Setyaningsih et al. [5] have presented a review paper on performance of different compression and encryption methodologies.The performance of two hierarchies, one is cryptographic techniques followed by compression and second is compression followed by encryption process, are analysed.Compression followed by encryption process shows better performance in terms of security and reconstruction of image.In 2017 Kumar and Vaish [16] proposed a combined CE methodology for fast and secure transmission of image.The first step is the DWT transformation process and then pseudo random encryption process (PRNG) is applied.The test results demonstrate that the use of biorthogonal wavelet filter produces better compression performance.Authors show that PSNR and compression ratio for Lina test image under biorthogonal compression method are 45.66 dB and 0.2883 respectively.In 2019 S. ambadekar et al. [17] have proposed a technique for digital watermarking using DWT and encryption technology.Authors have used watermark embedding algorithm to provide digital signature at the transmitting end and watermark extraction algorithm is used at receiver end to extract the digital signature.The multi resolution DWT is used to transform the watermarked embedded image and input image for compression.The multi resolution DWT also provides simplicity in embedding and extracting digital water marking.Author presented PSNR more than 50dB with security of data from different attacks.In 2019 P. Ramasamy et al. [18] have proposed an enhanced logistic map (ELM), a different form of chaotic map with state of the art encryption techniques.Authors have shown the encryption efficiency through histogram analysis, differential analysis and statistical analysis.In 2020 Anand et al. [19] have proposed an improved watermark technique to protect medical images from unethical attacks during transmission.In this technique Hamming code is applied to text watermark.The combinations of two types of encryption, chaotic and hyper chaotic, and three types of compression techniques, Huffman, LZW and Hybrid, are analysed in terms of PSNR, compression ratio, SSIM, NPCR and UACI.In 2020 Guodeng Ye et al. [20] proposed an encryption algorithm based on compressive sensing and information hiding technology.After applying DWT to plain image, confusion sequence using logistic tent map is applied for encryption.Authors have validated the results through key space analysis, Histograms analysis.The quality of reconstructed images are analysed based on PSNR values for different test images.From the literature review it is observed compression prior to encryption process has tremendous advantages and the performance measurement of CE algorithms must be analysed.The proposed techniques must be capable to reproduce the original image after decryptiondecompression process for faithful reproduction of original image and secure transmission, compression and encryption performance parameters must attain their threshold values.

Image Transformation
With the fast advancement of remote detection development, a great deal of image data can be put on viably which causes massive load on limited structures and frameworks.Thus, image compression strategies are right now critical for image storing and correspondence.Since the lossy compression method can make much higher compression ratios than the lossless ones, various lossy compression methodologies like, discrete cosine change (DCT), pyramid coding, vector quantization, and fractal coding, discrete wavelet transform (DWT) etc., have been developed.Since in JPEG compression methods, large number of bits is assigned to low frequency data and few numbers of bits remains to represent the high frequency data [21].This mismatch in assigning the bits to low frequency and high frequency data tends to increase in blocking artifacts.This shortcoming of JPEG compression methods can be overcome by using discrete wavelet transform [11].

Figure 1. Block diagram of proposed architecture
In discrete wavelet transform, the wavelets are sampled to transform them in discrete form.In this paper, Biorthogonal DWT based compression algorithm is proposed to receive the discrete signal in less redundant form.

Proposed Biorthogonal DWT compression algorithm
The proposed technique of DWT based compression method decomposes the original image into coefficients called sub bands using biorthogonal 4.4 with 5 th level of decomposition and resulting coefficients are compared with a threshold value.

Figure 2. Wavelet filter decomposition
DWT has block artifacts that can be minimized by selecting small size of block.By using 8x8 block size and applying quantization minimize each pixel value 0 to 32 so 5 bits needed to represent pixel value.The following steps are used for compression of original image.
Step 1: Original image is loaded into workspace of MATLAB and if original image is colored then it is converted into gray scale using Rgb2gray(orig_I) Step 2: Biorthogonal wavelet filter "bior 4.4" is used to decompose the original image into subbands.In the proposed methodology, 5 level of decomposition is applied using command [c,s]=wavedec2(Orig_I,5,Lo_D,Hi_D) Step 3: Computation of four low pass and high pass decomposition levels are achieved using command [Lo_D,Hi_D,Lo_R,Hi_R] = wfilters('bior4.4')Step 4: A Threshold level is selected for quantization of sub bands using Floor(.4* OrigSize 2) The coefficients which are below than threshold level are marked at 0 level and the coefficients above the threshold level are encoded using Huffman encoder.
Step 5: Calculate SSIM, Compression Ratio, PSNR and MSE for compressed image.
Step 6: Compressed image is encrypted using AES or DES encryption techniques.

