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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.

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