Cryptanalysis and Improvement of Medical Image Cryptosystem via Fractional-Order Memristive Hopfield Neural Network

Chaos-based image cryptosystems often produce noise-like ciphertexts, but dynamical complexity does not establish security. This paper presents a structural cryptanalysis of the fractional-order memristive Hopfield neural network (FMHNN)-based medical-image cryptosystem proposed by Sun et al. For fixed parameters and dimensions, the published data path is formalized as a plaintext-independent permutation followed by a fixed exclusive-or (XOR) mask. Chosen-plaintext attack (CPA), known-plaintext attack (KPA), chosen-ciphertext attack (CCA), and fixed-key differential analyses then derive equivalent-secret recovery, leakage, and malleability relations. CPA and CCA recover the complete equivalent secret in 1+⌈log256N⌉ queries for an N-pixel image; KPA resolves positions with unique cross-image signatures under secret reuse. Numerical validation, including a black-box encryption-oracle experiment, confirms the recovery relations. On the public BreastMNIST+ 128 benchmark, complete KPA recovery occurs at m=7, and the recovered equivalent secret decrypts an independent held-out image exactly. The analysis shows that favorable entropy, correlation, number-of-pixels change rate (NPCR), and unified average changing intensity (UACI) cannot substitute for structural cryptanalysis. Attack-guided module-level countermeasures are formulated to provide per-image diversification, feedback diffusion, and integrity verification, and are evaluated through exact decryption and integrity checks. The study offers an attack-based assessment and design guidance for chaos-based image-encryption systems.