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26E083MOK - Mathematical Foundations of Cryptography

Course specification
Course title Mathematical Foundations of Cryptography
Acronym 26E083MOK
Study programme Electrical Engineering and Computing
Module Computer Engineering and Informatics
Type of study bachelor academic studies
Lecturer (for classes)
Lecturer/Associate (for practice)
Lecturer/Associate (for OTC)
ESPB 3.0 Status elective
Condition Mathematics 1
The goal Acquisition of general knowledge in cryptography and cryptanalysis, with an emphasis on number theory. Theoretical and practical understanding and implementation of fundamental principles, algorithms, and standards used in the field of cryptography.
The outcome Upon completion of the course, the student has mastered the concepts of modern cipher systems that are applied in contemporary information technologies.
Contents
Contents of lectures A brief overview of number theory: Euler’s and Fermat’s Little Theorem, prime numbers, integer factorization (GNFS – complexity), Miller–Rabin algorithm, the Chinese Remainder Theorem; Elliptic curves, algebra of discrete elliptic curves; Lattices, q-ary lattices, SVP (Shortest Vector Problem) and CVP (Closest Vector Problem) algorithms, the Learning with Errors problem (LWE).
Contents of exercises Practical implementation of fundamental principles, algorithms, and standards used in the field of cryptography using Python programming language, applying the knowledge acquired during theoretical instruction. Stream and block ciphers. Construction of hash functions and their applications in cryptography. Implementation of Diffie–Hellman protocol and protocols based on elliptic curves.
Literature
  1. Nigel P. Smart, Cryptography made simple, Springer, 2016. (Original title)
  2. Miodrag Živković, Cryptography - Lecture Notes, Faculty of Mathematics, Belgrade, 2020.
  3. Neal Koblitz, A course in Number Theory and Cryptography, Springer-Verlag, 1994. (Original title)
  4. Micciancio, D., Regev, O. (2009). Lattice-based Cryptography. In: Bernstein, D.J., Buchmann, J., Dahmen, E. (eds) Post-Quantum Cryptography. Springer, Berlin, Heidelberg. (Original title)
Number of hours per week during the semester/trimester/year
Lectures Exercises OTC Study and Research Other classes
1 1 1
Methods of teaching A combination of traditional blackboard instruction and the use of presentations. 15 hours of lectures + 15 hours of problem-solving sessions on the blackboard and computer-based exercises + 15 hours of consultations related to the course material, with a final examination at the end of the course.
Knowledge score (maximum points 100)
Pre obligations Points Final exam Points
Activites during lectures Test paper 70
Practical lessons Oral examination
Projects
Colloquia 30
Seminars