A Matrix Multiplication Approach to Quantum-Safe Cryptographic Systems

This paper introduces a novel approach based on matrix multiplication in 𝔽𝑛×𝑛𝑝, which enables methods for public key exchange, user authentication, digital signatures, blockchain integration, and homomorphic encryption. Unlike traditional algorithms that rely on integer factorization or discrete logarithms, our approach utilizes matrix factorization, rendering it resistant to current quantum cryptanalysis techniques. This method enhances confidentiality by ensuring secure communication and facilitating user authentication through public key validation. We have incorporated a method that allows a Certification Authority to certify the public keys. Furthermore, the incorporation of digital signatures ensures nonrepudiation, while the system functions as a blockchain technology to enhance transaction security. A key innovation of this approach is its capability to perform homomorphic encryption. Our approach has practical applications in artificial intelligence, robotics, and image processing.