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Medical Image Encryption via CSPRNG-HKDF Key Scheduling, Fractional-Order Modified Chen Hyperchaos, and Dynamic
Kaan Doğan Erdoğan1, Nurettin Doğan2
1Department of Property Protection and Security, Selcuk University, Konya 42400, Türkiye.
Abstract:
Protecting medical images requires encryption methods that combine cryptographic key management with validated nonlinear transformations and effective diffusion mechanisms. This study proposes an encryption-instance-specific framework based on a CSPRNG-generated 256-bit session secret, HMAC-SHA-512-based HKDF with public NOAA/SWPC temporal context, a modified four-dimensional fractional-order Chen system, adaptive bit-plane permutation, position-dependent dynamic DNA transformation, and SPARKLE256-based two-pass ARX-duplex diffusion. The fractional operating region was evaluated through boundedness, Lyapunov-spectrum, bifurcation, phase-portrait, and modified 0-1 chaos analyses. All 10,000 sampled parameter triplets remained finite and bounded, all 1000 Lyapunov-grid configurations satisfied the hyperchaos criterion, and the minimum second Lyapunov exponent was 0.0546; the modified 0-1 test accepted all 35 representative cases with a median K value of 0.9971. For encrypted standard benchmark and medical images, entropy ranged from 7.9966 to 7.9978 bits. Across the 11 test images, the mean RGB NPCR and UACI values were 99.6115% and 33.4546%, respectively, while the corresponding grayscale means were 99.5999% and 33.4608%. Under NIST SP 800-22, the fractional modified Chen keystream satisfied 187 of 188 subtest rows (99.47%), while the operational ciphertext satisfied 185 of 188 rows (98.40%). In the 111-row Dieharder evaluation, the keystream produced 109 passed, 2 weak, and 0 failed outcomes, whereas the ciphertext produced 106 passed, 5 weak, and 0 failed outcomes. The optimized CPU implementation encrypted a 256 × 256 RGB image in 1356.327 ms, representing a 74.26-fold speedup relative to the 100,722.174 ms pure-Python 3.10.20 baseline. Overall, the results demonstrate strong statistical and differential characteristics while showing that the fractional-order chaotic generator remains the principal computational component of the proposed framework.
