A novel cryptographic framework and mathematical modeling for secure transmission of Parkinson's disease data using RSA and block-based secret sharing.

The secure transmission of medical data is an essential requirement in modern telemedicine systems, particularly for chronic neurological disorders such as Parkinson's disease. This paper proposes a novel hybrid cryptographic framework that combines RSA encryption with block-based secret sharing enhanced by a Hilbert matrix-driven mathematical model. The framework introduces dynamic block-wise key generation and adaptive sharing to strengthen data confidentiality and robustness against cryptanalytic attacks. Mathematical modeling is employed to analyze encryption stability, numerical conditioning of the Hilbert matrix, and the diffusion properties of the key space. The proposed method is validated using publicly available Parkinson's EEG and spiral drawing datasets, with quantitative analysis including encryption/decryption time, computational overhead, and image quality metrics (PSNR, SSIM). The framework is further benchmarked against AES-Shamir and ECC-based hybrid models. Experimental results indicate that the proposed system achieves higher security entropy and lower computational cost, making it suitable for deployment in resource-constrained medical IoT environments.