New crytography course explores Internet data protection.
The Battle of the Atlantic was the longest continuous military campaign of World War II, running six years through Germany’s defeat in 1945 and claiming more than 100,000 lives.
It might have stretched on even longer without the work of British code breakers, including the famous Alan Turing.
The German navy used cryptography to encode messages between submarines seeking to enforce a blockade of the United Kingdom. But Turing—a founding father of computer science—and other cryptanalysts cracked the code, enabling safe passage for merchant ships and helping hasten the war’s end.
“The minimal estimate by historians is that British cryptanalytic work shortened the war by at least two years,” said Eugene Luks, head of the Department of Computer and Information Science at the UO. “A less conservative appraisal is that it was the key to victory.”
Luks’ department has long recognized the historical importance of cryptography in course offerings and research. Now the Department of Mathematics is teaching cryptography, too—an acknowledgment of the ubiquity of this security measure in the Internet age.
A new math course, The Mathematics of Cryptography, based on the numerical concepts underpinning cryptography, explores the basic cryptosystems used in most Internet communication.
“The mathematics involved is both elegant and interesting,” said Hal Sadofsky, head of the Department of Mathematics. “One of the fascinating things about cryptography is that it uses number theory in an essential way.”
In computer and information science, cryptography course work includes two classes taught by Luks: a 400-level course and a freshman seminar, both of which cover WWII code-breaking efforts.
The department is also experimenting with 400- and 500-level courses, aiming to establish a permanent offering. The math department’s entry into the world of cryptography adds another dimension for students.
“Mathematics had been critically applied in pre-Internet cryptography, and much modern cryptography applies number theory as well as other branches of mathematics,” Luks said. “We were delighted to see the mathematics department add the course.”
The math course, a standard offering taught for the first time last fall, covers finite field arithmetic, the discrete logarithm problem, Monte Carlo methods for generation of large prime numbers and techniques for factorization of large integers.
While this might sound like a daunting array of concepts, the real-world applications of cryptography make the topic easier for students to grasp, said Dan Dugger, an associate professor of mathematics who was instrumental in launching the course.
Dugger has been pushing the department to add math courses that are relevant for other majors, and he believes there is broad interest among students who enjoy math simply for math’s sake. Fifteen students took the course last fall, including some who are majoring in biology or physics.
“A lot of students have seen number theory or algorithms, but it doesn’t stick in your brain the first time around,” Dugger said. “It’s the same way with anything—if you’re learning an abstract concept, you don’t necessarily engage with it fully. If you’re learning it for a reason, you can engage with it in a more solid way.”
In the online world, encrypted data is only as secure as the complicated mathematical algorithms that act as “keys” for two parties in communication—say, you and your bank. If a third party can solve the math equation, the code is broken.
During the first third of the course, students learn techniques for public- key cryptography, which requires the production of large prime numbers, about 300 digits long. Dugger next explores the computationally difficult problem of factorization of huge numbers that are not prime, as this is believed to be the only way the codes can be broken. The final third of the syllabus is left to the instructor’s discretion; Dugger covered the basics of quantum computation.
Junior Travis Scholl, a math major who is considering careers in cryptography, said he enjoyed putting into practice algorithms and other concepts that heretofore had resided only in textbooks and lectures.
“I really enjoyed the end where we studied quantum cryptography,” Scholl said. “It made me want to go more in- depth into the subject.”
-Matt Cooper
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