Analytical Study of Hybrid Techniques for Image Encryption and Decryption
Abstract
:1. Introduction
 A new image encryption approach using symmetric hybrid algorithms ECC with Hill Cipher, ECC with AES, and ElGamal with Double Playfair Cipher.
 The hybrid decryption algorithms using random permutation and dynamic keys.
 Our proposed hybridization of algorithm ensure the ease of implementation with increase in speed from symmetric algorithms. This also improved the security from asymmetric algorithms.
 The efficiency of the proposed algorithm is seen in several tests and comparisons performed.
 The results show that the proposed algorithm is effective to outperform some key cryptographic algorithms.
2. Literature Review
3. Background Study for Proposed Hybrid Algorithms
 ECC with Hill Cipher,
 ECC with AES,
 ElGamal with Double Playfair Cipher.
3.1. Key Generation of ECC
Algorithm 1: Key Generation 
Receiver establishes Elliptic curve parameters: $\left(Fp\right)=\{a,b,p,G\}$; 
Choose a private key nB in the range: $\{1,p1\}$; 
Find the public key: PB = nBG point multiplication over the curve; 
Publish the public key PB and the curve parameters $\left(Fp\right)=\{a,b,p,G\}$; 
Sender gets the public key of receiver $PB$ along with associated curve parameters; 
Sender chooses a private key $nA$ in the range: $\{1,p1\}$; 
Sender computes his public key as $PA=nAG$; 
The shared secret key $\left(SSK\right)$ as computed by the sender will be: 
$\left(SSK\right)=nAPB=nAnBG=(x,y)$; 
3.2. ECC with Hill Cipher Algorithm for Image Encryption and Decryption
Algorithm 2: ECC with Hill Cipher 
Input: The image of size 256 ×256 to be encrypted or decrypted. 
Elliptic curve parameters: $\left(Fp\right)=\{a,b,p,G\}$. 
Output: The corresponding cipher image or original image of size 256 × 256. 
1. Key Generation for ECC (The ECC keys are generated as shown in Section 3.1, Algorithm 1; 
2. Computing the selfinvertible matrix 
(a) Compute: ${K}_{1}=xG=({k}_{11},{k}_{12})$ and ${K}_{2}=yG=({k}_{21}+{k}_{22})$; 
(b) Compute: ${K}_{12}={I}_{2}{k}_{11};{K}_{21}={I}_{2}+{k}_{11}$; and ${k}_{11}+{k}_{22}=0$; 
(c) The $4\times 4$ selfinvertible matrix is derived as:
$${K}_{m}=\left[\begin{array}{cc}{k}_{11}& {k}_{12}\\ {k}_{k21}& {k}_{22}\end{array}\right]$$

where, ${K}_{11}=\left[\begin{array}{cc}{k}_{11}& {k}_{12}\\ {k}_{21}& {k}_{22}\end{array}\right]$ 
3. Encryption process: 
(a) Read the image to be encrypted and collect the image pixels separately for the 
channels R, G, and B. 
(b) Group every channel of pixels into 4 × 4 matrices and perform matrix multiplication 
with computed selfinvertible matrix. 
(c) The encryption is done using the subsequent formula:

