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
About the Author: Jiang Zhang is an Associate Researcher at the State Key Laboratory of Cryptology, Beijing, China. His interests include post-quantum cryptography, multiparty computation and data privacy. In the area of post-quantum cryptography, he has proposed a set of lattice-based cryptosystems and presented them at leading security and cryptography conferences, including the three flagship events organized by the International Association for Cryptologic Research.
Zhenfeng Zhang is a Researcher at the Trusted Computing and Information Assurance Laboratory Institute of Software, Chinese Academy of Sciences. His research interests include trusted computing, applied cryptography and information security, areas in which he has published more than 60 papers in leading security journals.
