Course Calendar, Reading and Hmw Assignments for Math 328

It is expected that you read all the sections to be covered BEFORE the class and come to class prepared to present and discuss the topics.

Date Section/Topic Covered Written Homework to be Collected and Reading Assignment Problems to be presented/discussed in class
Tue, Jan 15 Course Overview and Introduction

Due Thu, Jan 17 (sections 1.2-1.6)
Read 1.1, do all exercises in 1.2 and 1.3: 4,5, 1.4.1, 1.6:2ab,5,.7
Important Note: In all homework problems in this course, show your work and reasoning. Simply giving answers is not good enough.

 1.3:6-8, 1.6:2cd,6, 9,10 
Thu, Jan 17 1.2-1.6

Due Tue, Jan 22
1.7.1-.3, 1.8.1, 1.9:5,6, 1.10: 2,4,5d

 1.8.2-4,1.9.7ab , 1.10.5a,b
Tue, Jan 22 1.7-1.10 Due Thu, Jan 24
1.11: 2,4,10d,12abd,20     1.12: 12e(part ii only),13a(part iii only),14e 		1.11: 3c, 5,10a,12f,13,18,19f,     1.12: 5-8,12a,15,16
Thu, Jan 24 1.11-1.12 Due Tue, Jan 29
2.1: 1f,2,     2.2: 3c,7c,8,     2.3: 4f,8c,10bc,16,21,23ae		 2.1: 1abcd, 4    2.2: 3bd,4,5,7b,10     2.3: 4cg,7bd,8bd,10ad,17,18, Give a proof for Thm 2.3.19
Tue, Jan 29 2.1-2.3 Due Thu, Jan 31
2.4: 1,2,6BD    2.5: 3b,6b,10a    2.6: 5d,6a,7e,10a,11		 2.4: 3,4,6C    2.5: 3f,6f,10g,11,12f    2.6: 7d,12,13 (for 2.6.7d)
Thu Jan 31 2.4-2.6 Note: The definition of a parity check matrix of a code in the textbook is the transpose of the standard definition that is universally agreed upon in the literature.
Due Tue, Feb5
2.7: 4e,5h,9c    2.8: 4b,10b,12a    2.9: 4a (no need to check the weight of each codeword), 5a

 2.7: 4f,9b,10, 11   2.8:   5,6,11a,13,14     2.9: 4b,5b
Tue Feb 5 2.7-2.9 Due Thu, Feb7
2.10: 7b,8c    2.11: 2ab,8a,14,20   		 2.10: 6ab,7f,8a,9    2.11: 2cd,9b,11,16,17,19a,21    2.12: (2.10.6b, 2.10.7b)
Thu, Feb 7 2.10-2.12 Study for the test  
Tue, Feb 12 Midterm Exam I

Project 1 handed out, due Thu Feb 28.

  
Thu, Feb 14 Introduction to Magma


Due Tue, Feb 19: Magma Hmw     3.1: 5c,18e, 19e, 20;   3.2: 5,6 

 3.1: 5aef, 19f ,22
Tue, Feb 19 3.1, 3.2 Due Thu, Feb 21:    3.3: 4ab,5ab(figure out how to use Magma for this);   3.4:3,7     3.5:1  3.3: 5c,7,8,10;   3.4:3,5,6     3.5: 2,3,4 
Thu, Feb 21 3.3-3.5 Due Tue, Feb 26:    3.6: 5i,6bc;   3.7:3a,4 3.6: 5i,6bc;   3.7:3a,7-10
Tue, Feb 26 3.6-3.7 Due Thu, Feb 28:    4.1: 11b,14,21c;   A.4a, 4.2: 7c, 8, 9

4.1: 3,7,11c,19b,20b,21b,22   A.6, 4.2: 7ab
Learn how to factor polynomials in Magma.
Learn how to compute gcd of two polynomials is Magma
Thu, Feb 28 4.1, AppA, 4.2 Due Tue, March 19:  4.3: 4,5b,6,8  4.4: 6cde,8,9ac(gen poly only)15b, 4.5: 5g (you can use Magma) 4.3: 4,5ab;6,8,9d,   4.4: 6cde,8,9ac,10,15b, 4.5: 5fg
SPRING BREAK
Tue, March 19 4.3-4.5

Read Chp1, 2.1-2.10 of T&W, and Module pages 3-7. Turn in problems 1-5 from the module. Optional video lecture on an overview of cryptography. Reading Quiz next class.

 
Thu, March 21 Intro Crypto & Classical Cryptosystems

Read pages 7-17 of the module. Due Tue, March 26: Problems 6, 8, 10, 11, 12, 13, 14 from the module. Reading Quiz next class.

Problems 6-15 from the module.
Tue, March 26 NT and Comp Complexity

Read sections 3.2-3.7 from Trappe & Washington. Reading Quiz next class.

Due Thu, March 28: Problems 1-4, 8-17,20,24 from Chp3 exercises in Trappe & Washington.

Problems 1-4, 8-17,20,24 from Chp3 exercises in Trappe & Washington.

Check out this seminal paper: PRIMES are in P. Also see these papers A breakthrough, The Status of P vs NP
Thu, March 28 Square-and-Multiply, NT

Read pages 17-27 from the module, and section 6.1 from T&W.

Due Tue, Apr 2: Problems 16-18 from the module and Problems 1-5 from Chp6 exercises in T&W

  Problems 16-18 from the module and Problems 1-5 from Chp6 exercises in T&W
Tue, Apr 2 RSA    
Thu, Apr 4 RSA Problems

Project Proposal is due today.

Guidelines for Exam Review

 
Tue, Apr 9 Midterm Exam II

Work on the final project

  
Thu, Apr 11 Discrete Log, DH Key Exchange and ElGamal. A video.

Work on the final project

Tue, Apr 16 Digital Signatures, Hash Functions

Project Outline is due today. Read this article before Thu. Work on the final project

 
Thu, Apr 18 Code-Based Cryptography, Zero Knowledge Proofs, Eq of Int Fact and Computing Sqrt mod n

Work on the final project

 
Tue, Apr 23 Finite Fields and Irreducible Polynomials

Work on the final project

 
Thu, Apr 25 Roots of Unity, Factorization of x^n-1, and BCH codes

Complete draft is due today. Prepare project presentation. Everyone must be ready to present on Tue, Apr 30. The last hmw set is due Thu May 2.

 
Tue, Apr 30 Project Presentations

 

  
Thu, May 2 Project Presentations Final Paper due Wed, May 8, 1:30 pm. Submit it electronically as an email attachment.