where, ${K}_{m}$ is the selfinvertible matrix and ${P}_{i}$ is the current input image block to be encrypted; 
(d) Allocate the cipher pixels exactly to the same position as of the corresponding input 
image pixels. A cipher image is formed of size identical to the size of input image. 
(e) Send the cipher image and ECC public key to the receiver. The encryption process 
can be visualized as in Figure 1. 
4. Decryption process 
(a) Compute the shared secret key from the public key of sender as: 
$SSK=nBPA=nBnAG=nAnBG=(x,y)$ 
(b) Compute the selfinvertible matrix exactly as described above using the shared 
secret key. 
(c) Group the cipher pixels into $4\times 4$ matrices and perform matrix multiplication with 
selfinvertible matrix from Step 2. 
(d) Allocate the plain text pixels to the same position as of the corresponding cipher 
pixels. The original image is formed back and retrieved as without any intensity loss. 
3.3. ECC with AES for Image Encryption and Decryption
Algorithm 3: ECC with AES 
Input: The image of size 256 × 256 to be encrypted or decrypted. 
Elliptic curve parameters: $\left(Fp\right)=\{a,b,p,G\}$. 
AES symmetric key and initialization vector (IV). 
Output: The corresponding cipher image or original image of size 256 × 256. 
1. Key Generation for ECC 
(The ECC keys are generated as shown in Section 3.1); 
2. Key Generation for AES 
(a) Sender randomly generates 16 bytes long AES symmetric key and the 
Initialization Vector; 
(b) These parameters must be securely transmitted to receiver; 
3. AES Encryption 
(a) Read the image to be encrypted and collect the image pixels separately for the 
channels R, G, and B. 
(b) Convert the pixels in each channel to bytes using the function (PL) where PL 
denotes the list of pixels. The function returns an immutable array of bytes. 
(c) Perform AES encryption for each of the channel bytes. This generates bytes in the 
encrypted form. 
4. ECC Encryption 
(a) Choose a base of representing the numbers. We have chosen 256 to represent the 
range of 8bit pixel values; 
(b) Represent the prime number p in base 256 as a list of integers from 0 to 255. 
Measure the length of this representation as L. Initialize group size as $L1$ 
(c) Group the cipher bytes from each channel separately with group size initialized 
as above. For each of the channels, convert each group of cipher bytes to big 
integers treating base of representation as 256. If numbers of big integers are odd, 
append with a random value (possibly less than 256); 
(d) Pair up the big integers to represent it as a point on the XYplane. If the 
X coordinate of the pair and that of the shared secret key are identical, then we 
apply point doubling formula over the pair coordinates. Otherwise apply point 
addition formula with SSK coordinates. 
(e) From Step 4, we get a point on XY plane not at all necessary to be on the 
curve chosen. Represent its coordinates in base 256 digits. Each of these. 
representations must be of size equal to $L=groupsize+1$. Append 0 zeros 
otherwise to make the required length. 
(f) The base 256 representations of cipher points are treated as image pixels and cipher 
image is constructed correspondingly. The width of cipher image is kept same as 
width of input image and height is computed based on the total number of cipher 
pixels collected. We observe that size of cipher image is generally more than the 
input image. 
(g) Send the cipher image, original image size and ECC public key to receiver. 
5. ECC Decryption 
(a) Compute the shared secret key from the public key of sender as: 
SSK = nBPA = nBnAG + nAnBG = (x, y); 
(b) Represent the prime number p in base 256 as a list of integers from 0 to 255. 
Measure he length of this representation as L. Initialize group size as: 
$groupsize=L1$ 
(c) Collect the cipher pixels for each channel and group them with each group size 
equal to groupsize + 1; 
(d) Convert each group in respective channels to corresponding big integers taking 
base to be 256. Pair up the big integers treating them as points on the XYplane. 
(e) Perform reflection of $SSK$ point with respect xaxis: $(x,y\phantom{\rule{2.0pt}{0ex}}mod\phantom{\rule{2.0pt}{0ex}}p)$; 
(f) Perform point doubling with reflected $SSK$ coordinates if the x coordinates are 
same or perform point addition formula otherwise. The point obtained for each 
pair lies on XYplane but need not be a point the elliptic curve 
(g) Represent each of the points obtained in base 256 with each representation of 
length equal to groupsize. Append zeros if required. 
(h) Obtained values are bytes obtained from AES encryption. 
6. AES Decryption 
(a) Obtain the AES key and IV from secure communication. 
(b) Perform AES decryption for the bytes obtained from above for each of the respective 
image channels. 
(c) Represent the bytes as the plain text image of size as mentioned by the sender. 
3.4. ElGamal with Double Playfair Cipher for Image Encryption and Decryption
Algorithm 4: ElGamal with Double Playfair Cipher 
Input: The image of size 256 × 256 to be encrypted or decrypted. 
The key matrices corresponding to Double Playfair Cipher. 
The ElGamal cryptosystem parameters. 
Output: The corresponding cipher image or original image of size 256 × 256. 
1. Key Generation for Double Playfair Cipher 
(a) A modified key space of 2 matrices, each of size 16 × 16 is used instead of standard 
5 × 5 key matrices used in Double Playfair cipher. 
(d) Create 2 key maps, 1 corresponding to each of the keys. The key maps have pixel 
intensities as keys and their location in the respective key matrix as the 
corresponding value (represented by a tuple of row and column). 
2. Key Generation for ElGamal Cryptosystem 
(a) Receiver chooses a prime number p and computes its generator $g\equiv gd\left(mod\phantom{\rule{2.0pt}{0ex}}p\right)$ 
(b) Publish the public key, prime number p, and generator g. 
(c) Sender chooses a random integer i in the range: $\{2,p2\}$. 
