Honors Math 103 – Cryptography
(01:640:103 H1)
A special honors section of the Topics in Mathematics course was
introduced in the Fall 1999 semester by Professor Stephen
Greenfield under the name: The Mathematics of Communications: keeping
secrets.
History and philosophy of the course
The catalog description of 103 is not relevant. The following description applies in Spring 2008 and should give a good general sense of the course, though details will vary with the instructor.
Imagine an internet without privacy: your e-mails could be read by any motivated eavesdropper, your credit card and bank account information would be public knowledge, and the passwords you enter could never be secret. You could pretend to be anyone, and anyone could pretend to be you. The internet would be brought to its knees without its users trusting that it could keep secrets. But do we actually live in such a world?
This course is about cryptology, the science of hiding information. Historically, sharing secrets over long distances typically meant two parties first had to agree on a password, and then send messages to each other using their secret password. But how can they agree on a password in the first place unless they meet in person, or have a trusted courier?
We will focus mainly on the amazing breakthroughs made in the last 30 years which effectively exploit difficult mathematics problems as a trusted courier. It used to be that these problems frustrated mathematicians; now they are used as locks, challenging problem solvers to pick them. They enable two people who have never met nor communicated with each other to share secrets in public. The problems are typically very simple to state and understand, but practically speaking nobody knows how to solve them fast enough to break these "locks". How do they work? What would it take for someone to break them? What would happen then?
The course will consist of three parts. In the first part we describe some traditional cryptographic ciphers, and the mathematics which breaks them. The second consists of the mathematical "locks and keys" used to keep secrets. In the third part, we explore aspects of mathematics in security, for example in ATM machines, cell phones, remote control car locks, electronic voting machines, DVD encryption, cable TV, ID cards, and more. The mathematics needed is at an elementary level. Assignments include term papers about topics in security.
Not usable as an elective toward the Math major or minor.
Current Semester: Fall 2008
Most Recent Semester Given: Fall 2007
Syllabus
Sample: Fall 2006
Previous semester resources
- Fall 2006, Prof. S. Miller.
- Math 103-H, Spring and Fall 1999, Prof. S. Greenfield.
Regular sections of Math 103 (Topics in Mathematics)
Created 5/07. ugvc -AT- math.rutgers.edu
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