The impetus behind the freshman seminar Cryptology (Math 190) is
"For me, it’s largely an issue of paranoia," said
its instructor, Skip Garibaldi, assistant professor of mathematics
and computer science. "Once you know a little bit about a network—how
the wires are laid out—you realize that when you buy something
on the Internet, your credit card is being broadcast to a lot of
different computers. It’s not like you’re just calling
up the company and talking to an operator. It’s very easy
to download some software that can just capture credit card numbers."
To curb that sort of criminal activity, companies encrypt their
websites so that credit card numbers are protected. Those encryption
programs are based on mathematics rules, which form the basis of
"I’ve never taught a class like this before," said
Garibaldi, who is leading his first freshman seminar since coming
to Emory from UCLA in 2002. "It’s one-third humanities,
one-third math and one-third lab." The seminar is one of three
classes he is teaching this semester. The others are a freshman-level
course in life sciences calculus and a graduate seminar in algebra
and number theory.
Right now the class is in the midst of the mathematics portion,
which focuses on computations dealing with prime numbers and divisibility.
These exercises will set up the final portion of the class introducing
encryption codes used on credit cards and the Internet. Those codes
are based on the mathematic properties the students are exploring.
"Sometimes when you swipe your credit card, the computer already
knows it’s bad in the sense that you didn’t get a good
swipe," Garibaldi said. "How do they tell? Sometimes they
get the data, but it is scrambled for whatever reason. There is
a way to check if that number is correct without having a full list
of the numbers, because that’s private information. There’s
a way to tell from just the first few numbers whether it’s
valid or not, and it’s all based on divisibility. My end goal
is to try and relate cryptology and the mathematics behind it to
things people see every day."
The class uses just one textbook—a dictionary-sized, 1,180-page
tome called The Code-breakers—which Garibaldi said
is the only reputable historical text on cryptography. It’s
not exactly new (it was published in 1967), but its description
of the subject’s history and the tools of the cryptographer
was so accurate that the manuscript had to be submitted to the Department
of Defense for approval.
The rest of the classroom materials—including a handful of
articles on the history of cryptography, two websites describing
the modern, electronic cryptography, and selections from the book
Identification Numbers and Check Digit Schemes, which provides
the class with most of their math problems—were not as stringently
reviewed but are no less crucial to the course.
"Books either fall into this ‘historical/no math’
category or they cover junior- or senior-level mathematics,"
Garibaldi said. "A cryptology course at this level is a very
Garibaldi spent the beginning of the semester discussing
the history of cryptology and some of the social issues surrounding
it. He split the 15-member class into four groups and gave them
messages to encrypt (some used encrypting techniques dating to
time). Once that was complete, the messages were given to the other
groups to decrypt.
"In the old days, people had to do things by hand," Garibaldi
said. "This way the students got to experience that, like
if they had worked for the National Security Agency."
The algebra-tinged math portion was augmented by writing assignments.
Not only did students have to solve problems numerically, they
had to describe how they did it. That wasn’t always easy,
Garibaldi said, because we are not conditioned to think about mathematics
While Garibaldi’s historical discussion provided students
the tools past cryptographers used in their art, that is not the
goal of the course’s portion on modern cryptography. Instead,
Garibaldi wants to point out the strength of current technology.
"The minimum goal of this class," he said, "is to
teach everyone that they should never send their credit card number
on the Internet without that little padlock on the bottom of the page."