Lattice Reduction Algorithm and Applications

Abstract

Cryptography is a fundamental field in ensuring secure communication, with public key cryptosystems playing a crucial role in modern security protocols. This thesis begins by dis cussing the GGH (Goldwasser-Goldwasser-Halevi) cryptosystem, a lattice-based encryption scheme, and then focuses on NTRU cryptosystem. NTRU is a lattice-based public-key cryp tosystem known for its efficiency and resistance to quantum attacks and is used widely. The thesis explores its security, especially in the context of lattice reduction techniques like the Lenstra-Lenstra-Lov´asz (LLL) algorithm, highlighting how parameter selection and lattice dimensions impact decryption success. Through experimental analysis, the thesis concludes that NTRU demonstrates stronger security at higher dimensions but remains vulnerable to lattice-based attacks for smaller parameters. The results offer insights into optimizing NTRU’s parameters to enhance its cryptographic resilience.