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    Modern Cryptography Volume 2

    A Classical Introduction to Informational and Mathematical Principle

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    Author(s)
    Zheng, Zhiyong
    Tian, Kun
    Liu, Fengxia
    Language
    English
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    Abstract
    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.
    URI
    https://library.oapen.org/handle/20.500.12657/60195
    Keywords
    Post-Quantum Cryptography; Gauss Lattice; Reduction; Learning With Errors; FHE; Fourier transform; Ideal lattice; NTRU; Smoothing parameters; Discrete Gaussian measure
    DOI
    10.1007/978-981-19-7644-5
    ISBN
    9789811976445, 9789811976445
    Publisher
    Springer Nature
    Publisher website
    https://www.springernature.com/gp/products/books
    Publication date and place
    Singapore, 2023
    Grantor
    • Renmin University of China - [...]
    Imprint
    Springer
    Series
    Financial Mathematics and Fintech,
    Classification
    Macroeconomics
    Applied mathematics
    Pages
    191
    Rights
    http://creativecommons.org/licenses/by/4.0/
    • Imported or submitted locally

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    License

    • If not noted otherwise all contents are available under Attribution 4.0 International (CC BY 4.0)

    Credits

    • logo EU
    • This project received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No 683680, 810640, 871069 and 964352.

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