Math 314 Spring 2022

Math 314: Cryptography

Fall 2022

Instructor and Meeting Times

Instructor: Nathan McNew -
Undergraduate Student Hours: (AKA Office Hours) Feel free to email to make an appointment to meet outside those times. Tuesdays and Thursdays 3pm-4pm (in person, feel free to drop by, no appt necessary)
Friday 10am-11am (Virtually, find link in email.)
Office: 229 (The 50th prime number) 7800 York Road
Lecture: Section 001: Tuesday (YR 125) and Thursday (YR 216) 11:00--12:15
Section 002: Tuesday (YR 125) and Thursday (YR 216) 12:30--1:45

Course Description and Objectives

Course description:
A broad introduction to cryptography and its mathematical foundations. The course will also cover applications to computer-network security services and mechanisms (confidentiality, integrity, authentication, electronic cash, and others), and to various protocols in distributed computation.

Course objectives: The course provides a broad overview of the mathematical basis of modern cryptography and presents the main cryptosystems currently in use. Students are exposed to relevant chapters of number theory and computational number theory (modular arithmetic, finite fields, primality testing, quadratic residues, discrete logarithms, and others) at the undergraduate level. The course covers the most important cryptosystems (DES, AES, RSA) and the basic tools used in building security mechanisms (one-way functions, hash functions, message authentication codes, pseudo-random generators, bit commitment, hash functions, etc.). Some basic principles of cryptanalysis are presented as well. At the end of the course, students will have a good understanding of the theoretical foundations of cryptography and of the basic techniques for achieving different cryptographic services.

Prerequisites: COSC 236, MATH 263 or MATH 267, and either MATH 330 or MATH 331 (may be taken concurrently).


Understanding Cryptography: A Textbook for Students and Practitioners Textbook by Christof Paar and Jan Pelzl


Homework will consist of two components, written assignments and computational assignments in CoCalc.

Expect to spend a substantial amount of time studying and working on homework. The general rule is two to three hours outside class for each hour inside; this translates to about 6-9 hours of homework and personal study per week.

Quizzes will be given periodically covering aspects of the assigned reading and homework assignments (including recommended questions.)

Additionally, each student is responsible for writing up notes describing what was covered during one of the lectures during the term. These notes should be written up clearly using latex and submitted to the instructor within a week of the class period. Students are also encouraged to include additional examples/explanation. Notes will be posted for use by the rest of the class. Sign up for class periods here. Note: this will count as one homework assignment.


There are three scheduled exams: two midterms, held during class time, and the final exam.

Section Midterm 1 Midterm 2 Final Exam
Section 001 Thursday March 10th Thursday April 28th Thursday, May 19
12:30--2:30 pm
Section 002 Thursday March 10th Thursday April 28th Tuesday, May 24
12:30--2:30 pm

If you have a conflict with a scheduled exam contact the instructor as soon as possible.


Individual grades will be weighted in the students final grade as follows:

Homework, quizzes and typed course notes 20%
Projects, Group Discussion Questions 20%
Midterms (each) 15%
Final Exam 30%

Academic Integrity and Plagiarism

Academic Integrity: This class is conducted in accordance with the Academic Integrity Policy. Cheating or plagiarism in any form is unacceptable. In particular:

On Exams: No assistance may be given or received except that you may ask the instructor for clarification of a problem.

On Homework and Projects: You are permitted and encouraged to collaborate with other students on the homework. However, after discussing the problems, you must write up the final solutions in your own words. You may use calculators and CoCalc/SageMath. You are encouraged to consult your class notes and text. It is not permitted for someone to provide the answers for you.

It is not permitted to submit answers found on the internet as your own work. If you copy code from outside sources, you must cite it.
Examples of things that are not academic dishonesty:

Examples of things which constitute academic dishonesty: See this page for more about plagiarism and how to avoid it.

Course Policies

Class attendance is expected. If you miss a class, it is your responsibility to get the material and the homework assignment from your fellow students.

Diversity Statement: Towson University values diversity and fosters a climate that is grounded in respect and inclusion, enriches the educational experience of students, supports positive classroom and workplace environments, promotes excellence, and cultivates the intellectual and personal growth of the entire university community.

Disability Statement: This course is in compliance with Towson University policies for students with disabilities. Students with disabilities are encouraged to register with Accessibility & Disability Services (ADS), 7720 York Road, Suite 232, 410-704-2638 (Voice) or 410-704- 4423 (TDD). Students who suspect that they have a disability but do not have documentation are encouraged to contact ADS for advice on how to obtain appropriate evaluation. A memo from ADS authorizing your accommodation is needed before any accommodation can be made. For more details, see:

Title IX policy: “Towson University (TU) is committed to ensuring a safe, productive learning environment on our campus that does not tolerate sexual misconduct, including harassment, stalking, sexual assault, sexual exploitation, or intimate partner violence [Policy 06.01.60]. It is important for you to know that there are resources available if you or someone you know needs assistance. You may speak to a member of university administration, faculty, or staff, but keep in mind that they have an obligation to report the incident to the Title IX Coordinator. It is a goal that you feel able to share information related to your life experiences in classroom discussions and in one-on-one meetings. However, it is required to share information with the Title IX Coordinator regarding disclosures, but know that the information will be kept private to the greatest extent possible. If you want to speak to someone who is permitted to keep your disclosure confidential, please seek assistance from the TU Counseling Center 410-704-2512 to schedule an appointment, and locally within the community at TurnAround, Inc., 443-279-0379 (24-hour hotline) or 410-377-8111 to schedule an appointment. For more information see

Masking:The University has set clear expectations about mask wearing for the safety of all in our community. Face coverings over the nose and mouth are required at all times while indoors. There are no exceptions to this rule. Students not wearing a mask--or wearing a mask improperly--will be asked to wear a mask or to fix their mask position. Any student refusing to put on or wear a mask will be asked to leave the classroom immediately. Students who have additional incidents with the mask expectation after a first warning will be referred to the Office of Student Conduct for failure to comply with this University directive.