Lattice Public-Key Encryption: Richer, Tighter, Stronger

Public-key encryption allows anyone to encrypt messages that only the intended recipient can decrypt. It is an essential component of most network security protocols; however, the algorithms in widespread use are inherently vulnerable to attacks by quantum computers, should they become a practical reality. This thesis looks at public-key encryption from computationally hard problems based on high-dimensional lattices, believed to resist classical and quantum attacks. On those foundations, it proposes three post-quantum public-key encryption schemes, respectively featuring richer access control, tighter reductionist security proofs, and stronger confidentiality in the presence of external leakage