1 Introduction 1.1 Cryptography based on number theory problems 1.2 Post-quantum cryptography 1.3 Lattice-based cryptosystems 2. Lattices 2.1 Definition 2.2 Discrete Gaussian 2.3 Small Integer Solutions 2.4 Learning with Errors 2.5 Trapdoor Generation 3. Public-key encryption 3.1 Definition 3.2 PKE against CPA attacks 3.2 Achieving CCA-Security...