Geometric Mean Labeling in Cryptography: A Graph-Based Approach to Enhanced Security and Performance (Contemporary Mathematics, 2025)
Cryptographic security is essential for ensuring data integrity and secure communication. Traditional encryption methods such as RSA and elliptic curve cryptography (ECC), while widely used, suffer from high computational complexity, large key sizes, and vulnerability to evolving attack strategies. This paper introduces geometric mean labeling(GML), a novel graph-based cryptographic technique that enhances encryption efficiency, key management, and security. Unlike RSA, which relies on prime factorization, or ECC, which depends on elliptic curve logarithms, GML applies geometric mean-based transformations to encrypt data using structured graph relationships, making it computationally efficient. Specifically, GML achieves encryption in just 0.085 ms with a 512-bit key, compared to 600 ms (RSA, 2,048-bit) and 30 ms (ECC, 256-bit), leading to a 99.99% speed improvement over RSA and 99.7% over ECC. Theoretical analysis confirms that GML operates with a computational complexity of O(V3), making it scalable for large-scale encryption while maintaining strong security against brute-force and chosen-plaintext attacks. Experimental validation was conducted on an Intel i7-based system, confirming the efficiency and reliability of GML for real-world applications such as IoT security and cloud encryption. By integrating GML into modern cryptographic frameworks, this study provides a scalable, efficient, and future-ready encryption solution, with potential applications in post-quantum cryptography.
Keywords: geometric mean labeling, encryption and decryption, cryptographic algorithms, secure communications