(d) Sender computes the temporary key or ephemeral key as: $KE={g}_{i}\left(mod\phantom{\rule{2.0pt}{0ex}}p\right)$ 
(e) The masking key is computed by sender as: $KE\equiv {K}_{pubi}\left(mod\phantom{\rule{2.0pt}{0ex}}p\right)$. 
3. Encryption process 
(a) Read the image to be encrypted and separate it to different channels as R, G, B. 
Pair up pixels in 2 for each of the channels separately. 
(b) To apply Vertical Double Playfair Cipher find the location of first value from pixel 
pair from the first key map and the location of second pixel value from the second 
key map. Then if the pixels are in same column keep them unchanged, else find the 
pixel intensities at the opposite corners of the rectangle formed by the pair of input 
pixels considered. Place them in the same order as they correspond to the order of 
pixel values in the input pair. 
(c) Substitute the cipher pixel values to create the cipher image of size identical to that 
of the input image. 
(d) Encrypt each of the key matrices using the masking key from ElGamal Encryption as: 
${c}_{ij}\equiv {p}_{ij}\times KM\left(mod\phantom{\rule{2.0pt}{0ex}}p\right)$ 
where ${p}_{ij}$ denotes the corresponding pixel intensity in a cell of a key matrix. 
(e) Send the encrypted image and encrypted key matrices along with ElGamal public key 
(ephemeral key) of sender to the receiver. 
4. Decryption process 
(a) The masking key will be computed by receiver as: $KM\equiv KE\left(mod\phantom{\rule{2.0pt}{0ex}}p\right)$. 
(b) The key matrices for Double Playfair Cipher are decrypted as: 
${p}_{ij}={c}_{ij}\times (KM1)\left(mod\phantom{\rule{2.0pt}{0ex}}p\right)$. 
(c) Read the image to be decrypted and separate it to different channels as R, G, B. 
Pair up pixels in 2 for each of the channels separately. 
(d) To apply Vertical Double Playfair Cipher find the location of first value from pixel 
pair from the first key map and the location of second pixel value from the second 
key map. Then if the pixels are in same column, keep them unchanged. 
Otherwise, find the pixel intensities at the opposite corners of the rectangle 
formed by the pair of input pixels considered. Place them in the same order as they 
correspond to the order of pixel values in the input pair. 
(e) Substitute the decrypted pixel values to create the original image. 
4. Image Encryption and Decryption Implementation
5. Performance Analysis of Proposed Hybrid Algorithms
5.1. General Constraints
 The size of the image to be encrypted is $256\times 256$ pixels. The size of the encrypted image is the same as the input image except for the AES with ECC algorithm where the size of the encrypted image is slightly larger. All decryption algorithms produce a decrypted image of the same size as the original image.
 To hold both Grayscale and RGB images as the user’s choice, we deploy an algorithm that both encrypts and decrypts all 3 channels (RGB) of the picture separately.
5.2. Parameters for Comparison
 Encryption Time: Encryption is the method used to convert information to a secret code that masks the true meaning of the information. The time it takes to encrypt the image is the time to encrypt it.
 Decryption Time: Decryption is generally the reverse encryption process. It is the method of decoding data that has been encrypted in a hidden format. The time it takes to get the original image back is the time to decrypt it.
 Metric Values for Entropy: 8 expected value for good Encryption process. Entropy is the randomness of the pixel intensities in the encrypted image. An entropy value close to 8 is a good encryption algorithm for an 8bit image. Values obtained for Eggs (Grayscale), Eggs (Coloured), Mona Lisa (Grayscale) and Mona Lisa (Coloured) are closure to 8.
 Metric Values for PSNR (dB): 10 dB expected value for reconstructed image. The PSNR block calculates the peak signaltonoise ratio between two images in decibels. This ratio is used to measure the quality between the original and the compressed image. The higher the PSNR, the higher the quality of the compressed or reconstructed image. Values obtained for Eggs (Grayscale), Eggs (Coloured), Mona Lisa (Grayscale) and Mona Lisa (Coloured) are between 8 and 9.5.
 Metric Values for NPCR (%): 100% expected value for varying number of pixels from the input image in the encrypted image. NPCR is the change in the number of pixels of the cipher image when only one pixel of the plain image is changed. It is an indicative measure of the number of pixels that vary from the input image in the encrypted image and is expressed as a percentage. Values obtained for Eggs (Grayscale), Eggs (Coloured), Mona Lisa (Grayscale) and Mona Lisa (Coloured) are closure to 100%.
 Metric Values for UACI (%): 30% expected value for varying number of pixels from the input image in the encrypted image. UACI measure indicates the security of the algorithm against differential attacks, such as a plaintext attack, a cipheronly attack, or a known plaintext attack. Higher value indicates that it is safer against such attacks. Values obtained for Eggs (Grayscale), Eggs (Coloured), Mona Lisa (Grayscale) and Mona Lisa (Coloured) are between 26% to 30.5%.
 Squared Error in Decrypted image: The discrepancy between the decrypted image pixels and the original one. It should be closer to zero for a good algorithm.
6. Evaluation and Result Analysis
6.1. Sample Input and Output
6.2. Metric Measurements
6.2.1. Eggs (Grayscale 256 × 256 Pixels) Image
6.2.2. Eggs (coloured $256\times 256$ Pixels) Image
6.2.3. Mona Lisa (Grayscale $256\times 256$ Pixels) Image
6.2.4. Mona Lisa (Coloured $256\times 256$ Pixels) Image
6.3. Histogram Analysis of the Encrypted Images
7. Discussion and Comparative Analysis
7.1. Discussion
7.2. Comparative Analysis
8. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Image Name  Original Image  Encrypted Image (ECC with Hill Cipher)  Encrypted Image (ECC with AES)  Encrypted Image (ElGamal with Double Playfair) Cipher  Encrypted Image (Decrypted Image) 

