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A Practical and Computational Introduction to Mathematical Cryptography

About this Book

Chapters

1. What is Cryptography?
2. Introduction to Python, Sage, and Jupyter Notebooks
3. Number Theory
4. Modular Arithmetic
5. Powers in \(\mathbb{Z}/m\mathbb{Z}\)
6. Discrete Logs, Diffie-Hellman Key Exchange, and the ElGamal Cryptosystem
7. Computing Discrete Logs
8. The Chinese Remainder Theorem and Generalized Bezout’s Lemma
9. Improvements on Computations of Discrete Logs
10. The RSA Cryptosystem
11. Primality Testing
12. Factorization
13. Square Roots Modulo \(m\)
14. Quadratic Sieve and Index Calculus
15. Digital Signatures
16. Elliptic Curves
17. Finite Fields and the Advanced Encryption Standard (AES)

Endmatter

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By Luís Finotti

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