Preserving Health Care Data Security and Privacy Using Carmichael's Theorem-Based Homomorphic Encryption and Modified...

Area of Science:

• Cryptography
• Data Security
• Applied Mathematics

Background:

• Critical applications like smart grids, healthcare, and military require robust data security against increasing external threats.
• Standard encryption methods protect data but prevent computations on encrypted information.
• Existing homomorphic encryption (HE) schemes face performance and storage limitations, hindering real-time application.

Purpose of the Study:

• To design novel homomorphic encryption (HE) schemes that are simple, efficient, and secure for real-time applications.
• Introduce Carmichael's Theorem-based Homomorphic Encryption (CTHE) and Modified Enhanced Homomorphic Encryption (MEHE).
• Ensure schemes are unimpeachable against attacks and suitable for sensitive data processing.

Main Methods:

• Developed two new HE schemes: CTHE based on Carmichael's Theorem and MEHE as an improvement on Gorti's scheme.
• Proved security under the hardness of integer factorization, discrete logarithm, and quadratic residuosity problems.
• Employed modulus switching for theoretical noise reduction and validated efficiency using cardiovascular and blood pressure data.

Main Results:

• CTHE and MEHE schemes provide provable security against common cryptographic hardness assumptions.
• Modulus switching effectively reduces noise in the HE schemes.
• Demonstrated practical efficiency by performing analysis on encrypted health data (hypotension/hypertension detection).

Conclusions:

• The proposed CTHE and MEHE schemes offer a viable solution for secure, real-time computation on encrypted data.
• These schemes enhance data security in critical sectors without compromising analytical capabilities.
• The probabilistic nature of the schemes makes them computationally infeasible to break within polynomial time.