# Math 314: Cryptography

Spring 2020

Date Lecture Notes Section 002 Notes Section 101 Assigned Reading What is Due
Week 1 January 27--February 1st
Day 1 Historical Cryptography. Intro to Sage and Latex.
Classical Cryptography: Caesar cipher and modular arithmetic
Notes Notes
Day 2 Classical Cryptography: Cryptanalysis and the Affine Cipher (Multiplication table modulo 26) Notes Notes Chapter 1, Sections 2.1 and 2.2 CoCalc Assignment 0 PDF
Week 2 February 3rd--8th
Day 1 Classical Cryptography: Substitution and Vigenere Ciphers Notes Notes Sections 2.3 (skip 2.3.3) and 2.4 CoCalc Assignment 1
Day 2 Classical Cryptography: The Hill Cipher Notes Notes Sections 2.6 and 2.7 Mission 1 PDF TEX
Week 3 February 10th--15th
2/10 Classical Cryptography: Known Plaintext Attacks against the Hill Cipher; One-time pad, perfect secrecy and conditional probability Notes Notes Sections 2.9, 2.12 and 15.1
2/12 Euclid's Algorithm, Modular Exponentiation, Fermat's Theorem Notes Notes Sections 3.1, 3.2 and 3.3 Mission 2 PDF TEX
Week 4 February 17th--22nd
2/17 3 Pass Protocol, Chinese Remainder Theorem, Rings Notes Sections 3.4 and 3.5 CoCalc Assignment 3
2/19 Euler Phi Function, Euler's Theorem Notes Section 3.6 Mission 3 PDF TEX
Week 5 February 24th--March 1st
2/24 Finite fields, polynomials over finite fields, Primitive Roots, Quadratic Residues Notes Section 3.11 CoCalc Assignment 4
2/26 Legendre and Jacobi Symbols, Fermat Primality Test Sections 3.7,3.9,3.10 Mission 4 PDF TEX
Week 6 March 3rd--8th
3/2 Number Theory Review and Feistel Ciphers Notes Section 4.1
3/4 SDES Section 4.2 Mission 5 PDF TEX
Week 7 March 10th--15th
3/9 Review and Modes of Operation Notes Section 4.3.1
3/11 CANCELLED
Spring Break
March 16th--23rd
Week 8 March 24th--29th
3/23 Modes of Operation Notes Section 4.3.1
3/25 Midterm 1 Cocalc Assignment 5 (Fermat)
Week 9 March 31st-5th
3/30 Modes of Operation and Meet in the Middle Attacks Section 4.5
4/1 Meet in the Middle Attacks and Intro to SAES Section 5
Week 10 April 6th--12th
4/6 SAES Notes Notes Section 5 Cocalc Assignment 6
Day 2 RSA and Public Key Cryptography Section 6.1 and 6.3
Week 11 April 13th--April 19th
4/13 Solovay-Strassen Primality Test Notes Notes Section 6.3 Mission 6 PDF
4/15 Miller-Rabin Primality Test Notes Sections 6.2 and 6.4
Week 12 April 21st--April 26th
4/20 Dixon's Factorization Algorithm Notes Sections 6.7, 7.1 and 7.4 Mission 7 PDF
4/22 Discrete Logarithms and Diffie Hellman, Baby-Step Giant Step Sections 7.2 and 7.5
Week 13 April 28th--May 3rd
4/27 El Gamal, Baby Step Giant Step Sections 8.1 and 8.4 Mission 8 PDF
4/29 Midterm 2
Week 14 May 5th--May 10th
5/4 Hash Functions and Digital Signatures Notes
5/6 Digital Signatures/Birthday Attacks Notes
Week 15 May 12th--17th
Day 1 Elliptic Curves Mission 9 PDF
Beginning of Finals Period
Week 16
5/13 Final Exam (Section 101)
5/18 Final Exam (Section 002)