Mathematics 103

Honors Section (H1)

Fall 2010

Prof. Stephen Miller

Topics in Mathematics for Liberal Arts: Cryptography

Meets TF3 at 11:30A-12:50 in Scott Hall room 219, on the College Avenue Campus

Our use of the internet depends strongly on secrets: secrets of what we send others, and secrets that enable us to authenticate ourselves to services we use. The methods that we use today to keep our information private and safe (or so we think...) are relatively recent, developed only in the late 1970s. The depend strongly on mathematics, mathematics that we will introduce in this course.  

Course Requirements and Grading Guidelines:

The grade will be based homework assignments, a short paper assignment (together 30%), two midterms (each 20%), and a final term paper project (30%).  The midterms will be held in class on Friday October 15th and Friday December 10th.

Syllabus:

Part A: Historical Principles of Cryptography

1. Brief history of cryptography
2. Caeser cipher
3. Vigenere cipher
4. Language attacks

Part B: Some Important Modern Questions

1. Can mathematics guarantee secure conversations despite eavesdroppers?
2. Why is it safe to use an ATM machine in the USA?  What about Europe?
3. Is it safe to use your credit card online?
4. Are Diebold's voting machines as secure as they claim, or insecure as many academic experts insist.  Can an election be stolen by hackers?
5. Besides cryptography, what else does internet security require?

Part C: Mathematical aspects of modern cryptosystems

1. Diffie-Hellman key exchange and discrete logarithms
2. RSA cryptosystem
3. Hash functions and their security

Assignments:

Problems are taken from Wesley Pegden’s course materials: click here for part 1, part 2, part 3, and errata.

Assignment 1: (Due in class Tuesday October 5) Exercises 1.7.1, 1.7.2, 1.7.4, 1.7.5, 1.7.6

Assignment 2: (Due in class Tuesday October 19) Exercises 2.1.1, 2.1.2, 2.1.3, 2.1.4, 2.1.5, 2.1.6, 2.1.7, 3.2.4, 3.2.5, 3.3.1, 3.3.2

Assignment 3: (Due in class Tuesday November 2) Exercises 3.3.3, 3.3.4, 3.4.1, 3.4.2, 3.5.1, 3.5.5, 3.5.6, 3.5.7, 3.5.8, 3.6.1

Assignment 4: (Due in class Tuesday November 16) Exercises 3.8.1, 3.8.2, 3.9.1, 3.9.2, 3.9.3, and 3.9.4

Assignment 5: (Due in class Tuesday December 7) click here for the assignment

Course Materials/Links:

• Rivest article on voting machines.
• Professor Greenfield's 1999-2000 course.
• External site about e-voting, with information about the Maryland case.
• Article in Discover Magazine about e-voting.
• RSA Security's excellent Crypto FAQ.
• Ron Rivest's Cryptography and Security page.
• Microsoft Research Cryptography and Anti-Piracy homepage.