Modified Caesar Cipher and Card Deck Shuffle Rearrangement Algorithm for Image Encryption

Figures & data

Figure 1. Block diagram of proposed methodology.

Algorithm 1. Key Extraction Algorithm

Key Extraction Algorithm

Input: Main n + 8 bit key

(1) Convert the main key which was taken as an string input into an array of integers.

(2) initialise $k1$ and $k2$ both to zero.

(3) Now separate the first n−8 bits of the array k and store into new array $\mathrm{key}1$. Separate the last 8 bits of array k and store in new array $\mathrm{key}2$.

(4) Convert the binary keys to their respective decimal number forms. c=0

for $i\leftarrow \mathrm{keyX}.\mathrm{length}-1$ to 0 do

|   keyX = keyX + $i\ast$ 2c

c = c + 1

end

Output: keys $k1$ and $k2$ in their decimal number formats

Figure 2. Classic Caesar Cipher encryption on Baboon image, (a) Original Baboon image, (b) Encrypted Baboon image, (c) Original Baboon image histogram, (d) Encrypted Baboon image histogram.

Figure 3. Classic Caesar Cipher encryption on Lena image, (a) Original Lena image, (b) Encrypted Lena image, (c) Original Lena image histogram, (d) Encrypted Lena image histogram.

Figure 4. Modified Caesar Cipher encryption on Baboon and Lena image, (a) Original Baboon image, (b) Encrypted Baboon image, (c) Original Baboon image histogram, (d) Encrypted Baboon image histogram.

Algorithm 2. Modified Caesar Cipher Algorithm

Input: Original image, key $k1$ and key $k2$

(1) Split the 3-dimensional array of the image so that each of the red, green, and blue channels can be accessed independently.

(2) Iterating through the respective colour channel

(3) Flatten the 2-dimensional channel into 1-dimensional array for easy manipulation of pixel values

(4) Initialize the index counter i to zero

i = 0

(5) Calculate the remainder of the division of index counter by 4

$\mathrm{remainder}=i\text{\%}4$

(6) Calculate the coefficients a and b based on the remainder and the following condition:

if remainder = 0 then

| a = 1, b = 1

else

| if remainder = 1 then

| a = 1, b = −1

else

| if remainder = 2 then

| a = −1, b = 1

else

| a = −1, b = −1

end

end

end

(7) Shift the value of the pixel by Caesar Cipher encryption using the coefficients and the key values according the following equation:

$\mathrm{arr}[i]=(\mathrm{arr}[i]+a\ast i\ast k1+b\ast k2)$ % 256

(8) Increment the counter i and check if i is less than the length of the flattened array. If yes, then go to step 5 else continue to the next step.

(9) Reshape the flattened array to the channel's original dimensions and merge the channel into the new encrypted image array. If not done with all channels then go to step 3 with the next channel else stop.

Output: The modified Caesar Cipher encrypted image

Figure 5. Modified Caesar Cipher encryption on Baboon and Lena image, (a) Original Lena image, (b) Encrypted Lena image, (c) Original Lena image histogram, (d) Encrypted Lena image histogram.

Figure 6. Block diagram of modified Caesar Cipher.

Figure 7. Block diagram for calculating decksizeArray.

Figure 8. Card Deck Shuffle Rearrangement.

Figure 9. Block diagram of Card Deck Shuffle Rearrangement Algorithm.

Algorithm 3. Decksize Array Calculation Algorithm

Input: variable size which is equal to size of the image i.e. total number of pixels and key $k1$.

(1) Initialize variable res equal to variable size and variable k equal to key $k1$. Here the variables are being duplicated as so as to not alter the original variables which are used further on in the algorithm.

$\mathrm{res}=\mathrm{size}=r\ast c$

k = k1

(2) Initialize an empty decksize Array

$\mathrm{deck}\mathrm{\_arr}=[]$

(3) Calculate the decksize for the current iteration given by equation:

$\mathrm{deck}\mathrm{\_size}=\mathrm{math}.\mathrm{ceil}(\mathrm{res}/k)$

The ceiling value is calculated so as to have nearly the same decksizes throughout the Decksize Array

(4) Append the calculated decksize into the Decksize Array

$\mathrm{deck}\mathrm{\_arr}.\mathrm{append}(\mathrm{deck}\mathrm{\_size})$

(5) Decrement the res and k variable for the next iteration.

res = res−1

k = k−1

(6) If res is greater than zero, than go to step 3, else stop.

Output: The Decksize Array: contains the size of all the decks in which the image has to be divided for the shuffling to take place.

Algorithm 4. Decksize Array Calculation Algorithm

Input: Decksize Array $\mathrm{deck}\mathrm{\_arr}$, size equal to size of the image i.e. total no of pixels, key $k1$, and the encrypted image $\mathrm{en}1$ from stage 1 i.e. after application of modified Caesar Cipher.

(1) Split the 3 dimensional array of the image $\mathrm{en}1$ so that each of the red, green and blue channels can be accessed independently.

