Introduction

With advancements in digital image processing, image encryption has become increasingly vital for information security. Chaotic encryption algorithms are a popular research focus due to their effective diffusion and confusion properties. However, traditional low-dimensional chaotic systems often suffer from small key spaces and limited security.

Image Encryption Algorithm Based on a 6D Hyperchaotic System

To address the limitations of low-dimensional chaotic systems, this article proposes an image encryption algorithm that utilizes a 6D hyperchaotic system combined with DNA encoding. This approach enhances security by employing a high-dimensional chaotic system as a pseudo-random sequence generator.

Algorithm Steps

The algorithm proceeds as follows:

1. Key Generation: Generate six initial values and control parameters to form the key for the 6D hyperchaotic system.
2. Image Preprocessing: Convert the original image into a binary format and partition it into 8×8 pixel blocks.
3. Diffusion: Apply six chaotic sequences to diffuse each pixel block, altering pixel values.
4. Scrambling: Use distinct chaotic sequences to scramble the diffused pixel blocks, changing pixel positions.
5. DNA Encoding: Transform the scrambled pixel blocks into DNA sequences, then diffuse and scramble these sequences using additional chaotic sequences.
6. Image Reconstruction: Combine the encoded sequences to produce the encrypted image.

Experimental Results

To evaluate the algorithm's performance, the following experimenst were conducted:

• Image Entropy: The encrypted image's entropy approaches 8, indicating strong randomness.
• Pixel Correlation: Low pixel correlation in the encrypted image demonstrates effective confusion.
• Image Complexity: A key space exceeding 2^300 suggests high security.
• Robustness: The encrypted image shows good resistance to geometric and truncation attacks.

Conclusion

The proposed image encryption algorithm, based on a 6D hyperchaotic system with DNA encoding, exhibits excellent entropy, pixel correlation, complexity, and robustness. It effectively secures image data and is suitable for various encryption applications.

Code Example

function entropyValues = computeImageEntropy(imageData)
% COMPUTEIMAGEENTROPY Calculates the entropy of an image.
%   entropyValues = computeImageEntropy(imageData) returns a vector of
%   entropy values for each color channel of the input image.

    entropyValues = zeros(1, 3);
    
    function channelEntropy = calculateChannelEntropy(channel)
        channel = double(channel);
        [rows, cols] = size(channel);
        pixelVector = channel(:)';
        probabilityDistribution = zeros(1, 256);
        
        for intensity = 0:255
            probabilityDistribution(intensity + 1) = sum(pixelVector == intensity) / (rows * cols);
        end
        
        nonZeroProbabilities = probabilityDistribution(probabilityDistribution > 0);
        channelEntropy = -nonZeroProbabilities * log2(nonZeroProbabilities)'; 
    end
    
    for channelIndex = 1:3
        entropyValues(channelIndex) = calculateChannelEntropy(imageData(:, :, channelIndex));
    end
end

References

Li, Q., Chen, L. An image encryption algorithm based on 6-dimensional hyper chaotic system and DNA encoding. Multimed Tools Appl 83, 5351–5368 (2024). https://doi.org/10.1007/s11042-023-15550-3