Cryptography Based on LWE

❖ Abstract

This work navigates the evolving world of post-quantum cryptography, particularly focusing on lattice-based cryptographic constructions. Starting with a thorough exploration of fundamental lattice concepts, the study progresses to delve into well-known hard lattice problems and the algorithms attempting to solve them. Afterwards, the focus is shifted to Learning with Errors (LWE), providing a comprehensive examination of LWE theory, its applications, and a concise study of Ring-LWE, a variant that provides more efficient constructions. The conclusion unfolds with an in-depth exploration of CRYSTALS-Kyber, a cryptographic scheme whose security is based on the hardness of solving hard lattice problems in (module) lattices. Beginning with the necessary preliminaries, we then delve into a detailed analysis of Kyber and its security, finishing with a recent real-world application of the scheme, the X25519Kyber768 hybrid KEM that is used to fortify Google Chrome’s security.

Details about my thesis can be also found in the depository of the university: link

❖ Files Included

• PDF (english)
• Presentation (english)

❖ Keywords

Post-Quantum Cryptography, Lattices, Lattice-based Cryptography, Learning with Errors (LWE), CRYSTALS-Kyber, Module-Lattice-Based Key-Encapsulation Mechanism Standard (ML-KEM), X25519Kyber768