(2) Initialize a count variable to zero and initialize an empty 1 dimensional new channel array of length size.

count = 0

$\mathrm{new}\mathrm{\_channel}=\mathrm{np}.\mathrm{zeros}(\mathrm{size})$

(3) Flatten the originally received 2 dimensional channel into 1 dimension array.

$\mathrm{og}\mathrm{\_channel}=\mathrm{channel}.\mathrm{flatten}()$

(4) Now rearrangement takes place. Pixels from original channel array are taken and are fed into the new channel array in scrambled manner.

for $i\leftarrow 0$ to $\mathrm{deck}\mathrm{\_arr}[0]$ do

index = i

| for $j\leftarrow 0$ to $k1$ do

| if index<size−1 then

| $\mathrm{new}\mathrm{\_channel}[\mathrm{count}]=\mathrm{og}\mathrm{\_channel}[\mathrm{index}]$

else

| continue

end

count = count + 1

$\mathrm{index}=\mathrm{index}+\mathrm{dec}{k}_a\mathrm{rr}[j]$

end

end

(5) Reshape the $\mathrm{new}\mathrm{\_channel}$ flattened array to channel's original dimensions

$\mathrm{new}\mathrm{\_channel}=\mathrm{np}.\mathrm{reshape}(\mathrm{new}\mathrm{\_channel},(r,c))$

(6) Merge the channel into final encrypted image array.

(7) If not done with all channels then go to step 2 with next channel else stop.

Output: The final encrypted image.

Figure 10. (a) Original Peppers image, (b) Image after Modified Caesar Cipher encryption, (c) Final encrypted image after Card Deck Shuffle Rearrangement, (d) Decrypted image.

Figure 11. (a) Original Tulips image, (b) Image after Modified Caesar Cipher encryption, (c) Final encrypted image after Card Deck Shuffle Rearrangement, (d) Decrypted image.

Figure 12. (a) Original Cat image, (b) Image after Modified Caesar Cipher encryption, (c) Final encrypted image after Card Deck Shuffle Rearrangement, (d) Decrypted image.

Figure 13. (a) Original House image, (b) Image after Modified Caesar Cipher encryption, (c) Final encrypted image after Card Deck Shuffle Rearrangement, (d) Decrypted image.

Figure 14. (a) Original Lena image, (b) Image after Modified Caesar Cipher encryption, (c) Final encrypted image after Card Deck Shuffle Rearrangement, (d) Decrypted image.

Figure 15. (a) Original Baboon image, (b) Image after modified Caesar Cipher encryption, (c) Final encrypted image after Card Deck Shuffle Rearrangement, (d) Decrypted image.

Figure 16. Image encryption results by applying modified Caeser Cipher and Card Deck Shuffle rearrangement algorithm. Histograms are for the entire image. (a) Encrypted Peppers image. (b) Overall Histogram of (a). (c) Histogram of Red Channel of (a). (d) Histogram of Green Channel of (a). (e) Histogram of Blue Channel of (a). (f) Encrypted Cat image. (g) Overall Histogram of (f). (h) Histogram of Red Channel of (f). (i) Histogram of Green Channel of (f). (j) Histogram of Blue Channel of (f). (k) Encrypted Tulips image. (l) Overall Histogram of (k). (m) Histogram of Red Channel of (k). (n) Histogram of Green Channel of (k) (o) Histogram of Blue Channel of (k). (p) Encrypted House image. (q) Overall Histogram of (p). (r) Histogram of Red Channel of (p). (s) Histogram of Green Channel of (p). (t) Histogram of Blue Channel of (p). (u) Encrypted Lena image. (v) Overall Histogram of (u). (w) Histogram of Red Channel of (u). (x) Histogram of Green Channel of (u). (y) Histogram of Blue Channel of (u) (z) Encrypted Baboon image. (aa) Overall Histogram of (z). (ab) Histogram of Red Channel of (z). (ac) Histogram of Green Channel of (z) and (ad) Histogram of Blue Channel of (z).

Figure 17. Key Sensitivity Analysis for Cat Image (Key B was obtained when one bit was changed in key A). (a) Original Cat Image. (b) Encrypted Image with key A. (c) Encrypted Image with key B and (d) Difference between (b) and (c).

Figure 18. Correlation analysis: Visualisation of the (input) original Lena image along the, (a) horizontal, (b) vertical, (c) diagonal directions respectively. Visualisation of the encrypted image along the, (d) horizontal, (e) vertical, (f) diagonal directions respectively.

Figure 19. Tulips, (a) source image (b) decrypted image (c) image depicting difference in (a) and (b).

Figure 20. House, (a) source image (b) decrypted image (c) image depicting difference in (a) and (b).

Figure 21. Noise resistance analysis: (a) original Peppers image, (b) encrypted Peppers image, (c) encrypted Peppers image with noise added by changing values of 128*128 = 16,384 pixels, (d) decrypted Peppers image.

Figure 22. Noise resistance analysis: (a) original Lena image, (b) encrypted Lena image, (c) encrypted Lena image with noise added by changing values of 128*128 = 16,384 pixels, (d) decrypted Lena image.