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Table of Contents
1. Introduction
2. Simple Ciphers
3. Divisibility, Congruences, and Modular Arithmetic
4. Groups, Rings, Fields
5. Square Roots and Quadratic Symbols
6. Finite Fields of Characteristic 2
7. Elliptic Curves
8. Mathematics, Computing, and Arithmetic
9. Modern Symmetric Ciphers DES and AES
10. Asymmetric Ciphers RSA and Others
11. How to Factor a Number
12. How to Factor More Effectively
13. Cycles, Randomness, Discrete Logarithms, and Key Exchange
14. Elliptic Curve Cryptography
15. Quantum Computing and Cryptography
16. Lattice-Based Cryptography
17. Homomorphic Encryption
18. Exercises.
2. Simple Ciphers
3. Divisibility, Congruences, and Modular Arithmetic
4. Groups, Rings, Fields
5. Square Roots and Quadratic Symbols
6. Finite Fields of Characteristic 2
7. Elliptic Curves
8. Mathematics, Computing, and Arithmetic
9. Modern Symmetric Ciphers DES and AES
10. Asymmetric Ciphers RSA and Others
11. How to Factor a Number
12. How to Factor More Effectively
13. Cycles, Randomness, Discrete Logarithms, and Key Exchange
14. Elliptic Curve Cryptography
15. Quantum Computing and Cryptography
16. Lattice-Based Cryptography
17. Homomorphic Encryption
18. Exercises.