A Logic-Gate Driven Cryptographic System with Dual-Function Hashing and Homomorphic Encryption Capabilities

This paper introduces a cryptographic system that uses logic gate-based hashing with homomorphic encryption to securely generate digital signatures. The system is designed using a structure that applies basic logic gates such as AND, OR, NOT, NAND, and NOR along with XOR and XNOR encryption techniques. Implemented within a 2D matrix using MATLAB, the system allows secure data transformations while maintaining the ability to perform operations on encrypted data through additive homomorphism. This means that data can be processed without needing to decrypt it, preserving security throughout. A key feature of the system is its use of multiple logic paths, which adds redundancy and strengthens overall reliability. Security analysis shows that the encrypted outputs maintain high entropy values (≥ 0.95), and the uniqueness of digital signatures exceeds 98%, indicating strong resistance to duplication and attacks. Due to its low computational requirements and strong performance, this system is well-suited for embedded systems, IoT applications, and other environments where both efficiency and data protection are critical.