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Modern Cryptography Volume 1 : A Classical Introduction to Informational and Mathematical Principle.

Bibliographic Details
Main Author: Zheng, Zhiyong.
Format: eBook
Language:English
Published: Singapore : Springer, 2022.
Edition:1st ed.
Series:Financial Mathematics and Fintech Series
Subjects:
Electronic books.
Online Access:Click to View
Table of Contents:
  • Intro
  • Preface
  • Contents
  • Acronyms
  • 1 Preparatory Knowledge
  • 1.1 Injective
  • 1.2 Computational Complexity
  • 1.3 Jensen Inequality
  • 1.4 Stirling Formula
  • 1.5 n-fold Bernoulli Experiment
  • 1.6 Chebyshev Inequality
  • 1.7 Stochastic Process
  • References
  • 2 The Basis of Code Theory
  • 2.1 Hamming Distance
  • 2.2 Linear Code
  • 2.3 Lee Distance
  • 2.4 Some Typical Codes
  • 2.4.1 Hadamard Codes
  • 2.4.2 Binary Golay Codes
  • 2.4.3 3-Ary Golay Code
  • 2.4.4 Reed-Muller Codes
  • 2.5 Shannon Theorem
  • References
  • 3 Shannon Theory
  • 3.1 Information Space
  • 3.2 Joint Entropy, Conditional Entropy, Mutual Information
  • 3.3 Redundancy
  • 3.4 Markov Chain
  • 3.5 Source Coding Theorem
  • 3.6 Optimal Code Theory
  • 3.7 Several Examples of Compression Coding
  • 3.7.1 Morse Codes
  • 3.7.2 Huffman Codes
  • 3.7.3 Shannon-Fano Codes
  • 3.8 Channel Coding Theorem
  • References
  • 4 Cryptosystem and Authentication System
  • 4.1 Definition and Statistical Characteristics of Cryptosystem
  • 4.2 Fully Confidential System
  • 4.3 Ideal Security System
  • 4.4 Message Authentication
  • 4.5 Forgery Attack
  • 4.6 Substitute Attack
  • 4.7 Basic Algorithm
  • 4.7.1 Affine Transformation
  • 4.7.2 RSA
  • 4.7.3 Discrete Logarithm
  • 4.7.4 Knapsack Problem
  • References
  • 5 Prime Test
  • 5.1 Fermat Test
  • 5.2 Euler Test
  • 5.3 Monte Carlo Method
  • 5.4 Fermat Decomposition and Factor Basis Method
  • 5.5 Continued Fraction Method
  • References
  • 6 Elliptic Curve
  • 6.1 Basic Theory
  • 6.2 Elliptic Curve Public Key Cryptosystem
  • 6.3 Elliptic Curve Factorization
  • References
  • 7 Lattice-Based Cryptography
  • 7.1 Geometry of Numbers
  • 7.2 Basic Properties of Lattice
  • 7.3 Integer Lattice and q-Ary Lattice
  • 7.4 Reduced Basis
  • 7.5 Approximation of SVP and CVP
  • 7.6 GGH/HNF Cryptosystem
  • 7.7 NTRU Cryptosystem
  • 7.8 McEliece/Niederreiter Cryptosystem.
  • 7.9 Ajtai/Dwork Cryptosystem
  • References
  • Appendix References.

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