Math 314: Cryptography

Fall 2019



Date Lecture Notes 001 Notes 001 Assigned Reading What is Due
Week 1
8/26 Historical Cryptography. Intro to Sage and Latex.
Classical Cryptography: Caesar cipher and modular arithmetic		 Notes
8/28 Classical Cryptography: Cryptanalysis and the Affine Cipher (Multiplication table modulo 26) Notes Notes Chapter 1, Section 2.1 Mission 0
Week 2
9/2 Labor Day
9/4 Classical Cryptography: Substitution and Vigenere Ciphers Notes Notes Sections 2.2, 2.3 (skip 2.3.3) and 2.4 CoCalc Assignment 1
Week 3
9/9 Classical Cryptography: The Hill Cipher Notes Notes Sections 2.6 and 2.7 Mission 1 Latex
9/11 Classical Cryptography: One-time pad, Euclid's Algorithm Notes Notes Sections 2.9, 2.12 CoCalc Assignment 2
Week 4
9/16 Euclid's Algorithm, Rings Notes Notes Sections 3.1, 3.2 and 3.3 Mission 2 Tex
9/18 Chinese Remainder Theorem, Modular Exponentiation, Fermat's Theorem Notes Sections 3.4 and 3.5 CoCalc Assignment 3
Week 5
9/23 3 Pass Protocol, Euler Phi Function, Euler's Theorem, Fermat Primality Test Notes Notes Section 3.6 Mission 3 Tex
9/25 Finite fields, polynomials over finite fields Notes Section 3.11 CoCalc Assignment 4
Week 6
9/30 Primitive Roots, Quadratic Residues, Legendre and Jacobi Symbols Notes Sections 3.7,3.9,3.10 Mission 4 Tex
10/2 Midterm 1CoCalc Assignment 5
Week 7
10/7 Fermat Primality test, Jacobi symbols and Feistel ciphers Notes Sections 3.10 and 4.1
10/9 SDES Notes Section 4.2, 4.4 CoCalc Assignment 6
Week 8
10/14 2DES, Meet in the middle Attacks, Modes of Operation Notes Sections 4.5, 4.6, 4.7 Mission 5 Tex
10/16 SAES Notes Chapter 5 CoCalc Assignment 7
Week 9
10/21 SAES Example, and Public Key Cryptography Chapter 5
10/23 RSA Notes Notes Chapter 6 Mission 6 Tex
Week 10
10/28 Primality Testing Notes Section 6.3 CoCalc Assignment 8
10/30 Dixon's Factorization Algorithm Notes Section 6.4 and 6.5 CoCalc Assignment 9 (Thursday)
Week 11
11/4 Discrete Logarithm Problem and the Diffie-Hellman Key Exchange Section 6.3
11/6 ElGamal Cryptosystem Notes Section 6.4 Mission 7 TEX
Week 12
11/11 Digital Signatures Section 7.1, 7.2.2 and 7.4
11/13 Cryptographic Hash Functions, Birthday Attacks Notes Section 7.5 Mission 9 TEX
Week 13
11/18 Midterm 2
11/20 Discrete Log hash and Birthday attacks Notes Notes Section 8.4 and 9.1
Week 14
11/25 Elliptic Curves Notes Section 8.1
11/27 THANKSGIVING
Week 15
12/2 DSA, Birthday Attacks and Elliptic Curves Section 9.5
12/4 Elliptic Curves Sections 16.1 and 16.2
Week 16
12/9 Review and Flipping a coin over the phone CoCalc Assignment 10
12/11 Final Exam Section 101 (7:30 PM)
12/13 Final Exam Section 001 (12:30 PM)