Certainly! Here's a brief explanation of the Henon map image encryption algorithm. The Henon map is a two-dimensional discrete dynamical system that exhibits chaotic behavior. To encrypt an image using this algorithm, first, convert the image into a grayscale format. Then, apply the Henon map equations to each pixel of the image iteratively. The Henon map equations are defined as follows: x_n+1 = y_n + 1 - a * x_n^2, and y_n+1 = b * x_n. Here, 'a' and 'b' are the parameters that determine the chaotic behavior of the map. Choose appropriate values for these parameters. For encryption, use the initial conditions (x_0, y_0) as the secret key. Iterate the Henon map equations for a specific number of iterations, and use the resulting (x_n, y_n) values as the encryption key. XOR the grayscale pixel values with the encryption key to encrypt the image. For decryption, generate the same encryption key using the initial conditions, and XOR the encrypted pixel values with the key to obtain the original image. Implementing this algorithm in MATLAB or Python involves defining functions for the Henon map equations, reading and processing the image, and performing the encryption and decryption steps using loops or vectorized operations.

Md. Akiful Islam Fahim

Code:

import numpy as np

from PIL import Image

def henon_map(x, y, a=1.4, b=0.3):

new_x = y + 1 - a * x**2

new_y = b * x

return new_x, new_y

def encrypt_image(image_path, iterations=10000):

image = Image.open(image_path).convert("L") # Convert to grayscale

pixels = np.array(image)

height, width = pixels.shape

# Initialize Henon map parameters

x, y = 0.1, 0.1

# Encryption loop

for i in range(iterations):

# Update Henon map

x, y = henon_map(x, y)

# Pixel scrambling

pixel_index = i % (height * width)

row = pixel_index // width

col = pixel_index % width

# Swap pixels

pixels[row, col], pixels[int(x * height) % height, int(y * width) % width] = \

pixels[int(x * height) % height, int(y * width) % width], pixels[row, col]

encrypted_image = Image.fromarray(pixels)

return encrypted_image

# Usage example

image_path = "path_to_your_image.jpg"

encrypted_image = encrypt_image(image_path)

encrypted_image.save("encrypted_image.jpg")

Make careful you substitute the correct path to the image file you wish to encrypt for "path_to_your_image.jpg". This code repeatedly scrambles the image's pixels using the Henon map as a chaotic map. The degree of encryption can be altered by varying the number of iterations.

Please be aware that the Henon map picture encryption algorithm is provided as a simple implementation in this code solely for instructional purposes. In reality, other methods like key creation, diffusion, and numerous encryption rounds might be needed for secure encryption.

Similar ideas can also be used to create the Henon map image encryption technique in MATLAB.

Matlab: % Henon Map Image Encryption Algorithm

% Parameters

a = 1.4; % Henon map parameter

b = 0.3; % Henon map parameter

iterations = 10000; % Number of iterations

% Load and display the image

image = imread('input_image.png');

imshow(image);

title('Original Image');

% Convert the image to grayscale if necessary

if size(image, 3) > 1

image = rgb2gray(image);

end

% Normalize the image to the range [0, 1]

image = double(image) / 255;

Matlab code Continuation : % Generate encryption keys using Henon map

x = zeros(1, iterations);

y = zeros(1, iterations);

x(1) = 0.1; % Initial value for x

y(1) = 0.1; % Initial value for y

for i = 2:iterations

x(i) = 1 - a * x(i - 1)^2 + y(i - 1);

y(i) = b * x(i - 1);

end

% Encrypt the image using XOR operation with the Henon map

encrypted_image = bitxor(image, x(1:numel(image)));

% Display the encrypted image

figure;

imshow(encrypted_image);

title('Encrypted Image');

Matlab code Continuation : % Decrypt the encrypted image using XOR operation with the Henon map

decrypted_image = bitxor(encrypted_image, x(1:numel(image)));

% Display the decrypted image

figure;

imshow(decrypted_image);

title('Decrypted Image');

Pyton 1/3 : import numpy as np

from PIL import Image

# Henon Map Image Encryption Algorithm

# Parameters

a = 1.4 # Henon map parameter

b = 0.3 # Henon map parameter

iterations = 10000 # Number of iterations

# Load and display the image

image = Image.open('input_image.png')

image.show()

image_array = np.array(image)

# Convert the image to grayscale if necessary

if len(image_array.shape) > 2:

image_array = np.dot(image_array[..., :3], [0.2989, 0.5870, 0.1140])

Pyton 2/4: # Normalize the image to the range [0, 1]

image_array = image_array / 255.0

# Generate encryption keys using Henon map

x = np.zeros(iterations)

y = np.zeros(iterations)

x[0] = 0.1 # Initial value for x

y[0] = 0.1 # Initial value for y

for i in range(1, iterations):

x[i] = 1 - a * x[i - 1]**2 + y[i - 1]

y[i] = b * x[i - 1]

# Reshape the image array to 1D

encrypted_image = image_array.flatten()

# Encrypt the image using XOR operation with the Henon map

encrypted_image = np.bitwise_xor(encrypted_image, x[:len(encrypted_image)])

python 3/4 : # Reshape the encrypted image array back to the original shape

encrypted_image = encrypted_image.reshape(image_array.shape)

# Convert the encrypted image array to the range [0, 255]

encrypted_image = (encrypted_image * 255.0).astype(np.uint8)

# Display the encrypted image

encrypted_image = Image.fromarray(encrypted_image)

encrypted_image.show()

Python 4/4 : # Decrypt the encrypted image using XOR operation with the Henon map

decrypted_image = np.bitwise_xor(encrypted_image, x[:len(encrypted_image)])

# Convert the decrypted image array to the range [0, 255]

decrypted_image = (decrypted_image * 255.0).astype(np.uint8)

# Display the decrypted image

decrypted_image = Image.fromarray(decrypted_image)

decrypted_image.show()

Key generation code of Henon map???

import numpy as np

from PIL import Image

def henon_map(x, y, a=1.4, b=0.3):

new_x = y + 1 - a * x**2

new_y = b * x

return new_x, new_y

def encrypt_image(image_path, iterations, key):

img = Image.open(image_path)

width, height = img.size

encrypted_img = Image.new('RGB', (width, height))

x, y = key[0], key[1]

for _ in range(iterations):

x, y = henon_map(x, y)

pixel_index = int((x + y) * 100000) % (width * height)

row = pixel_index // width

col = pixel_index % width

original_pixel = np.array(img.getpixel((col, row)))

encrypted_img.putpixel((col, row), tuple(original_pixel))

return encrypted_img

# Example usage

image_path = 'path_to_your_image.png'

iterations = 10000

key = (0.1, 0.2)

encrypted_image = encrypt_image(image_path, iterations, key)

encrypted_image.save('encrypted_image.png')

Please note that this code provides a basic implementation of the Henon map encryption algorithm and may not provide strong security. If you're looking for more robust encryption methods, it's recommended to use established cryptographic libraries and algorithms. Also, consider using modern encryption techniques that are widely recognized and tested for security.

Make sure to have the required libraries installed using:

pip install numpy pillow

Remember that encryption is a complex field, and the security of an encryption method depends on factors beyond just the code implementation, such as key management, cryptographic strength, and proper use of secure libraries and practices.