Rapid growth in digital communication and online platforms has increased the volume of data transmitted across public networks. Multimedia files, including medical images, are frequently shared between devices, cloud environments and institutional systems. Smartphones and digital devices allow users to capture and distribute images instantly, creating large flows of visual data through the internet. Medical images contain sensitive clinical information and therefore require strong protection during storage and transmission. When images move through public networks or remain stored in digital repositories, unauthorised interception or access may occur. Encryption converts readable image data into an unintelligible format that prevents exposure of sensitive information. Digital image encryption transforms colour or grayscale images into cipher forms that can only be restored using the correct decryption key. A method combining chaotic mapping, substitution boxes and finite-field operations offers a structured approach to protecting medical images while maintaining efficient processing.
Logistic Map-Based Substitution Box Construction
Chaotic systems provide characteristics useful for encryption, including pseudorandom behaviour and strong sensitivity to small variations in parameters. The logistic map generates numerical sequences that change significantly when initial values or control parameters shift slightly. These properties enable the creation of unpredictable sequences suitable for cryptographic operations. Construction of the substitution box begins with selecting an irreducible polynomial with the highest power equal to eight and coefficients drawn from a binary field. The logistic map then generates coordinate pairs through iterative computation.
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The x-coordinate from each pair forms a sequence used in substitution box generation. Processing occurs within a finite field of order 256. The finite-field inverse applies to each non-zero value while zero values remain unchanged. Values below 256 are selected to construct an 8×8 substitution box containing 256 unique elements. The substitution structure introduces nonlinear transformation of image data. Strong nonlinearity increases resistance against cryptanalytic techniques that attempt to identify mathematical relationships within encrypted information.
Integration of logistic map sequences directly into substitution box construction embeds chaotic behaviour within the substitution structure. This design strengthens diffusion and increases key dependency. Variation of the logistic map control parameter and initial value allows generation of multiple key-dependent substitution boxes. Increased variability improves unpredictability and strengthens resistance to linear, differential and algebraic cryptanalysis.
Image Encryption Using Chaotic Mapping and XNOR Diffusion
The encryption procedure combines substitution boxes, chaotic sequences and matrix operations to transform medical images into encrypted data. The process begins by resizing the original image to a dimension of 128 by 128 pixels. A random image of the same size supports diffusion operations during encryption. Both the original and random images are divided into blocks with identical dimensions determined by a formula based on the image size.
Each block undergoes several transformations. Blocks from the original and random images are converted into line vectors. A bitwise XNOR operation between these vectors produces a new vector. A logistic map then generates pseudorandom numbers used to reorganise pixel positions within the vector. Pixel intensities are modified using a transformation that combines the generated vector with a key stream derived from the logistic map.
The transformed vector is reconstructed into a block of the original dimension. After processing all blocks, an additional XNOR operation between the substitution box and the image matrix produces the encrypted image. The use of XNOR instead of XOR introduces complementary nonlinear transformation during the diffusion stage. Bitwise comparison generates balanced bit flipping across encrypted data, strengthening confusion and diffusion properties. This transformation improves statistical uniformity and increases resistance against linear and differential attacks.
Security and Performance Evaluation
Implementation of the encryption process used MATLAB software and medical images including chest X-ray, hand X-ray and MRI scans. Testing occurred on a system equipped with an Intel Core i3-1005G1 processor operating at 1.2 GHz with 6 GB of RAM. Encryption and decryption operations processed images of 128×128 and 512×512 pixels within a few seconds, demonstrating computational efficiency.
Statistical analysis evaluated pixel distributions before and after encryption. Original images showed structured histograms reflecting natural intensity patterns. Encrypted images produced nearly uniform histograms, indicating strong diffusion of pixel values. Correlation analysis measured relationships between neighbouring pixels in horizontal, vertical and diagonal directions. Original images exhibited strong correlations between adjacent pixels. After encryption, correlation values approached zero, indicating removal of statistical relationships between neighbouring pixels.
Entropy measurements assessed randomness within encrypted images. Entropy values approached the theoretical maximum of eight, demonstrating strong unpredictability. Additional evaluation used the net pixel conversion rate and unified average changing intensity to measure sensitivity to small modifications in plaintext images. Results showed high pixel conversion rates and significant intensity variation, confirming resistance to differential attacks.
Combining chaotic dynamics, substitution boxes and finite-field operations provides an approach for securing medical images transmitted across digital networks. Logistic map sequences generate unpredictable values that support substitution box construction and pixel diffusion. Integration of chaotic behaviour with substitution structures increases nonlinearity and strengthens resistance to cryptanalytic attacks. Block-based processing and XNOR diffusion remove statistical relationships present in original images. Experimental evaluation using medical images demonstrated efficient encryption performance alongside strong statistical security characteristics, including low pixel correlation, high entropy and strong resistance to differential analysis. The modular structure of the encryption framework also supports future integration with medical imaging environments such as picture archiving and communication systems and DICOM-based workflows.
Source: Computational and Mathematical Methods
Image Credit: iStock