DES based proposed algorithm for encryption
The Data Encryption Standard (DES) is an encryption algorithm to provide security to the information during its transmission.In DES encryption algorithm plain text bits are divided in group of 64 bits called as one block and each block of 64 bits is encrypt by a key of length 56 bits [22].
Initial key having 64 bits but every 8 th bit of the key is discarded before the DES process begins.So, 8,16,24,32,40,48,56 and 64 bit positions are discarded and key length becomes 56 bits.Input binary data is divided into blocks of size 64 bits that is encrypted by using key of length 56 bits.DES encryption methodology is based on two fundamental steps: Confusion (substitution) and diffusion (transposition).In Data encryption standard algorithm, 16 identical rounds are performed and each round consists following operations:  Step 5: Reverse process is applied for decryption.during decryption process subkeys are used in reverse order.

The image compression performance parameters
The quality of reconstructed image from lossy compression algorithm can be access by calculating PSNR and MSE.PSNR is the ratio of square of maximum possible pixel values of an image and mean square error MSE.The quality of reconstructed image will be better if PSNR value lies in the range of 30dB to 50dB or more [23].3. It is observed that the PSNR under compression-encryption schemes is higher than the PSNR under only DWT compression methodology.It can be observed that if encryption is performed after compression of image, then PSNR value of compressed image can be increased.Table 3

also indicates that the combination of DWT-DES compression-encryption algorithm has higher PSNR than DWT-AES combination of cryptanalysis.
The quality of reconstructed image is inversely proportional to MSE i.e. the compressed image quality increases as the MSE decreases [5].The Mean Square Error can be expressed as, MSE =

Image encryption performance parameter
Image encryption is an important step before the transmission of image data.Image encryption minimizes the possibility to capture the information by fictitious attacks.The encrypted image should have random pattern of encryption and extraneous from original image.The quality of encryption algorithm can be analyzed with the help of statistical analysis as well as differential analysis.

A. Statistical Analysis:
Statistical analysis has its importance in analyzing the efficiency of encryption algorithms against statistical attacks.The different statistical tests are performed which are explained below: The correlation coefficients of the adjacent pixels of original images in vertical, horizontal and diagonal directions are in the range of 0.726 to 0.9866, which shows that adjacent pixels are strongly correlated with the original image in each direction.On the other side, encrypted images have very low value of correlation coefficient, which shows that adjacent pixels are weakly correlated with encrypted images.

B. Key sensitive analysis
A cipher key is used to encrypt and decrypt the image data.The encryption algorithm must be highly sensitive to cipher key.The size of the cipher key must be sufficiently large to make unauthorized attacks infeasible.
 The standard test image is encrypt using "9871236540123457" cipher key. The same test image is encrypted using slightly modified key "9871236540123456".
 Both encrypted images are analyzed pixel by pixel.This key sensitive analysis is performed on five test images and both encrypted images are having 99.71% difference with each other.The test results on one test image are shown in Fig. 10.The mean value or entropy of I(Xi ) with m different symbols is given by

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The entropy H(X) satisfies the following relationship 0≤ H(X) ≤ log 2 m (8) If a source is emitting 256 symbols then entropy of the source will be 8.The entropy analysis is also performed on five test images and results are shown in Table 7.

D. Differential analysis
The strength of the encryption methodology against external attacks can be analyzed through differential analysis.In differential analysis, the effects of variation in cipher image are observed if the input image is changed by a single bit.The effects on cipher image reflect the linkage between the input image and cipher image.If the variations in cipher image are significant with respect to small changes in original image, then the cipher image is secure from differential attacks.In this paper, Differential analysis is carried out to determine the efficiency of AES and DES encryption algorithms from unauthenticated differential attacks.NPCR and UACI are the two parameters used to find the differential analysis of DWT-DES and DWT-AES compression-encryption algorithms.
When one-pixel value is change in original image then Number of Pixels Change Rate (NPCR) gives difference in pixel values of two generated cipher text in terms of percentage.To show resistance of algorithm against differential attack percentage value of NPCR and UACI must be greater than 99% and 33% respectively during transmission [5].
Consider the two cipher-images, C 1 and C 2 , whose corresponding plain images have only one pixel difference the NPCR of these two images is defined as Table 8 and Table 9 are showing the comparison of NPCR and UACI respectively under DWT-DES and DWT-AES combination of cryptanalysis.It is observed that in both the encryption algorithms the values of NPCR and UACI is higher than the threshold limit for all 5 test images.The values of NPCR and UACI during DWT-DES compressionencryption algorithms are higher than the DWT-AES compression-encryption algorithms.
(i) The performance evaluation is carried out in two ways:  Image is compressed using DWT based compression algorithm.5 th level DWT Biorthogonal based lossy compression algorithm is used for compression. DWT based compressed image is followed by encryption algorithms.Symmetric encryption algorithms AES and DES are used for encryption of image.(ii) The effect on performance parameters, i.e. peak signal to noise ratio (PSNR), mean square error (MSE), structural similarity index metric (SSIM) and computational time during execution of compressionencryption algorithms is analysed.(iii) The efficiency of AES and DES symmetrical encryption algorithms over DWT compressed image is also compared on the basis of Number of Pixels Change Rate (NPCR) and Unified Averaged Changed Intensity (UACI), Correlation coefficient, Key sensitivity analysis and Entropy analysis.(iv) Histogram analysis is performed to show that encrypted image has no statistical similarity with original image and reconstructed images are similar with original images.In this paper, Literature review which comprises the different techniques for image compression and encryption and their outcomes is incorporated in section 2. The different algorithms (DWT, AES, DES) used in this study are explained in section 3. Results with performance evaluation parameters are illustrated in section 4. Conclusion and future work are presented in section 5.

