Currently many states are considering proposals to replace
old-fashioned ballot boxes and punchcards with computer kiosks.
This poses both an opportunity to enhance democracy (by reducing
counting errors and other human error), yet at the same time a very
dangerous possibility of fraud if the machines are poorly
designed. Our democracy crucially depends on
uncorruptible machines, so this is a serious matter. Mathematics
has a surprising amount to say about this, as well as other important
topics in information security. The connection will be the main
theme of the course.
Course Requirements and Grading Guidelines:
The grade will be based homework assignments, a short paper assignment,
and quizes (together 30%), two midterms (each 20%), and a final exam or
project
(30%). The midterms will be held in class on Tuesday October 17th
and Tuesday November 28th.
Syllabus:
Part A: Historical Principles of Cryptography
Brief history of cryptography
Caeser cipher
Vigenere cipher
Language attacks
Part B: Some Important Modern Questions
Can mathematics guarantee secure conversations despite
eavesdroppers?
Why is it safe to use an ATM machine in the USA? What about
Europe?
Is it safe to use your credit card online?
Are Diebold's voting machines as secure as they claim, or
insecure as many academic experts insist. Can an election be
stolen by hackers?
Besides cryptography, what else does internet security require?
Part C: Mathematical aspects of modern cryptosystems
Diffie-Hellman key exchange and discrete logarithms