About CPSC 418 / MATH 318, Winter 2024

Course Objectives

What would you want to see in a secure e-mail system? File transfer program? Social networking site? How do you guarantee that an e-mail originates from a legitimate sender and isn't a phishing or spoofing attempt? How can you ensure that your private files have not been accessed by unauthorized users? Or prevent hackers from tampering with your social media site? Cryptography is the foundation for solutions to these types of questions.

The main objective of this pair of courses is to provide students with a thorough understanding of the fundamentals of and current best practices in cryptography. Students who have completed CPSC 418 or MATH 318 will have a solid grasp, including some practical experience, of the basic cryptographic primitives and their proper usage. The learning outcomes for the two courses can be found at the end of the respective course information sheets and the course syllabus, available on the handouts tab.

Required Knowledge and Skills

Consult the course information sheets for the (different!) prerequisites for CPSC 418 and MATH 318. Cryptography falls squarely between mathematics and computer science, so the course combines aspects from both disciplines. In addition to a sufficient level of mathematical maturity, knowledge of the following mathematical topics is assumed:

• Binary logic and binary arithmetic
• Congruences and modular arithmetic
• Polynomial arithmetic
• Basic counting techniques
• Basic mathematical proof techniques
• Possibly some very elementary calculus (derivatives, local minima and maxima)
• Possibly some very elementary linear algebra (matrices and vectors)

Knowledge of elementary probability theory is an asset, but the required body of knowledge will be covered in class. Basic competency in the typesetting software LaTeX is also very helpful; an introduction and demo will be provided in tutorial. For CPSC 418, proficiency in Python programming is assumed.

Topics Covered

The University calendar course description provides a brief overview of the course content. A complete syllabus with a list of topics can be found on the handouts tab. Topics covered include:

• Security services provided by cryptography, limitations of cryptography.
• Symmetric key cryptography, including theoretical and classical background, perfect security (one-time pad), block ciphers (AES), proper usage of block ciphers, stream ciphers, mechanisms for data integrity.
• Public key cryptography, including Diffie-Hellman key exchange, RSA, probabilistic encryption (ElGamal), semantic security (Goldwasser-Micali), IND-CCA2 (RSA-OAEP), digital signatures from public-key cryptosystems (RSA signatures), ElGamal signatures, entity authentication and authenticated key exchange (station-to-station protocol).
• Practical cryptography, including key management, cryptographically secure pseudorandom bit generation, symmetric key hierarchies, public key infrastructures and certification authorities, and authentication.
• Real world comprehensive cryptographic solutions and applications.
• Other topics if time permits.

Development and Enhancement of Skills

The main primitives required for cryptographic applications will be presented during the lectures. Written problem-based assignment questions (for all students) will lead to further exploration of the underlying theory and of the practical and security issues. Programming questions (for CPSC 418 students) will provide hands-on experience in writing cryptographic software. Mathematical questions (for MATH 318) will enhance students' in-depth understanding of the mathematical foundations.

Tools

For the written problems, the typesetting software LaTeX will be used. All the programming work required for CPSC 418 will be done using Python. Class discussion is conducted on Piazza, while assignments will be submitted online through Gradescope.

Learning Methods

Students' skills will be developed using the following methods:

• For both CPSC 418 and MATH 318: shared lectures, during which most of the course material will be presented.
• For CPSC 418: tutorials, during which certain concepts and problems will be explored in more detail, and in a more interactive, student-driven format. Attendance for MATH 318 students is entirely optional and is welcome, subject to space in the classroom.
• Written problem-based assignments, to exercise students' understanding of the theoretical concepts presented and their ability to apply these concepts.
• For CPSC 418: additional programming assignments, to give students hands-on experience in implementing and working with the protocols and primitives presented in the course; MATH 318 student are welcome to do these problems for extra credit.
• For MATH 318: additional mathematical problem solving assignments, to enhance students' in-depth understanding of the mathematical foundations; CPSC 418 students are welcome to do these problems for extra credit.

CPSC 418 versus MATH 318

CPSC 418 and MATH 318 are different courses; one is not a substitute for the other. While both courses share lectures, exams and portions of homework assignments, there are significant differences:

• Performance expectations are reflected in the course level (third year for CPSC 418, second year for MATH 318).
• CPSC 418 has additional prerequisites (CPSC 331 and one of CPSC 351, MATH 271, MATH 273, MATH 315) compared to MATH 318.
• CPSC 418 has tutorials, while MATH 318 does not.
• Significant portions of the homework problems between the two courses are different, comprised of programming problems for CPSC 418 and mathematical proof-oriented problems for MATH 318.

Note that CPSC 418 and MATH 318 are anti-requisites; credit can not be obtained for both.

Beyond this Course

CPSC 418 and MATH 318 are highly suitable as stand-alone courses. In addition, CPSC 418 is a required course within the Concentration in Information Security offered as part of the BSc degree in Computer Science. The exact requirements for this concentration are listed at the end of Section 4.3.1 of the University calendar.

The University of Calgary offers professional Master's programs in data science, information security and quantum computing. Check that website for information sessions and lunch & learn events.

To find out more about research in cryptography and information security conducted at the University of Calgary, check out the U of C's Institute for Security, Privacy and Information Assurance (ISPIA).

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Last modified by Renate Scheidler
httpd://cspages.ucalgary.ca/~rscheidl/crypto/about.html