International Journal of Science, Engineering and TechnologyAuthors: Dr. S. Sreelatha, Assistant Professor, Dr. P. Pushpa, Assistant Professor
Abstract: The imminent arrival of large-scale quantum computers necessitates a transition from classical number-theoretic cryptography to post-quantum alternatives. Lattice-based cryptosystems represent the most mature and versatile family among NIST-standardized post-quantum algorithms. This paper presents a rigorous mathematical analysis of security margins for the Learning With Errors LWE and Ring-LWE problems under hybrid attack models that combine lattice reduction BKZ 2.0 with meet-in-the-middle techniques. We derive novel bounds for the root Hermite factor as a function of dimension and block size, proving that current parameter sets recommended by NIST provide a security margin of at least 2128 operations against classical and quantum adversaries. Experimental validation using the fplll library on instances up to dimension n = 1024 confirms our theoretical predictions with a margin of error <0.3%. We further propose a modified error distribution that improves resistance to dual attacks by 17.4% without significant performance degradation.
DOI: http://doi.org/10.5281/zenodo.20583308
