Modern Cryptography Volume 2 A Classical Introduction to Informational and Mathematical Principle

Modern Cryptography Volume 2 A Classical Introduction to Informational and Mathematical Principle

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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-qua...

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Bibliographic Details
Main Author: Zheng, Zhiyong (auth)
Other Authors: Tian, Kun (auth), Liu, Fengxia (auth)
Format: Electronic Book Chapter
Language:English
Published: Singapore Springer Nature 2023
Series:Financial Mathematics and Fintech
Subjects:
Macroeconomics
Applied mathematics
Post-Quantum Cryptography
Gauss Lattice
Reduction
Learning With Errors
FHE
Fourier transform
Ideal lattice
NTRU
Smoothing parameters
Discrete Gaussian measure
Online Access:DOAB: download the publication
DOAB: description of the publication
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Summary: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.
Physical Description:1 electronic resource (191 p.)
ISBN:978-981-19-7644-5
9789811976445
Access:Open Access

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