Two-dimensional multi-tooth hyperchaotic map and application in medical secure transmission

Designing two-dimensional discrete maps with robust hyperchaos, controllable amplitude, ultra wide parameters, and high performance metrics is of great significance for chaos theory and its applications. However, achieving such designs remains a significant challenge. This paper presents a two-dimensional bounded multi-tooth hyperchaotic map with provable boundedness. We analyze the invariant points and their stability, and explore the coexisting bifurcations induced by pitchfork and Neimark–Sacker bifurcations. Additionally, we reveal the multi-tooth hyperchaotic attractors with an increased number of sawteeth. Numerical simulations demonstrate that the proposed map exhibits robust hyperchaos and high performance metrics across a wide range of parameters. The amplitudes of the resulting multi-tooth hyperchaotic attractors are strictly controllable in both directions through parameter adjustments. FPGA hardware experiments are conducted to confirm the numerical results. Furthermore, using the proposed map, we design a chaos-state-based encryption system for medical secure transmission applications. The implementation achieves efficient resource utilization requiring only 9 additional BRAMs on FPGA, while maintaining high security with both plaintext and ciphertext sensitivity. Hardware implementation and encryption security experiments indicate that the proposed scheme achieves low resource utilization while maintaining high security.