TY  - BOOK
AU  - Zheng,Zhiyong
AU  - Tian,Kun
AU  - Liu,Fengxia
ED  - SpringerLink (Online service)
TI  - Modern Cryptography Volume 2: A Classical Introduction to Informational and Mathematical Principle 
T2  - Financial Mathematics and Fintech,
SN  - 9789811976445
AV  - HG1-9999 
U1  - 332 23
PY  - 2023///
CY  - Singapore
PB  - Springer Nature Singapore, Imprint: Springer
KW  - Finance
KW  - Social sciences
KW  - Mathematics
KW  - Financial Economics
KW  - Mathematics in Business, Economics and Finance
N1  - Chapter 1. Gauss lattice theory -- Chapter 2. Reduction principle of Ajtai -- Chapter 3. Learning with errors -- Chapter 4. LWE cryptosystem -- Chapter 5. Cyclic lattice and Ideal lattice -- Chapter 6. Fully Homomorphic Encryption -- Chapter 7. General NTRU cryptosystem; Open Access
N2  - This open access book covers the most cutting-edge and hot research topics and fields of post-quantum cryptography. The main purpose of this book is to focus on the computational complexity theory of lattice ciphers, especially the reduction principle of Ajtai, in order to fill the gap that post-quantum ciphers focus on the implementation of encryption and decryption algorithms, but the theoretical proof is insufficient. In Chapter 3, Chapter 4 and Chapter 6, author introduces the theory and technology of LWE distribution, LWE cipher and homomorphic encryption in detail. When using random analysis tools, there is a problem of "ambiguity" in both definition and algorithm. The greatest feature of this book is to use probability distribution to carry out rigorous mathematical definition and mathematical demonstration for various unclear or imprecise expressions, so as to make it a rigorous theoretical system for classroom teaching and dissemination. Chapters 5 and 7 further expand and improve the theory of cyclic lattice, ideal lattice and generalized NTRU cryptography. This book is used as a professional book for graduate students majoring in mathematics and cryptography, as well as a reference book for scientific and technological personnel engaged in cryptography research
UR  - https://doi.org/10.1007/978-981-19-7644-5
ER  -