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Modern Cryptography Volume 2

A Classical Introduction to Informational and Mathematical Principle

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  • Open Access
  • © 2023

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Overview

Authors:
  1. Zhiyong Zheng

    1. School of Mathematics, Renmin University of China, Beijing, China

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  2. Kun Tian

    1. School of Mathematics, Renmin University of China, Beijing, China

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  3. Fengxia Liu

    1. Artificial Intelligence Research Institute, Beihang University, Beijing, China

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  • This book is open access, which means that you have free and unlimited access
  • Covers cutting-edge topics and compiled from the latest scientific research achievements in the past 20 years
  • Uses probability distribution to carry out rigorous mathematical definitions and mathematical demonstrations
  • This book fills the gap in the insufficient theoretical proofs of post-quantum cryptographic algorithms

Part of the book series: Financial Mathematics and Fintech (FMF)

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-xi
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  2. Random Lattice Theory

    • Zhiyong Zheng, Kun Tian, Fengxia Liu
    Pages 1-32Open Access
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  3. Reduction Principle of Ajtai

    • Zhiyong Zheng, Kun Tian, Fengxia Liu
    Pages 33-52Open Access
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  4. Learning with Error

    • Zhiyong Zheng, Kun Tian, Fengxia Liu
    Pages 53-98Open Access
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  5. LWE Public Key Cryptosystem

    • Zhiyong Zheng, Kun Tian, Fengxia Liu
    Pages 99-118Open Access
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  6. Cyclic Lattices and Ideal Lattices

    • Zhiyong Zheng, Kun Tian, Fengxia Liu
    Pages 119-142Open Access
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  7. Fully Homomorphic Encryption

    • Zhiyong Zheng, Kun Tian, Fengxia Liu
    Pages 143-174Open Access
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  8. A Generalization of NTRUencrypt

    • Zhiyong Zheng, Kun Tian, Fengxia Liu
    Pages 175-188Open Access
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  9. Back Matter

    Pages 189-191
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Keywords

About this book

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.





Authors and Affiliations

  • School of Mathematics, Renmin University of China, Beijing, China

    Zhiyong Zheng, Kun Tian

  • Artificial Intelligence Research Institute, Beihang University, Beijing, China

    Fengxia Liu

About the authors

Zhiyong Zheng is Professor and Dean of School of Mathematics, Renmin University. His research and academic experiences include in 1995, Princeton University, as Visiting Scholar; in 1988-1991，Shandong University， Ph.D. He received Distinguished Paper Award (ICCM 2018), Qiu Shi Outstanding Young Scholar Award (1997) and The National Science Fund for Distinguished Young Scholars (1996). He was Dean of School of Mathematics, Renmin University of China. His research area includes Diophantine approximation, character sum and cryptography

Bibliographic Information

  • Book Title: Modern Cryptography Volume 2

  • Book Subtitle: A Classical Introduction to Informational and Mathematical Principle

  • Authors: Zhiyong Zheng, Kun Tian, Fengxia Liu

  • Series Title: Financial Mathematics and Fintech

  • DOI: https://doi.org/10.1007/978-981-19-7644-5

  • Publisher: Springer Singapore

  • eBook Packages: Economics and Finance, Economics and Finance (R0)

  • Copyright Information: The Editor(s) (if applicable) and The Author(s) 2023

  • Hardcover ISBN: 978-981-19-7643-8Published: 11 December 2022

  • Softcover ISBN: 978-981-19-7646-9Published: 11 December 2022

  • eBook ISBN: 978-981-19-7644-5Published: 10 December 2022

  • Series ISSN: 2662-7167

  • Series E-ISSN: 2662-7175

  • Edition Number: 1

  • Number of Pages: XI, 191

  • Number of Illustrations: 2 b/w illustrations

  • Topics: Macroeconomics/Monetary Economics//Financial Economics, Applications of Mathematics

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