Fundamentals of Cryptography

Duncan Buell, professor emeritus in the Dept. of Computer Science and Engineering at University of South Carolina, also has 15 years of experience at a research lab doing high-performance computing research in support of the US National Security Agency.

• 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 KeyExchange.- 14. Elliptic Curve Cryptography.- 15. Quantum Computing and Cryptography.- 16. Lattice-Based Cryptography.- 17. Homomorphic Encryption.- 18. Exercises.

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