Mehmet Sagbas, Shahram Minaei
Abstract The rapid expansion of the Internet of Medical Things (IoMT) necessitates lightweight and robust security mechanisms for protecting sensitive biomedical signals during transmission. While memristor-based chaotic systems have emerged as promising entropy sources for cryptographic applications, their reliance on conventional first-order memory often limits their dynamical complexity. To address this limitation, this paper proposes a high-order memristor-based ( 4 + n ) -dimensional hyperchaotic system. The memductance of the proposed hyperchaotic system depends on an n -stage internal memory chain that generalizes first-order memristive dynamics and enables richer routes to instability. The proposed 4 + n -dimensional framework is formulated for a general n and explicitly demonstrated for n = 1 (5D) and n = 2 (6D), corresponding to fifth- and sixth-order systems, respectively. The system’s fundamental properties are established through equilibria, dissipativity, bifurcation studies, and Lyapunov spectrum computation, yielding a Kaplan–Yorke dimension of D KY ≈ 5.05 for the n = 2 case. In addition, the effect of the memory order n on the attractor geometry is investigated. To validate practicality, the proposed model is digitally emulated on an STM32H7A3ZI microcontroller. Finally, a chaos-assisted biomedical protection pipeline in which the proposed dynamics provide signal-adaptive masking/permutation for electrocardiogram (ECG) streams prior to secure transport is presented. Experimental evaluations show a Miller–Madow entropy of 15.930 bits, adjacent-sample correlation reduced to 0.004, key-sensitivity with a BER of 0.501, and near-lossless plaintext recovery with PRD = 0.009% and SNR = 80.56 dB. In addition, the scheme achieves NPCR = 100.00% and UACI = 33.10%, supporting lightweight on-device confidentiality for IoMT applications.