Lattice-Based Cryptographic Scheme for Secure Blockchain Development and Financial Systems

Abstract

This paper introduces a robust and mathematically rigorous lattice-based cryptographic scheme to enhance the security of blockchain networks, with a focus on financial systems. With the advent of quantum computing, traditional cryptographic systems like RSA and ECC face vulnerabilities that lattice-based schemes can effectively mitigate. The proposed approach integrates lattice-based cryptography with group theory to ensure secure communication and data integrity within blockchain ecosystems. By leveraging a $4\times 4$ matrix-based key exchange, encryption, and decryption mechanism, this scheme ensures quantum-resistant security for money transfers, demonstrated here with the Naira (₦) as a practical example. Theoretical group-theoretical properties are utilized to achieve secure cryptographic operations over matrices, providing a practical, scalable, and quantum-resistant approach for financial transactions in blockchain systems.