# Math 314: Cryptography

Fall 2018

Date Lecture Notes Assigned Reading What is Due
Week 1
8/27 Historical Cryptography. Intro to Sage and Latex.
Classical Cryptography: Caesar cipher and modular arithmetic
Notes
8/29 Classical Cryptography: Cryptanalysis and the Affine Cipher (Multiplication table modulo 26) Notes Chapter 1, Section 2.1 Mission 0
Week 2
9/3 Labor Day
9/5 Classical Cryptography: Substitution and Vigenere Ciphers Notes Sections 2.2, 2.3 (skip 2.3.3) and 2.4 Cocalc Assignment 1
Week 3
9/10 Classical Cryptography: The Hill Cipher Notes Sections 2.6 and 2.7 Mission 1 TEX
9/12 Classical Cryptography: One-time pad, Euclid's Algorithm Notes Sections 2.9, 2.12 CoCalc Assignment 2
Week 4
9/17 Euclid's Algorithm, Rings Notes Sections 3.1, 3.2 and 3.3 Mission 2 TEX
9/19 Chinese Remainder Theorem, Modular Exponentiation, Fermat's Theorem Notes Sections 3.4 and 3.5 Cocalc Assignment 3
Week 5
9/24 3 Pass Protocol, Euler Phi Function, Euler's Theorem, Fermat Primality Test Notes Section 3.6 Mission 3 TEX
9/26 Finite fields, polynomials over finite fields Notes Section 3.11 Cocalc Assignment 4
Week 6
10/1 Primitive Roots, Quadratic Residues, Legendre and Jacobi Symbols Sections 3.7,3.9,3.10 Mission 4 TEX
10/3 Midterm 1
Week 7
10/8 Fermat Primality test, Jacobi symbols and Feistel ciphers Sections 3.10 and 4.1
10/10 SDES Notes Section 4.2
Week 8
10/15 Differential Cryptanalysis Notes Sections 4.3.1 Mission 5 TEX
10/17 2DES, Meet in the middle Attacks Notes Section 4.7
Week 9
10/22 Meet in the Middle Attacks, Modes of Operation 3DES Notes Section 4.5
10/24 SAES Notes Chapter 5 Mission 6
Week 10
10/29 SAES Example, and Public Key Cryptography Notes
10/31 RSA Notes Section 6.1 Mission 7
Week 11
11/5 Primality Testing Notes Section 6.3
11/7 Dixon's Factorization Algorithm Notes Section 6.4 Mission 8 TEX
Week 12
11/12 Discrete Logarithm Problem and the Diffie-Hellman Key Exchange Notes Section 7.1, 7.2.2 and 7.4 CoCalc Assignment 5
11/14 ElGamal Cryptosystem Notes Section 7.5
Week 13
11/19 Midterm 2 Mission 9 TEX
11/21 THANKSGIVING
Week 14
11/26 Cryptographic Hash Functions Notes Section 8.1
11/28 Birthday Attacks and Digital Signatures Notes Section 8.4 and 9.1
Week 15
12/3 DSA, Birthday Attacks and Elliptic Curves Notes Section 9.5 Mission 10 TEX
12/5 Elliptic Curves Notes Sections 16.1 and 16.2
Week 16
12/10 Elliptic Curve Diffie-Hellman Worksheet Mission 11 TEX
Week 17
12/17 Final Exam (3:00 PM)