Math 314: Cryptography

Spring 2019

Date Lecture Notes Assigned Reading What is Due
Week 1 January 29--February 1st
Jan 29 Historical Cryptography. Intro to Sage and Latex.
Classical Cryptography: Caesar cipher and modular arithmetic
SNOW DAY
Jan 31 Classical Cryptography: Cryptanalysis and the Affine Cipher (Multiplication table modulo 26) Notes Chapter 1, Sections 2.1 and 2.2 Mission 0 PDF
Week 2 February 5th--8th
Feb 5 Classical Cryptography: Affine and Substitution Ciphers Notes Sections 2.2 and 2.4 CoCalc Sage Assignment 1
Feb 7 Classical Cryptography: The Vigenere Cipher Notes Sections 2.3 (skip 2.3.3) 2.6 and 2.7 Mission 1 PDF TEX
Week 3 February 12th--15th
Feb 12 Classical Cryptography: Hill Cipher; One-time pad Notes Sections 2.9, 2.12 CoCalc Sage Assignment 2
Feb 14 One Time Pad, Euclid's Algorithm Notes Sections 3.1, 3.2 and 3.3 Mission 2 PDF TEX
Week 4 February 19th--22nd
Feb 19 Modular Exponentiation, Fermat's Theorem Notes Sections 3.4 and 3.5 CoCalc Sage Assignment 3
Feb 21 Rings, 3 Pass Protocol Notes Section 3.6 Mission 3 PDF TEX
Week 5 February 26th--March 1st
Feb 26 Chinese Remainder theorem, Euler's Theorem, Finite fields, polynomials over finite fields Notes Section 3.6 CoCalc Assignment 4 (Wednesday)
Feb 28 Finite Fields Notes Sections 3.7,3.9 Extra credit: Decrypt this (Encrypted using a 3x3 Hill Cipher).
Week 6 March 5th--8th
Mar 5 Primitive Roots, Quadratic Residues, Legendre and Jacobi Symbols Notes Section 3.10 Mission 4 PDF TEX
Mar 7 Fermat Primality Test, Jacobi Symobls, Pseudoprimes Notes CoCalc Assignment 5
Week 7 March 12th--15th
Mar 12 Feistel Systems, DES Notes Section 4.1 and 4.2 Mission 5 PDF TEX
Mar 14 Midterm 1
Spring Break
March 18th--24th
Week 8 March 26th--29th
Mar 26 SDES Notes Sections 4.1 and 4.2
Mar 28 Modes of Operation, One time pad, perfect secrecy and Entropy Notes Sections 4.5, 15.1, 15.2, 15.4 CoCalc Assignment: Code SDES
Week 9 April 2nd-5th
Apr 2 Meet in the Middle Attacks, 3DES and Intro to AES Notes Section 4.5
Week 10 April 9th--12th
Apr 9 Decrypting SAES and practice Notes Section 5
Apr 11 RSA and Public Key Cryptography Notes Section 6.1 and 6.3 Mission 7 PDF TEX
Week 11 April 16th--April 19th
Apr 16 Solovay-Strassen and Miller-Rabin Primality Tests Notes Section 6.3
Apr 18 Dixon's Factorization Algorithm Notes Sections 6.2 and 6.4 Mission 8 PDF TEX
Week 12 Aptil 23rd--April 26th
Apr 23 Discrete Logarithms and Diffie Hellman Sections 6.7, 7.1 and 7.4 Cocalc Assignment 6
Apr 25 El Gamal, Baby Step Giant Step Notes Sections 7.2 and 7.5 Mission 9 PDF TEX
Week 13 April 30th--May 3rd
Apr 30 Hash Functions and Digital Signatures Sections 8.1 and 8.4
May 2 Midterm 2
Week 14 May 7th--May 10th
May 7 Digital Signatures/Birthday Attacks Notes Section 8.4, 9.5
May 9 Elliptic Curves Sections 16.1 and 16.2
Week 15 May 14th--17th
May 14 Elliptic Curve Diffie Hellman Worksheet Worksheet Mission 10 PDF TEX
Beginning of Finals Period
Week 16
5/21 Final Exam