Mona Lisa (Grayscale)  
Mona Lisa (Coloured)  
Egg (Grayscale)  
Egg (Coloured) 
Evaluation Metrics  ECC with Hill Cipher  ECC with AES  ElGamal with Double Playfair Cipher 

Encryption Time (seconds)  0.33418  2.82401  0.18775 
Decryption Time (seconds)  0.36932  2.75127  0.17856 
Entropy  7.9434  7.99653  7.78708 
Mean Squared Error (MSE) in decrypted image  0.0000  0.0000  0.0000 
PSNR (dB)  9.45457  9.129  9.36168 
NPCR (%)  86.91254  99.60632  94.81812 
UACI (%)  26.06152  28.90828  27.91177 
Evaluation Metrics  ECC with Hill Cipher  ECC with AES  ElGamal with Double Playfair Cipher 

Encryption Time (seconds)  0.32915  2.52632  0.13013 
Decryption Time (seconds)  00.35193  2.50829  0.1486 
Entropy  (7.99701, 7.9971, 7.98925)  (7.99667, 7.99659, 7.99672)  (7.95568, 7.96154, 7.8657) 
Mean Squared Error (MSE) in decrypted image  (0, 0, 0)  (0, 0, 0)  (0, 0, 0) 
PSNR (dB)  (8.80367, 8.45589, 7.91148)  (8.86691, 8.54116, 7.9478)  (9.19181, 8.8655,8.27107) 
NPCR (%)  (99.48273, 99.38507, 99.47968)  (99.63379, 99.64142, 99.6109)  (93.57605, 93.23425, 93.7561) 
UACI (%)  (29.85083, 31.02715, 32.87405)  (29.60341, 30.65091, 32.69575)  (27.70115, 28.5317, 30.3973) 
Evaluation Metrics  ECC with Hill Cipher  ECC with AES  ElGamal with Double Playfair Cipher 

