CSC 7002, Graduate Computer Security (Spring 2008)

University of Colorado at Denver

Department of Computer Science

Automatically updated on 28 January 2008

[ Instructor | Class Time and Room | Textbooks | Prerequisites | Grades | Schedule | Student Page | Academic Deadlines (pdf) ]

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Instructor
Dr. Ellen Gethner
Email: ellen dot gethner at cudenver dot edu
Office: North Classroom 2604-A3
Phone: (303) 556 2358 (use at your own risk)
Office hours:

Mondays: 2:15-3:45pm; 8:15-9:15pm
Tuesdays: 11:30am-12:30pm
Wednesdays: 2:15-3:45pm
and by appointment

Class Time and Room
MONDAYS 5:30-8:15pm North Classroom 3004
Textbooks

Behrouz A. Forouzan, Cryptography and Network Security (required)
Richard Clark, Breakpoint (required)
Hutchinson and Albertson Undergraduate Discrete Math Text (optional help)

Prerequisites
CSC 5451 (graduate algorithms) or an Advanced Number Theory Course.
Subject Matter

As long as information (of any kind) is considered valuable, attempts will be made to steal it. In modern times, computers are the heaviest conveyors and receivers of information, and with the constant improvements in technology, the issue of security is a difficult, rapidly changing, and often fascinating subject. This course will be a broad overview of computer security, roughly divided into three (unequal) components: a) the history of codes and ciphers (including, for example, ancient forms of secret writing, the WWII Enigma machine, the Navajo Codetalkers), b) basic cryptographic techniques and c) applications to current and future computer-related technologies (for example, network security, wireless communication, and quantum cryptography).

Grades

Assignments: Homework assignments (4) will count toward 35% percent of your grade. Each assigment will have an assortment of straightforward problems as well as challenging problems. Write up your ideas on all of the problems that you have given some thought to, even if you do not believe you have a complete solution. Be sure to be neat, write in complete sentences, and do not leave out any steps: clarity of exposition may contribute toward a positive score. Please talk to one another about the assignments, but the write-ups should be done individually, giving credit where credit is due.
Late assignments: None. I will drop your lowest score. There are no exceptions.
Cheating: We will vigilantly ascribe to the UC Cheating Policy.
Projects

Project Proposal (10%): One page project proposal, due date to be announced.
Project Paper (35%): at most 8 pages not including tables, figures, and references, single spaced, fullpage margins, 12pt font
Class Presentation of Project (10%): About 45 minutes.

Current Events (10%): Each week one member of class will be charged with the computer security news for the week. Good (quality) sources are the New York Times, SlashDot, BBC webpage, and Google News (as well as many many others). This should take about fifteen minutes at the end of each class. I will be in charge of week 1.

Schedule (subject to change)

Lecture Date Current Events/ Pizza Orderer Topic Reading/Comments Assignments

One 28 January 2008 EG/ Joe W. History of Codes and Ciphers, From Queen Mary of Scots to the Navajo Code Talkers of WWII Class Notes

Two 4 February 2008 Jason B./ John C. Background Number Theory Selections from Chapters 1 and 2 in our textbook. Hierarchy of numbers; formal definition of division; divisors and proper divisors; prime numbers; GCD (You should review the Euclidean and Extended Euclidean Algorithm on your own in Ch 1); relatively prime numbers; Euler's Phi function; modular arithmetic; equivalence relation Homework 0 handed out in class on 28 Jan is due on 11 February. It is also posted on the Student Page.

Three 11 February 2008 Group Theory, Fermat's Little Theorem Equivlance relations revisited; examples of Groups both finite and infinite; order of an element in a group; order of a group; Theorem 2.9.2; order of a subgroup of a group (Theorem 2.10.9); Grand Finale: proof of Fermat's Little Theorem (needed for RSA later on)

Four 18 February 2008 Selections from Chapter 3 in Buchmann From Chapter 3: Encryption Schemes, Alphabets and Words, Permutations, Block Ciphers, Simple Example of Stream Cipher, Affine Ciphers. HW 1 coming soon

Five 25 Feb 2008 Secret Sharing Schemes Leftover from last time: affine and stream ciphers. For today: start Secret Sharing Schemes; this material is not in our book, but you should read and review basic properties of square matrices (See review of determinants ). The main scheme we will cover is the Threshold Scheme (two different approaches).

Six 3 March 2008 DES: Selections from Chapter 5 in Buchmann. History of DES; Encryption process; Decryption; Expander function; S-boxes and their output; Key; the function f that takes the modified key and part of the text as input; mulitple Rounds of DES; Present-day lack of Security in DES, which led to the new Encryption Standard, namely AES. Warmup for AES: the mathematics of Fields: Galois Fields, particularly the one of order 256 and its relation to the irreducible polynomial x^8 + x^4 + x^3 + x + 1 with coefficients from the field Z_2.

Seven 10 March 2008 AES Guest speaker: Bille Roche. Multiple Key Lengths; 10 Rounds; Input/Output sizes; ByteSubTransformation (non-linear); ShiftRow Transformation (diffuses bits over multiple rounds); MixColumn Transformation (same purpose as ShiftRow); AddRoundKey (XOR this key with the output of the previous layer)

Eight 17 March 2008 Public Key Cryptography and RSA: Selections from Chapter 7 Global Procedure (a high level view of RSA); tranlsation of plaintext to a numerical message; Encryption process [public key=(n,e)]; Decryption process [private key=(p,q,d)]; False proof of correctness; True Proof of correctness; Digital Signature; Discussion of the security of RSA and its history Project proposal due.

Nine 24-30 March 2008 Spring Break Read Breakpoint and be prepared for discussion after break.

Ten 31 March 2008 Quantum Cryptography and the breakage of RSA Peter Shor's 1994 quantum algorithm that led to the breakage of RSA on any classical computer: that is, integer factorization can be done in polynomial time.

Eleven 7 April 2007 Elliptic Curve Cryptosystems (and a few warmps) Finite Fields (again); Discrete Log Problem; ElGammal Cryptosystem; Elliptic Curve Cryptosystems; Elliptic Curves mod N; Representing Plaintext on an elliptic curve; Factoring integers using elliptic curves; An Elliptic Curve ElGammal Cryptosystem;

Twelve 14 April 2008 Flipping Coins and Playing Poker over the phone Tools: Fermat's Little Theorem and Quadratic Residues [NOT INCLUDED ON THE 2008 PhD COMPREHENSIVE EXAM]

Thirteen 21 April 2008 Project Presentations

Fourteen 28 April 2008 Project Presentations

Fifteen 5 May 2008 Project Presentations

Sixteen Finals Week Project Presentations