Mathematical Cryptography

Math 75, Spring 2018

Course info:

Lecture Plan

The following is a tentative schedule for the course. Please check back regularly for updates as the term progresses.


We live an information age, with technology increasingly integrated into our daily lives. As a result, the security of our information is of the utmost concern, even as the interconnectedness of the Internet makes our data more vulnerable to attack. The ability to encrypt secrets and to conduct a trusted exchange of digital information, once a subject of interest primarily to governments and the military, is now a matter of necessity for us all. At the end of the day, the foundation of modern cryptography relies upon the difficulty of solving certain mathematical problems; this course is intended to address them from both a mathematical and algorithmic point of view. We will cover some subset of the following topics: conventional encryption techniques, the Hill cipher, DES and SDES, RSA, the Rijndael cipher, discrete logarithms and the Diffie-Hellman key exchange, and elliptic curve cryptography. All mathematical objects will be defined, so the prerequisites are minimal. Really, all one needs is a healthy mathematical and computational appetite. The class will be driven by applications and examples.


The homework assignments will be assigned on a weekly basis and will be posted above. Homework is due in one week; no late homework will be accepted.

Please follow the homework submission guidelines.

Plagiarism, collusion, or other violations of the Academic Honor Principle, after consultation, will be referred to the The Committee on Standards.

Cooperation on homework is permitted (and encouraged), but if you work together, do not take any paper away with you--in other words, you can share your thoughts (say on a blackboard), but you have to walk away with only your understanding. In particular, you must write the solution up on your own. Please acknowledge any cooperative work at the end of each assignment.


Honor Principle

On Exams: Any student giving or receiving assistance during an examination or quiz violates the Academic Honor Principle.

On Homework: Collaboration is permitted and even encouraged, but obviously it is a violation of the honor code for someone to provide the answers for you. However, assistance of any kind should be properly acknowledged.


Students with learning, physical, or psychiatric disabilities enrolled in this course that may need disability-related classroom accommodations are encouraged to make an office appointment to see your instructor before the end of the second week of the term. All discussions will remain confidential, although the Student Accessibility Services office may be consulted to discuss appropriate implementation of any accommodation requested. At such a meeting please provide your instructor with a copy of a disability registration form, which lists the accommodations recommended for the student by Student Accessibility Services within the Academic Skills Center. The person you might want to contact at the Academic Skills center is Ward Newmeyer, Director of Student Accessibility Services 205 Collis Center - (603) 646-9900.

Student Religious Observances

Some students may wish to take part in religious observances that fall during this academic term. Should you have a religious observance that conflicts with your participation in the course, please come speak with your instructor before the end of the second week of the term to discuss appropriate accommodations.