NSCPHD1080 Introduction to Modern Cryptography

Volume 2016/2017

PhD programme in Mathematics



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  • review of basic concepts from probability theory and the theory of computation, random variables, turing machines, the circuit model;
  • basics of encryption schemes, perfect security vs practicality
  • Computational security and pseudorandomness: one-way functions, pseudorandom generators, pseudorandom functions, pseudorandom permutations
  • private-key encryption, security against chosen plaintext attacks
  • public-key cryptography 


We will also describe some example constructions; how many we cover depends on interest and time. Some options are: RSA, Diffie-Hellman, McEliece, lattice crypto, DES, AES.

If time permits, we may also explore some current topics, such as fully-homomorphic encryption, obfuscation, or quantum cryptography.

Learning Outcome
  • Knowledge: the students will have an understanding of the theoretical and mathematical basis of modern cryptographic systems, including some explicit examples.
  • Skills: the students will be able to give rigorous security proofs of basic cryptographic systems, and connect various cryptographic primitives with rigorous reductions.
  • Competencies: understanding theorems about theoretical cryptography; proving security reductions; reasoning about the limits of computationally-bounded adversaries.
Experience with rigorous mathematical proofs; some previous exposure to probability theory; some previous exposure to theory of computation (e.g., Turing Machines, boolean circuits, complexity).
4 hours of lecture and 2 hours of problem sessions every week, for 8 weeks.
This course is about the mathematical and theoretical basis of modern cryptography. Within this area, our focus will be on mathematical theorems, proofs and rigorous constructions. We will not discuss computer security in practice. There will be no programming.

The course is appropriate for students in both Mathematics and Computer Science.
  • Category
  • Hours
  • Exam
  • 60
  • Exercises
  • 16
  • Lectures
  • 32
  • Preparation
  • 98
  • Total
  • 206
7,5 ECTS
Type of assessment
Continuous assessment, 9 weeks
5 homework sets. All must be passed individually (60% grade or higher.) The first homework set can be resubmitted once.
Marking scale
passed/not passed
Censorship form
No external censorship

25 minute oral exam with no preparation time and no aids.

Criteria for exam assesment

The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.