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 in the random oracle model 3.3 CCA-secure PKE in the standard model 4. Identity-based encryption 4.1 Definition 4.2 The GPV IBE scheme 4.3 Short IBE in the standard model 5. Attribute-based encryption &nbs
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