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

• Superior document: Financial Mathematics and Fintech Series
• Author: Zheng, Zhiyong.
• Place / Publishing House: Singapore : : Springer,, 2022.; Ã2022.
• Year of Publication: 2022
• Edition: 1st ed.
• Language: English
• Series: Financial Mathematics and Fintech Series
• Physical Description: 1 online resource (364 pages)

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.