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 $g\equiv gd\left(modp\right)$

(b) Publish the public key, prime number p, and generator g.

(c) Sender chooses a random integer i in the range: $\{2,p-2\}$.

(d) Sender computes the temporary key or ephemeral key as: $KE=g_i\left(modp\right)$

(e) The masking key is computed by sender as: $KE\equiv K_{pubi}\left(modp\right)$.

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:

$c_{ij}\equiv p_{ij}\times KM\left(modp\right)$

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: $KM\equiv KE\left(modp\right)$.

(b) The key matrices for Double Playfair Cipher are decrypted as:

$p_{ij}=c_{ij}\times (KM-1)\left(modp\right)$.

(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.