Math 314: Cryptography

Spring 2018



Note: Day 1 is Monday (Section 001) and Tuesday (Section 002). Day 2 is Wednesday (Section 001) and Thursday (Section 002).
Date Lecture Notes Section 001 Notes Section 002 Assigned Reading What is Due
Week 1 January 29--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 Mission 0 PDF
Week 2 February 5th--8th
Day 1 Classical Cryptography: Substitution and Vigenere Ciphers Notes Notes Sections 2.3 (skip 2.3.3) and 2.4 CoCalc Sage Assignment 1
Day 2 Classical Cryptography: The Hill Cipher Notes Notes Sections 2.6 and 2.7 Mission 1 PDF TEX
Week 3 February 12th--15th
Day 1 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 Cocalc Sage Assignment 2
Day 2 Euclid's Algorithm, Rings Notes Notes Sections 3.1, 3.2 and 3.3 Mission 2 PDF TEX
Week 4 February 19th--22nd
Day 1 Chinese Remainder Theorem, Modular Exponentiation, Fermat's Theorem Notes Notes Sections 3.4 and 3.5 CoCalc Sage Assignment 3
Day 2 3 Pass Protocol, Euler Phi Function, Euler's Theorem Notes Notes Section 3.6 Mission 3 PDF TEX
Week 5 February 26th--March 1st
Day 1 Finite fields, polynomials over finite fields Notes Notes Section 3.11 CoCalc Assignment 4
Day 2 Primitive Roots, Quadratic Residues, Legendre and Jacobi Symbols Notes Notes Sections 3.7,3.9,3.10 Mission 4 PDF TEX
Week 6 March 5th--8th
Day 1 Number Theory Review and Feistel Ciphers Notes Section 4.1 CoCalc Assignment 5
Day 2 SDES Notes Notes Section 4.2 Mission 5 PDF TEX
Week 7 March 12th--15th
Day 1 SDES and Differential Cryptanalysis Section 4.3.1
Day 2 Midterm 1
Spring Break
March 18th--24th
Week 8 March 26th--29th
Day 1 SDES and Differential Cryptanalysis Notes Notes Section 4.3.1 CoCalc Assignment 6
Day 2 DES, 2DES, and Meet-In-The Middle Attacks, 3DES Notes Notes Sections 4.4.1 and 4.7
Week 9 April 2nd-5th
Day 1 Modes of Operation and Intro to AES Notes Notes Section 4.5 Mission 6 PDF
Day 2 SAES Notes Notes Section 5
Week 10 April 9th--12th
Day 1 Decrypting SAES and practice Notes Section 5
Day 2 RSA and Public Key Cryptography Notes Notes Section 6.1 and 6.3 Mission 7 PDF
Week 11 April 16th--April 19th
Day 1 Solovay-Strassen and Miller-Rabin Primality Tests Notes Notes Section 6.3
Day 2 Dixon's Factorization Algorithm Notes Notes Sections 6.2 and 6.4 Mission 8 PDF TEX
Week 12 Aptil 23rd--April 26th
Day 1 Discrete Logarithms and Diffie Hellman Notes Notes Sections 6.7, 7.1 and 7.4
Day 2 El Gamal, Baby Step Giant Step Sections 7.2 and 7.5 SMC Assignment 7
Week 13 April 30th--May 3rd
Day 1 Hash Functions and Digital Signatures Notes Sections 8.1 and 8.4 Mission 9 PDF TEX
Day 2 Midterm 2
Week 14 May 7th--May 10th
Day 1 Digital Signatures/Birthday Attacks Notes
Day 2 Elliptic Curves Notes
Week 15 May 14th--17th
Day 1 Elliptic Curve Diffie Hellman Worksheet Worksheet Mission 10 PDF TEX
Beginning of Finals Period
Week 16
5/21 Final Exam (Section 001)
5/22 Final Exam (Section 002)