PSNR = 10 𝑙𝑜𝑔 10 𝑀×𝑁} 2 𝑀𝑆𝐸 ( 1 )
Here, M×N represents maximum possible pixel value of image.Comparison of PSNR values of five test images under above discussed three cases is shown in Table )] 2 (2)Where  ,  and ,  represents the original and reconstructed pixel respectively.The comparison of mean square error (MSE) is represented in Table4.By analysing the different values of MSE, it can be concluded that if only compression is applied on test images, the MSE occurs in the range of 5-20%, but if this DWT compressed image is encrypted through symmetrical encryption algorithms, the MSE reduces to a great extent.The DWT-AES compression-encryption algorithms has MSE 0.16-0.25%while DWT-DES combination provides MSE in the range of 0.128-0.136%.It can be concluded that DWT-DES combination of CE algorithms gives minimum MSE as desired during transmission of images.SSIM is a parameter which gives the similarity index of reconstructed image and original image.The SSIM depends on luminance, contrast and structural term.The overall index is a multiplicative combination of the three terms.SSIM(x,y)=[l(x,y)] α .[c(x,y)]β .[s(x,y)]γ(3)  ,  = [2µ  µ  +  1 ] [µ  2 + µ  2 +  1 ] (3.1)  ,  = [2    +  2 ] [  +   +  2 ] (3.2)  ,  = [  +  3 ] [    +  3 ] (3.3)where µ  , µ  are the moment about the mean for x and y respectively and   2 ,   2 are variance of x and y respectively.α, β and γ are the weights. 1 = ( 1 ) 2 and  2 = ( 2 ) 2 are two variables and  = 2    − 1, showing the dynamic range of pixel values.EAI Endorsed Transactions on Scalable Information Systems Online First Neetu Gupta, Ritu Vijay and Hemant Kumar Gupta

(i)Figure 7 .
Figure 7. Column 2 and column 3 are DWT-AES compressed-encrypted image and its corresponding histograms respectively with respect to images as in column 1; Column 4 and Column 5 are decrypted-decompressed image and its corresponding histograms with respect to images as in column 1.

Fig. 7 andFigure 8 .Where
Fig. 7 and Fig. 8 are showing the pictorial representation of DWT-AES and DWT-DES joint compression-encryption outputs respectively.It can be viewed that these compressed encrypted histogram are having uniform response in comparison with histogram of original input images shown in row 2 of Fig. 6.The features of decrypted and decompressed image i.e. reconstructed image can not be compared with features of

Figure 9 .
Figure 9. Correlation distributions of two horizontally adjacent pixels for five test images

Figure 10 .
Figure 10.(a) Original plain image (b) Encrypted image using correct key (c) Encrypted using slightly different key (d) Decrypted image using slightly different key

Table 2 .
Initial permutation on 64 bit plain text

Table 5
showing the comparison of SSIM for different test images under three different scenarios as discussed earlier in this paper.SSIM for DWT compression algorithm,which showing the similarity index of decomressed image by inverse DWT algorithm and original images, has the values 81.7% to 95.9%.The SSIM of DWT-AES CE algorithms, which shows the similarity index of decrypted-decomressed image and original image, is in the range of 99.78% to 99.95%.SSIM for DWT-DES CE algorithms having range from 99.89% to 99.95%, which is better than DWT-AES combination of cryptanalysis.

Table 3 .
Comparison of PSNR for different compression encryption techniques

Table 4 .
Comparison of MSE for different Compression encryption techniques

Table 5 .
Comparison of SSIM for different compression encryption technique

Table 6 .
Comparison of correlation coefficient for different compression encryption techniques EAI Endorsed Transactions on Scalable Information SystemsOnline FirstPerformance Evaluation of Symmetrical Encryption Algorithms with Wavelet Based Compression Technique

Table 7 .
Comparison of entropy analysis for different compression encryption techniques 1,  2 = Performance Evaluation of Symmetrical Encryption Algorithms with Wavelet Based Compression Technique analysis and found that proposed algorithm shows robustness against different attacks.It has been authenticated that the DWT-DES combination of compression-encryption algorithms capable of removing redundancy in image data effectively and also provides better security during transmission.The proposed work can be further extended by apply on colour images of different pixel sizes.Researchers can also implement and analyse the proposed work over a system where encryption performed before compression.
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