This is an upper level MATH course. It is directed at
students in mathematics, electrical engineering, or computer science
who have strong interest in mathematics and want to learn about the
exciting applications of algebra and number theory to cryptography
(encryption/decryption) and cryptanalysis (attacking encrypted messages).
Topics to be covered include:
Cryptography: Simple Ciphers and Cryptograms.
Vigenere Cipher, Hill Cipher, Advanced Encryption Standard.
Cryptanalysis:
attacks on encrypted messages. Depth, probabilistic methods, trapdoors.
Public-Key ciphers:
Rivest-Shamir-Adleman (RSA), Diffie-Hellman. Public Key Protocols.
Number Theory: Congruences. Finite fields.
Finding large primes, pseudoprimes and primality testing.
| Week | Lecture dates | Sections | Topics | Links |
| 1 | 1/23, 1/27 | 1.1-1.2, 1.6 | Caesar, Affine and Substitution Ciphers, Integers mod 26 | Learn about Kryptos |
| 2 | 1/30, 2/3 | 1.2, 1.3, 1.4 | Division Algorithm, Euclidean Algorithm | |
| 3 | 2/6, 2/10 | 1.5, 1.7 | Modular Arithmetic, primes, Fermat's little theorem | Recent clue for Kryptos |
| 4 | 2/13, 2/17 | 2.1-2.3 | Discrete Logarithms and Diffie-Hellman key exchange | |
| 5 | 2/20, 2/24 | 2.4-2.7 | Elgamal Encryption, Discrete Logarithm and Collision | |
| 6 | 2/27, 3/2 | 2.8,2.9 | Quadratic Residues, Chinese Remainder Theorem, Pohlig-Hellman Algorithm | |
| 7 | 3/5, 3/9 | 3.1-3.3 | RSA public key encryption | |
| 8 | 3/12, 3/23 | 3.4, 3.5 | Factorization and Primes, Midterm Exam 3/23 | |
| 9 | 3/26, 3/30 | 3.6, 3.8 | Factorization via difference of squares, smooth numbers, Index Calculus | |
| 10 | 4/2, 4/6 | 3.8 | Index calculus and discrete logs | |
| 11 | 4/9, 4/13 | 4.1-4.3 | Digital signatures | |
| 12 | 4/16, 4/20 | 5.2-5.5 | Collision Attacks, Index of Coindence | |
| 13 | 4/23, 4/27 | 6.1-6.5 | Elliptic Curves and Cryptography
| |
| 14 | 5/4 | Last Class - Review of Cryptography |
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Last Updated: March 17, 2020