Kevin Milans : Teaching : Spring 2014 Math373/578

Kevin Milans (milans@math.wvu.edu)
Office: Armstrong Hall 408H
Office Hours: MW 9:30am-10:30am, Thurs 1pm-2pm, and by appointment
Class Meetings: MW 8:30am-9:20am in Armstrong Hall 117
Homework Workshops: W 5:00pm-6:00pm in Armstrong Hall 119
Text: An Introduction to Mathematical Cryptography, by J. Hoffstein, J. Pipher, and J. Silverman.

Home | Course Syllabus (PDF) | Homework

Course Schedule

No. Date Class Summary Section(s) Quiz Quiz Soln Comments
1 Jan 8 Introduction; Caesar Cipher 1.1 - - -
2 Jan 10 Substitution Ciphers 1.{1,2} pdf pdf Quiz 0 in class; HW1 available.
3 Jan 13 Divisibility 1.2 - - -
4 Jan 15 Greatest Common Divisor; Euclidean Algorithm 1.2 - - -
5 Jan 17 Algorithm Analysis 1.2 pdf pdf Quiz 1 in class; HW2 available.
6 Jan 22 Modular Arithmetic I 1.3 - - Note: HW2 has been modified.
7 Jan 24 Modular Arithmetic II 1.3 pdf pdf Quiz 2 in class; HW3 available.
8 Jan 27 Group of Units; Caeser Cipher and Modular Arithmetic 1.3 - - -
9 Jan 29 Fast Powering Algorithm; Primes; Fun. Thm. of Arith. 1.4 - - -
10 Jan 31 Test 1 in class 1.{1-3} pdf pdf HW4 available.
11 Feb 3 Order of primes in integers 1.4 - - -
12 Feb 5 Finite Fields; Modular Exponentiation 1.{4-5} - - -
13 Feb 7 Fermat's Little Theorem 1.5 pdf pdf Quiz 4 in class.
14 Feb 10 Applications of FLT; Order of elts. in finite fields 1.5 - - HW5 available.
15 Feb 12 Primitive Roots 1.5 - - -
16 Feb 14 History of Cryptography; Formal Cryptosystems 1.{6-7} pdf pdf Quiz 5 in class; HW6 available.
17 Feb 17 Properties of ciphers 1.7 - - -
18 Feb 19 Examples: multiplicative cipher; affine cipher 1.7 - - -
19 Feb 21 Exclusive-or; Pseudorandom generators 1.7 pdf pdf Quiz 6 in class; HW7 available.
20 Feb 24 Asymetric ciphers; Discrete Logarithm; Diffe-Hellman 1.7,2.2,2.3 - - HW7 updated.
21 Feb 26 ElGamal 1 2.4 - - -
22 Feb 28 Test 2 1.4-1.7, 2.2, 2.3 pdf pdf -
23 Mar 3 Snow Day: No Class - - - -
24 Mar 5 ElGamal vs. Discrete Log Problem 2.4 - - -
25 Mar 7 Class canceled due to jury duty - - - No quiz today.
26 Mar 17 Big-Oh notation; algorithm analysis 2.6 - - HW8 assigned.
27 Mar 19 Shanks's Algorithm for DLP 2.7 - - -
28 Mar 21 Chinese Remainder Theorem I 2.8 pdf pdf Quiz 8 in class
29 Mar 24 Chinese Remainder Thm II; Choice of p and g 2.8,2.9 - - HW9 assigned.
30 Mar 26 Euler's formula for pq 3.1 - - -
31 Mar 28 Euler's formula for pq 3.1 pdf pdf Quiz 9 in class
32 Mar 31 Euler's formula for pq; RSA 3.1,3.2 - - HW10 assigned.
33 Apr 2 RSA; Equivalence of factoring N and computing N' 3.2 - - -
34 Apr 4 Test 3 2.4-3.1 pdf pdf HW10 due.
35 Apr 7 Factoring N vs computing N'; Man-in-the-middle 3.2, 3.3 - - HW11 assigned.
36 Apr 9 Other Implementation Concerns 3.3 - - -
37 Apr 11 Miller--Rabin Primality Testing I 3.4 pdf pdf HW11 due; Quiz 11 in class
38 Apr 14 Miller--Rabin Primality Testing II 3.4 - - -
39 Apr 16 Elliptic Curves 5.1 pdf pdf HW12 due; Quiz 12 in class
40 Apr 21 Elliptic Curves II 5.1 - - HW13 assigned.
41 Apr 23 Elliptic Curve Cryptography 5.2,5.4 - - -
42 Apr 25 Other topics: Quantum Computers, Lattice Based Cryptography, Digital Signatures - - - HW13 due.
- Apr 30 Final Exam: 11am-1pm - - - -

milans@math.wvu.edu