Lattice-Based Cryptosystems: A Design Perspective
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Book Overview
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
5.1 Definition
5.2 ABE supporting and-gate policy
5.3 ABE supporting flexible threshold policy
5.4 Functional encryption
6. Key Exchanges
6.1 Definition
6.2 Key exchange against passive attacks
6.3 Implicit authenticated key exchange
6.4 Password-based authenticate key exchange
7. Digital signatures
7.1 Definition
7.2 Signatures in the random oracle model
7.3 Short signatures with tight security
7.4 Group signatures
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