Math 328:Coding Theory and Cryptography, Spring 2019

Instructor: Noah Aydin
Office/Phone
: RBH 319, 5674
Office Hours: MWF 10:10-11; T&R: 4:30-5:30 and by appointment. Here is my weekly schedule. Send me an e-mail to request an appointment.
Room & Time
: RBH 311, TR: 2:40-4 pm
Textbooks:
1) Coding Theory and Cryptography The Essentials, D. R. Hankerson et al., 2nd ed, revised and expanded, Marcel Dekker. 2) Introduction to Cryptography with Coding Theory, W. Trappe and L. C. Washington. 2nd ed, Pearson

Course Description: The theory of error-correcting codes and cryptography are two recent applications of algebra and discrete mathematics to information and communications systems. Students will learn the basic ideas of coding theory and cryptography, understand their mathematical foundations, and learn how mathematical tools can be used to devise useful error correcting codes and cryptographic systems. Since ideas from computational complexity theory are essential for cryptography, we will discuss basic principals of computational complexity as well. While coding theory is concerned with the reliability of communication, the main problem of cryptography is the security and privacy of communication. Applications of coding theory range from enabling the clear transmission of pictures from distant planets to quality of sound in compact disks and wireless communication. Cryptography is a key aspect of electronic security systems. With the ever increasing role of digital communication, online transactions, and general dependence on electronic systems in modern life, the importance these fields grows each day. A selection of topics from these two disciplines will be discussed including basics of block coding, linear codes, Hamming codes, cyclic codes, BCH codes, symmetric-key and public-key cryptography and digital signatures. Other topics may be included depending on the availability of time and the background and interests of the students. Each student will write a final research paper in a topic of their choice and present it to the class. Other than some basic linear algebra, the necessary mathematical background (mostly abstract algebra) will be covered within the course. Active learning methods will be used throughout the semester.

Syllabus