Math 485:  Mathematical Cryptography

Fall 2023

Homework Assignments

Reading Schedule

BYU Learning Suite

Cocalc : https://cocalc.com/

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InstructorKyle Pratt
Office:  208 TMCB
Email:  kyle.pratt@math.byu.edu (for most questions)
Lecture:  2:00-2:50 PM MWF, 112 TMCB
Office hours:  M, 12-1; W, 3-4; Th, 2-3; Fri, 11-12, 3-4
TA: Joseph James, jhjames@mathematics.byu.edu
TA office hours: TTh 3-4 PM in 149 TMCB computer lab
Textbook:  Introduction to Cryptography with Coding Theory, Second Edition, Wade Trappe and Lawrence C. Washington, Pearson Prentice Hall, ISBN 0-13-186239-1. Please note the list of known errors in the textbook online at http://www.math.umd.edu/~lcw/cryptoerrata2.pdf and mark your book accordingly if you wish.

Grading:  Homework and projects 40%, two midterms 15% each, final exam 30%. Grades will be available on BYU Learning Suite.

Exams:  Two midterm exams in the testing center on October 6-10 and November 16-20. You can find a study guide for the first midterm here, and some practice problems here. You can find a study guide for the second midterm here, and some practice problems here. The final exam will be a take-home exam, due at the scheduled final exam time (2:30 PM, Tuesday December 19).  The final exam will cover all material studied this semester.

Homework:  Homework will be due on Mondays, Wednesdays, and Fridays at 5:00 PM (7:00 PM, beginning with HW20), submitted on Learning Suite (unless otherwise indicated).  Homework assignments will be posted on the course website.  Your homework should be neat and should include enough detail that another student from the class could follow your arguments.  Homework that is excessively sloppy may receive less than full credit.  Late homework will not be accepted. Working in groups on homework is encouraged, but each student should write up each problem, without looking at other students’ written solutions. The three homework assignments with the lowest score will be dropped. There will also be larger projects assigned from time to time; details will be announced in class and will appear on the course website. Project scores may not be dropped.

Prerequisites:  Math 213 (linear algebra) or equivalent, or instructor's consent. Math 371 is recommended. Some prior experience with programming and with a computer algebra system such as Sage, Maple, or Mathematica is desirable, but not essential.

Course Description: This is a course in the mathematics and algorithms of modern cryptography. It complements, rather than being equivalent to, the CS course on Computer Security (CS 465) and the IT course on Cybersecurity and Penetration Testing (IT 567).

Minimal Learning Outcomes: The student should gain a understanding of the following topics. In particular this includes knowing the definitions, being familiar with standard examples, and being able to solve mathematical and algorithmic problems by directly using the material taught in the course. This includes appropriate use of Sage, Maple, Mathematica, or other software.

  1. Classical systems, including
  2. Elementary number theory as follows.
  3. The DES and AES encryption standards
  4. RSA and its strengths and weaknesses; attacks on RSA
  5. Primality testing algorithms
  6. Factorization techniques
  7. Discrete logarithms, Diffie-Hellman key exchange

Additional topics may include, but are not limited to: Elliptic curve cryptography, birthday attacks and probability, quantum cryptography (key distribution, Shor's algorithm), hash functions, digital signatures, secret sharing, and lattices and lattice algorithms (the LLL algorithm, NTRU system).

This is a 3 credit class.  BYU policy states that “the expectation for undergraduate courses is three hours of work per week per credit hour for the average student who is appropriately prepared; much more time may be required to achieve excellence.”  Thus, an average student should expect to spend at least 6 hours per week outside of lecture on working problems, reading the textbook, reviewing concepts, and completing assignments.

Electronic devices:  Computers will be necessary to complete some homework problems. On midterm exams, only testing center calculators may be used. Do not use mobile phones or permit them to ring during class. Office hours will be held by the TA in the computer lab in 149 TMCB on Tuesdays and Thursdays from 3:00 to 4:00 PM to answer computer questions.

Preventing & Responding to Sexual Misconduct: In accordance with Title IX of the Education Amendments of 1972, BYU prohibits unlawful sex discrimination, including sexual harassment, against any participant in its education programs or activities. The university also prohibits sexual harassment by its personnel and students. Sexual harassment occurs when


University policy requires all faculty members to promptly report incidents of sexual harassment that come to their attention in any way, including through face-to-face conversations, a written class assignment or paper, class discussion, email, text, or social media post. Incidents of sexual harassment should be reported to the Title IX Coordinator at t9coordinator@byu.edu or (801) 422-8692 or 1085 WSC. Reports may also be submitted online at https://titleix.byu.edu/report or 1-888-238-1062 (24-hours a day).

BYU offers confidential resources for those affected by sexual harassment, including the university’s Sexual Assault Survivor Advocate, as well as a number of non-confidential resources and services that may be helpful. Additional information about Title IX, the university’s Sexual Harassment Policy, reporting requirements, and resources can be found at http://titleix.byu.edu or by contacting the university’s Title IX Coordinator.

Student Disability: Brigham Young University is committed to providing a working and learning atmosphere that reasonably accommodates qualified persons with disabilities. A disability is a physical or mental impairment that substantially limits one or more major life activities. Whether an impairment is substantially limiting depends on its nature and severity, its duration or expected duration, and its permanent or expected permanent or long-term impact. Examples include vision or hearing impairments, physical disabilities, chronic illnesses, emotional disorders (e.g., depression, anxiety), learning disorders, and attention disorders (e.g., ADHD). If you have a disability which impairs your ability to complete this course successfully, please contact the University Accessibility Center (UAC), 2170 WSC or 801-422-2767 to request a reasonable accommodation. The UAC can also assess students for learning, attention, and emotional concerns. If you feel you have been unlawfully discriminated against on the basis of disability, please contact the Equal Opportunity Office at 801-422-5895, eo_manager@byu.edu, or visit https://hrs.byu.edu/equal-opportunity for help.”

Honor Code: In keeping with the principles of the BYU Honor Code, students are expected to be honest in all of their academic work. Academic honesty means, most fundamentally, that any work you present as your own must in fact be your own work and not that of another. Violations of this principle may result in a failing grade in the course and additional disciplinary action by the university. Students are also expected to adhere to the Dress and Grooming Standards. Adherence demonstrates respect for yourself and others and ensures an effective learning and working environment. It is the university's expectation, and every instructor's expectation in class, that each student will abide by all Honor Code standards. Please call the Honor Code Office at 422-2847 if you have questions about those standards.