Mathematics 135, Spring 2004

Course information

under construction

Prerequites

The official prerequisite is math at the level of Math 100 (precalculus),
and exposure to use of a computer as a calculating tool, for example, a spread sheet program.

The course should be accessible to those with a thorough
command of addition and multiplication of integers and
motivated to do some creative problem solving.

If it has been a few years since you touched math, you might want to brush up on the basics.

Topics

Historical overview

The natural numbers
    Induction
    The infinitude of prime numbers
    Euclid's division algorithm (greatest common divisor)

Functions

Substitution ciphers
    arithmetic mod N
    examples -- Atbash, Caesar, Vignere, others

Transposition ciphers
Block ciphers

Classical cryptanalysis
    statistical tests
    Enigma

Computer based symmetric cryptography
    stream ciphers and bit blenders

Public key cryptography
    RSA
    factorization problem
    digital signatures

Ongoing themes:
Alternative uses of cryptography
    authenication, error correction, monuments
Cryptographic protocols and pitfalls
    attacks and counters
Complexity theory and the difficulty of decryption.

Paper

There will be a short (5 page) paper assignment. You will have to write an opinion on an issue of public policy relevant to the course. Part of the support for your argument should be based on quantitative reasoning, for example, sound estimates of how long, how expensive, or how likely.

Examples. How can electronic voting machines be made secure? What cryptographic measures are appropriate to protect copyrighted material from piracy? How should the government regulate the use of strong cryptography?

Exams

There will be in class prelims (tentative, Feb. 23, Mar. 29, Apr. 19) and a final (Tuesday, May 18, 3pm)

Homework

There will be weekly homework assignments. There may also be an occasional short quiz,
always announced in advance. The homework is an important part of the course. Much of your
learning will take place while doing it.

The homework covers material to go along with the class.  Please keep current with the homework.
As a rule, late homework will not be accepted.

Homework solutions will be placed on reserve in the math library.

Write homework solutions carefully, using good English, complete sentences, adequate detail, and
so on.

Working together on Homework

Discussion about the course in general and homework is encouraged; however,
I expect you will write up the solutions by yourself.
If the ideas come from other than you and the textbook, reference their source.

Working together on exams, prelims, quizzes: don't.

Permitted aids will be specified. Cornell has an academic integrity policy. 'nuff said. Remember too, it's a cryptology course.
 

Grading

The grade will be based on the homework and quizzes, the prelims, a writing assignment,
and the final.

A rough breakdown of the weights is:
Prelims, 50%
Final, 30%
Homework, 10%
Paper, 10%

Homework grading

Text

T. Barr, Invitation to cryptology.

H. Davenport, The higher arithmetic, chapter 1 handout.

Back to course home page. 
lawren@math.cornell.edu

Last modified: Sat Aug 19 09:29:56 EDT 2000