Mathematics 342, Algebra, Coding theory and Cryptography, Section 201

Term 2, 2012. MWF 10- 10:50 in LSK, Rm. 460

  • Course description : The course is intended as an introduction to error-correcting codes and cryptography, with the necessary algebra background covered along the way. Approximately 2/3 of the term will be spent on error-correcting codes and approximately 1/3 on cryptography. Both proof and algorithmic techniques will be emphasized. Topics will include coding and decoding schemes, congruences and finite fields, linear codes, syndrome decoding, Hamming codes, classical and public key cryptosystems, RSA cryptography. If time permits, I will also discuss cyclic codes.

  • Reading materials : The main textbook for the term is

    Raymond Hill, A first course in coding theory, published by Clarendon Press.

    For the cryptography part of the course, we will use the original paper A method for obtaining digital signatures and public-key cryptosystems by Rivest, Shamir and Adleman, where the RSA cryptosystem was first introduced.

    See also
    the Wikipedia article on the Euclidean algorithm,
    the Wikipedia article on the Plotkin bound.

  • Registration : Questions regarding registering for this class, switching sections, etc., should be addressed to the Mathematics Department office staff, Rm. 121 Mathematics Building.

  • Homework : Homework assignments will be posted here and collected in class.

    Problem set 1. Due Monday, January 16.
    Solutions to Problem Set 1.

    Problem set 2. Due Monday, January 23.
    Solutions to Problem Set 2.

    Problem set 3. Due Monday, January 30.
    Solutions to Problem Set 3.

    Problem set 4. Due Wednesday, February 15.
    Solutions to Problem Set 4.

    Problem set 5. Due Monday, March 5.
    Solutions to Problem Set 5.

    Problem set 6. Due Monday, March 19.
    Solutions to Problem Set 6.

    Problem set 7. Due Monday, April 2.
    Solutions to Problem Set 7.

    A portion of each assignment will be graded by the course marker. Late homework will not be accepted but the lowest score will be dropped. Students are allowed to consult one another concerning the homework problems, but solutions submitted for credit must be written by the student in his or her own words. Copying solutions from another student, from the web or from any other source, and turning them in as your own is illegal (see the Academic Integrity section below).

  • Evaluation : Course mark will be based on the homework, two midterms and the final exam. The midterms will be given in class on Friday, February 3 and Friday, March 9 and the final on Friday, April 13 at 12 noon (room to be announced). You can use a two-sided standard size (8" by 11") note sheet on the exams, but no other notes, books or calculators.

    Final exam overview

    Midterm 1 topics.

    Midterm 1 problems and solutions.

    Midterm 2 problems and solutions.

    The total course mark will be the higher of the following:

    Total1 := HW /20 + Midterm1 /15 + Midterm2 /15 + Final /50 or

    Total2 := HW /20 + Best Midterm /15 + Final /65

  • Missed exams and exam hardship : Please make sure you do not make travel plans, work plans, etc., without regard to the examination schedule in this class. There will be no make-up or alternate exams.

    If you miss a midterm, your score will be recorded as 0, unless you have a serious documented reason (an illness, a death in the family, etc.), in which case you should discuss your circumstances with me as soon as possible, and at least 24 hours in advance of the test. Note that you may still get a 100% in the course, even if you get a score of 0 on one midterm (see the marking scheme above).

    Students with legitimate reasons for missing the final exam should request a ``Standing Deferred" status through their faculty. UBC allows a student's exam to be moved to another date if they have an exam hardship. This is defined as three exams within a 24 hour period. For example, April 11th at 3:30 p.m., April 12th at 8:00 a.m., and April 12th at 12:00 noon. If the third exam was April 12th at 3:30 p.m., that would not be considered to be an exam hardship. It is always the middle of the three exams that gets rescheduled. All students reporting an exam hardship or exam conflict (two exams at the same time) should be referred to Margaret Ness in the Mathematics Office. She will assess their situation and arrange any accommodation legitimately necessary. Another reason for moving an exam is a conflict due to religious practice, for example, a Saturday exam can conflict with religious practices.

  • Students with disabilities : Students with documented disabilities who may need accommodations, have any emergency medical information, or who need special arrangements in the event of evacuation, should make an appointment with me as early as possible.

  • Academic Integrity. The Mathematics Department strictly enforces UBC's Academic Integrity code. Violations can result in supension, expulsion and, in some cases, criminal charges. Please don't even consider cheating; it is wrong, it is unfair to the other students, and it can get you into far more serious trouble than failing a single exam or a single course.