Math 3159B: Introduction to Cryptography (Winter 2019)

Essential information

  • Lectures: MF 2:30-3:30 in WSC 240, W 2:30-3:30 in PAB 150
  • Office hours: 
    Chris: Wednesday, 10-11 in MC 116, or by appointment
    Alex: Friday 1:30-2:30 in MC 104
    Luis: Friday 3:30-4:30 in MC 104
  • Instructor: Chris Kapulkin
  • Email: kkapulki (at)
  • Office: MC 116
  • Teaching assistants: Alex Rolle and Luis Scoccola
  • Website:
  • Prerequisites: Math 1600A/B and (at least) one of: Math 2120A/B, 2124A/B, 2151A/B, 2155F/G, 3150A/B, ApplMath 2811B, or CompSci 2214A/B


The course will follow:

  • Hoffstein, Pipher, Silverman, Introduction to Mathematical Cryptography, 2nd Edition, 2014.

The entire book is available for free download in pdf format from Western library. Students are also welcome to consult:

  • Koblitz, A Course in Number Theory and Cryptography, 2nd Edition, 1994.

Course content

The topics will include:

  • Elementary Number Theory
  • Introduction to Computational Complexity
  • Discrete Logarithm Problem and Diffie-Hellman Key Exchange
  • RSA Encryption, Primality Test, Factorization Algorithms, and Quadratic Reciprocity
  • Elliptic Curve Cryptography
  • Post-Quantum Cryptography (time permitting)


The final grades will be based on the following components:

  • weekly quizzes: 40%
  • assignments: 20%
  • final exam: 40%

Final exam

  • Date: April 18, 2019 (Thursday)
  • Time: 7-10 PM
  • Room: Social Science Center 2050


There will be four assignments, each worth 5% of the final grade.

The assignments are submitted electronically via Crowdmark. Handwritten assignments will be accepted, however students are encouraged to typeset their assignments using LaTeX, using the template provided by the instructor.

Each assignment will consist of two problems of which students need to choose one. One of the problems will require proving a statement and the other writing a program. Students choosing the latter must write their programs in Python.


There will be weekly quizzes on Mondays in the beginning of the class (2:30-2:45).

Recommended homework problems

Chapter Recommended exercises
1 11, 14, 15, 19, 20, 21, 22, 23, 26, 31, 33a, 35, 36, 49
2 3, 6, 9, 12, 15, 17, 20, 27, 28a, 30abcd, 34, 37, 41ab
3 5abcd, 7, 11, 12, 15, 21, 22a, 26ab, 34a, 39ab, 41
4 4, 7, 9
6 2, 3, 7, 8, 10, 17a, 18a, 21a, 31, 32, 33, 40, 48

Accommodation and Accesibility

If you are unable to meet a course requirement due to illness or other serious circumstances, you must provide valid medical or supporting documentation to the Academic Counselling Office of your home faculty as soon as possible. If you are a Science student, the Academic Counselling Office of the Faculty of Science is located in WSC 140, and can be contacted at

For further information, please consult the university’s medical illness policy at

If you miss the Final Exam, please contact your faculty’s Academic Counselling Office as soon as you are able to do so. They will assess your eligibility to write the Special Exam (the name given by the university to a makeup Final Exam). You may also be eligible to write the Special Exam if you are in a “Multiple Exam Situation”

Academic Policies

The website for Registrarial Services is

In accordance with policy, centrally administered e-mail account provided to students will be considered the individual’s official university e-mail address. It is the responsibility of the account holder to ensure that e-mail received from the University at his/her official university address is attended to in a timely manner.


Scholastic offences are taken seriously and students are directed to read the appropriate policy, specifically, the definition of what constitutes a Scholastic Offence, at this website:

Support Services

Please contact the course instructor if you require lecture or printed material in an alternate format or if any other arrangements can make this course more accessible to you. You may also wish to contact Services for Students with Disabilities (SSD) at 661-2111 ext. 82147 if you have questions regarding accommodation. The policy on Accommodation for Students with Disabilities can be found here:

The policy on Accommodation for Religious Holidays can be found here:

Students who are in emotional/mental distress should refer to Mental Health@Western ( for a complete list of options about how to obtain help.