Publication

Abstract : This research focuses on advancing quantumresistant cryptographic keys to address the vulnerabilities introduced by quantum computing. Traditional cybersecurity algorithms generate keys considered secure based on their bit length, but these keys become ineffective as quantum computing can factor them in in minutes. Mathematics and complex number theory provide a robust foundation for overcoming these challenges. Specifically, lattice-based cryptography, a polynomial-time lattice reduction algorithm, leverages highdimensional lattice structures-grids of points in multidimensional space-to construct classical and quantum attackresistant cryptographic schemes. The empirical study demonstrates implementing the Lenstra-Lenstra-Lovász (LLL) algorithm in Python and its optimization using basic, readily available infrastructure such as local laptops and desktop computers. Our Python code implementation of LLL implementation tests indicates ∼50% betterment across many key performance parameters, including CPU usage, memory consumption, and runtime efficiency. This confirms our implementation of its practical feasibility and effectiveness.)