Encryption Time (seconds)  0.44584  2.84150  0.24519 
Decryption Time (seconds)  0.35107  2.7866  0.20224 
Entropy  7.99442  7.99671  7.92129 
Mean Squared Error (MSE) in decrypted image  0.0000  0.0000  0.0000 
PSNR (dB)  8.5959  8.62078  9.12066 
NPCR (%)  97.41669  99.58191  94.13757 
UACI (%)  30.26131  30.37332  27.97823 
Evaluation  ECC with  ECC with  ElGamal with Double 

Metrics  Hill Cipher  AES  Playfair Cipher 
Encryption Time (s)  0.32507  2.53642  0.13366 
Decryption Time (s)  0.35904  2.52728  0.16954 
Entropy  (7.98534, 7.98371, 7.98925)  (7.99652, 7.99585, 7.99638)  (7.85019, 7.87646, 7.90649) 
Mean Squared Error (MSE) in decrypted image  (0, 0, 0)  (0, 0, 0)  (0, 0, 0) 
PSNR (dB)  (9.41053, 8.95845, 8.74391)  (9.39128, 8.98602, 8.7218)  (9.86406, 9.45456, 9.069) 
NPCR (%)  (96.67358, 96.81854, 96.99249)  (99.646, 99.63684, 99.62463)  (94.05823, 94.08875, 94.1803) 
UACI (%)  (27.87552, 29.14918, 29.73587)  (28.15297, 29.32043, 30.11092)  (26.05094, 27.09534, 28.17803) 
Image  Encrypted Image (ECC with Hill Cipher)  Encrypted Image (ECC with AES)  Encrypted Image (ElGamal with Double Playfair Cipher) 

Mona Lisa (Grayscale)  
Mona Lisa (Coloured) 
Image  Encrypted Image (ECC with Hill Cipher)  Encrypted Image (ECC with AES)  Encrypted Image (ElGamal with Double Playfair Cipher) 

Egg (Grayscale)  
Egg (Coloured) 
S. No.  Image Encryption and Decryption Algorithms  Proposed Hybrid Algorithms 

1  Encryption and Decryption algorithms proposed either for only symmetric or Asymmetric Encryption and Decryption only.  The proposed symmetric and Asymmetric hybrid algorithms are ECC with Hill Cipher, ECC with AES and ElGamal with Double Playfair cipher. 
2  Symmetric Key provides faster processing, less protection for message transfer.  Proposed algorithm solves the problem of computation and high protection. 
3  Several techniques adopted without compression of the images required more space.  The techniques proposed here compress the image, which is the less space needed to provide the same information. 
4  Requires high bandwidth without compression.  We have proposed with compression that results in a low bandwidth, less storage space and less computation time. 
5  Most researchers use only some measure for the security analysis.  Different metric measures such as Entropy, PSNR, NPCR, and UACI in decrypted image are taken into account. 
© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
Share and Cite
Chowdhary, C.L.; Patel, P.V.; Kathrotia, K.J.; Attique, M.; Perumal, K.; Ijaz, M.F. Analytical Study of Hybrid Techniques for Image Encryption and Decryption. Sensors 2020, 20, 5162. https://doi.org/10.3390/s20185162
Chowdhary CL, Patel PV, Kathrotia KJ, Attique M, Perumal K, Ijaz MF. Analytical Study of Hybrid Techniques for Image Encryption and Decryption. Sensors. 2020; 20(18):5162. https://doi.org/10.3390/s20185162
Chicago/Turabian StyleChowdhary, Chiranji Lal, Pushpam Virenbhai Patel, Krupal Jaysukhbhai Kathrotia, Muhammad Attique, Kumaresan Perumal, and Muhammad Fazal Ijaz. 2020. "Analytical Study of Hybrid Techniques for Image Encryption and Decryption" Sensors 20, no. 18: 5162. https://doi.org/10.3390/s20185162