Modern Cryptography Volume 1 A Classical Introduction to Informational and Mathematical Principle
This open access book systematically explores the statistical characteristics of cryptographic systems, the computational complexity theory of cryptographic algorithms and the mathematical principles behind various encryption and decryption algorithms. The theory stems from technology. Based on Shan...
Saved in:
| Main Author: | |
|---|---|
| Format: | eBook Publication |
| Language: | English |
| Published: |
Singapore
Springer Nature
2022
Springer Springer Singapore Renmin University of China |
| Edition: | 1 |
| Series: | Financial Mathematics and Fintech |
| Subjects: | |
| ISBN: | 9811909202, 9789811909207, 9789811909191, 9811909199 |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- 7.9 Ajtai/Dwork Cryptosystem -- References -- Appendix References
- 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