Module Handbook

  • Dynamischer Default-Fachbereich geändert auf MAT

Module MAT-40-14-M-4

Cryptography (M, 9.0 LP)

Module Identification

Module Number Module Name CP (Effort)
MAT-40-14-M-4 Cryptography 9.0 CP (270 h)


CP, Effort 9.0 CP = 270 h
Position of the semester 1 Sem. in SuSe
Level [4] Bachelor (Specialization)
Language [EN] English
Module Manager
+ further Lecturers of the department Mathematics
Area of study [MAT-AGCA] Algebra, Geometry and Computer Algebra
Reference course of study [MAT-88.105-SG] M.Sc. Mathematics
Livecycle-State [NORM] Active


Without a proof of successful participation in the exercise classes, only 6 credit points will be awarded for the module.


Type/SWS Course Number Title Choice in
Presence-Time /
SL SL is
required for exa.
PL CP Sem.
4V+2U MAT-40-14-K-4
P 84 h 186 h
- PL1 9.0 SuSe
  • About [MAT-40-14-K-4]: Title: "Cryptography"; Presence-Time: 84 h; Self-Study: 186 h
  • About [MAT-40-14-K-4]: The study achievement [U-Schein] proof of successful participation in the exercise classes (ungraded) must be obtained.

Examination achievement PL1

  • Form of examination: oral examination (20-30 Min.)
  • Examination Frequency: each semester
  • Examination number: 84160 ("Cryptography")

Evaluation of grades

The grade of the module examination is also the module grade.


Symmetric cryptosystems:
  • Stream and block ciphers
  • Frequency analysis
  • Modern ciphers

Asymmetric cryptosystems:

  • Factorization of large numbers, RSA
  • Primality tests
  • Discrete logarithm, Diffie-Hellman key exchange, ElGamal encryption, hash functions, signature
  • Elliptic curve cryptography (ECC)
  • Attack on the discrete logarithm problem
  • Factorization algorithms (e.g. quadratic sieve, Pollard's ρ, Lenstra)

Competencies / intended learning achievements

Upon completion of this module, the students have understood how basic algebraic and number-theoretical results can be applied to modern cryptography. They know how to deduce algorithms from these results and they are able to critically assess the applicability and limitations of the algorithms.They have understood the proofs presented in the lecture and are able to comprehend and explain them.

By completing the given exercises, students have developed a skilled, precise and independent handling of the terms, propositions and techniques taught in the lecture. In addition, they have learnt how to apply these techniques to new problems, analyse them and develop solution strategies.


  • D.R. Kohel: Cryptography,
  • J. Buchmann: Einführung in die Kryptographie.

Zur Wiederholung der algebraischen und zahlentheoretischen Voraussetzungen bieten sich zudem die folgenden beiden Bücher an:

  • N. Koblitz, A Course in Number Theory and Cryptography,
  • N. Koblitz: Algebraic Aspects of Cryptography.


Registration for the exercise classes via the online administration system URM (

References to Module / Module Number [MAT-40-14-M-4]

Course of Study Section Choice/Obligation
[INF-88.79-SG] M.Sc. Computer Science Formal Fundamentals [WP] Compulsory Elective
[MAT-88.105-SG] M.Sc. Mathematics Pure Mathematics [WP] Compulsory Elective
[MAT-88.105-SG] M.Sc. Mathematics Applied Mathematics [WP] Compulsory Elective
[MAT-88.706-SG] M.Sc. Mathematics International Pure Mathematics [WP] Compulsory Elective
[MAT-88.706-SG] M.Sc. Mathematics International Applied Mathematics [WP] Compulsory Elective
Module-Pool Name
[MAT-GM-MPOOL-5] General Mathematics (Introductory Modules M.Sc.)