Cryptography and Coding Theory

This site provides slides, assignments, and other resources that I use in my Codes and Encryption class (MA/CS-124, Westmont College).

Slides

1. Introduction: Cryptography and Coding Theory
2. Affine Ciphers and the GCD
3. Substitution and Vigenère Ciphers
4. Attacks on Vigenère Ciphers
5. Matrices and the Hill Cipher
6. Linear Feedback Shift Registers
7. Data Encryption Standard (DES); Finite Fields
8. Advanced Encryption Standard (AES)
9. RSA Public Key Encryption
10. Attacks on RSA and Primality Testing
11. Discrete Logarithms, Diffie-Hellman, ElGamal
12. Hash Functions
13. Digital Signatures
14. Real Elliptic Curves
15. Mod p Elliptic Curves
16. Elliptic Curve Cryptography
17. Introduction to Codes
18. Codes: Definitions and Theorems
19. Linear Codes
20. Cyclic Codes
21. BCH and Reed-Solomon Codes
22. Codes and Encryption

Written Assignments

1. Modular arithmetic
2. Shift ciphers and affine ciphers
3. Substitution and Vigenère Ciphers
4. Properties of Vigenère Ciphers
5. Matrices and the Hill Cipher
6. Matrices and LFSR’s
7. Meet-in-the-middle; Finite Fields
8. AES and Modes of Operation
9. Some RSA Calculations
10. Prime Numbers and RSA
11. Discrete Logarithms
12. Hash Functions and the Birthday Theorem
13. Digital Signatures
14. Real Elliptic Curves
15. Mod p Elliptic Curves
16. Elliptic Curve Cryptography
17. Codes: Introductory Examples
18. Codes: Theoretical Limitations
19. Systematic Codes
20. Cyclic Codes
21. BCH and Reed-Solomon Codes
22. The McEliece Cryptosystem

Programming Assignments

1. Getting started with R packages
2. Tools for Breaking a Vigenère Cipher
3. LFSR tools
4. GF(256) Addition and Multiplication
5. RSA tools
6. Hash Functions and DSA
7. Mod p Elliptic Curves
8. Code Distance and Generation

Other Resources

• Syllabus (PDF)

All of the pages and slides on this site were authored in RMarkdown. The source code is available on GitHub: https://github.com/djhunter/cryptography