Kevin Milans : Teaching : Spring 2022 Math373

Kevin Milans (milans@math.wvu.edu)
Office: Armstrong Hall 408H
Office Hours: MW 2:30pm-3:30pm, and by appointment
Class Meetings: MWF 10:30am-11:30am in Hodges Hall 220
Home | Course Syllabus (PDF) | Homework

Course Schedule

No. Date Class Summary Section(s) Quiz Quiz Soln Comments
1 Jan 10 Introduction; Caesar cyhpers 1.1 - - -
2 Jan 12 Substitution cyphers 1.1 - - HW1 posted.
3 Jan 14 Divisibility; Extended Euclidean Algorithm 1.2 quiz0.pdf quiz0-soln.pdf Quiz 0 in class.
- Jan 21 No Class: MLK Day - - - -
4 Jan 19 Class Canceled. HW1 extended to Fri Jan 21. - - - HW2 posted.
5 Jan 21 Analysis of Extended Euclidean Algorithm 1.2 quiz1.pdf quiz1-soln.pdf HW1 due. Quiz 1 in class.
6 Jan 24 Modular Arithmetic 1.3 - - -
7 Jan 26 EEA Pseudocode; Multiplicative Inverses 1.3 - - HW2 due. HW3 posted.
8 Jan 28 Group of units; Euler Phi Function 1.3 quiz2.pdf quiz2-soln.pdf Quiz 2 in class.
9 Jan 31 Modular Exponentiation 1.3.2 - - -
10 Feb 2 Fundamental Theorem of Arithmetic; Finite Fields 1.4 - - HW3 due. HW4 posted.
11 Feb 4 Powers; Fermat's Little Theorem; Fermat Primality Test 1.5 - - Test 1 postponed (weather)
12 Feb 7 Test 1: Classes 1 through 10; 1.1-1.4 - test1.pdf test1-soln.pdf -
13 Feb 9 Primitive Roots; Brief history 1.5,1.6 - - HW4 due. HW5 posted.
14 Feb 11 Simple ciphers: Definitions, Theory 1.7 quiz4.pdf quiz4-soln.pdf Quiz 4 in class.
15 Feb 14 Encodings; Multiplicative cipher 1.7 - - -
16 Feb 16 Block ciphers; Exclusive-OR cipher; Pseudorandom sequences 1.7 - - HW5 due. HW6 posted.
17 Feb 18 Discrete Logarithm 2.2 quiz5.pdf quiz5-soln.pdf Quiz 5 in class.
18 Feb 21 Diffie--Hellman Key Exchange; ElGamal Cryptosystem 2.3, 2.4 - - -
19 Feb 23 Elgamal Cryptosystem II 2.4,2.6 - - HW6 due. HW7 posted.
20 Feb 25 Algorithm Analysis; Complexity; Big-Oh Notation 2.6 quiz6.pdf quiz6-soln.pdf Quiz 6 in class.
21 Feb 28 Shanks's Baby-step/Giant-step Algorithm 2.7 - - -
22 Mar 2 Chinese Remainder Theorem 2.8 - - HW7 due. HW8 posted.
23 Mar 4 Test 2: Classes 11 through 21; Sections 1.5-1.7, 2.2-2.4, 2.6, 2.7 - test2.pdf test2-soln.pdf -
24 Mar 7 CRT: Complex example 2.8 - - -
25 Mar 9 Discrete Root Problem 3.1 - - HW8 due.
26 Mar 11 Euler's Theorem for Products of 2 Primes 3.1 quiz8.pdf quiz8-soln.pdf Quiz 8 in class.
27 Mar 21 RSA Cryptosystem 3.2 - - -
28 Mar 23 RSA Cryptosystem II 3.2 - - HW9 posted.
29 Mar 25 Implementation/Security Concerns; RSA Signatures 3.3,4.2 - - -
30 Mar 28 Prime Number Theorem; Carmichael numbers; Miller-Rabin Primality Test I 3.4 - - HW10 posted.
31 Mar 30 Miller-Rabin Primality Test II 3.4 - - HW9 due.
32 Apr 1 Elliptic Curves: background 5.1 quiz9.pdf quiz9-soln.pdf Quiz 9 in class.
33 Apr 4 Elliptic Curve Groups; Multiplicataion of points 5.1 - - -
34 Apr 6 Elliptic Curves: Point at infinity/identity element 5.2 - - HW10 due. HW11 posted.
35 Apr 8 Test 3: Classes 22 through 33; Sections 2.8, 3.1-3.4, 4.2, 6.1 - test3.pdf test3-soln.pdf -
36 Apr 11 Elliptic Curves over Finite Fields 5.2 - - -
37 Apr 13 Elliptic Curve Cryptography 5.3,5.4 - - HW11 due. HW12 posted.
38 Apr 18 Post-quantum cryptography; polynomial rings 8.11,2.10 - - -
39 Apr 20 Polynomial GCDs, Extended Euclidean Algorithm for polynomials 2.10 - - HW12 due. HW13 posted.
40 Apr 22 Polynomial Quotient Rings 2.10,7.9 quiz12.pdf quiz12-soln.pdf Quiz 12 in class
41 Apr 25 NTRU Cryptosystem 7.10 - - -
42 Apr 27 Lattice Problems: SVP, CVP; NTRU Key Recovery as an SVP problem 7.10 - - HW13 due.
43 Apr 29 Review - - - -
- May 5 Final Exam: Thursday May 5, 2pm-4pm - - - -
milans@math.wvu.edu