Module Handbook

  • Dynamischer Default-Fachbereich geändert auf MAT

Module MAT-41-18-M-7

Class Groups in Cryptography (M, 4.5 LP)

Module Identification

Module Number Module Name CP (Effort)
MAT-41-18-M-7 Class Groups in Cryptography 4.5 CP (135 h)


CP, Effort 4.5 CP = 135 h
Position of the semester 1 Sem. irreg.
Level [7] Master (Advanced)
Language [EN] English
Module Manager
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


Type/SWS Course Number Title Choice in
Presence-Time /
SL SL is
required for exa.
PL CP Sem.
2V MAT-41-18-K-7
Class Groups in Cryptography
P 28 h 107 h - - PL1 4.5 irreg.
  • About [MAT-41-18-K-7]: Title: "Class Groups in Cryptography"; Presence-Time: 28 h; Self-Study: 107 h

Examination achievement PL1

  • Form of examination: oral examination (20-30 Min.)
  • Examination Frequency: each semester
  • Examination number: 86153 ("Class Groups in Cryptography")


  • definition and simple properties of class groups,
  • algorithms for ideal arithmetic in class fields,
  • complexity analysis,
  • applications to Diffie-Hellman method, safety evaluation.

Competencies / intended learning achievements

Upon successful completion of this module, the students understand the basics of the theory of class groups of number fields and know how to apply this theory to cryptography. In particular, they are familiarized with the complexity of the methods used and understand the assessment of security of class group methods. They are able to analyze the algorithms and to apply them to concrete problems.They are able to name the essential propositions of the lecture as well as to classify and to explain the connections. They understand the proofs presented in the lecture and are able to comprehend and explain them.


  • J. Buchmann, T. Takagi, U. Vollmer: Number field cryptography.

Requirements for attendance (informal)



Requirements for attendance (formal)


References to Module / Module Number [MAT-41-18-M-7]

Module-Pool Name
[MAT-43-MPOOL-7] Specialisation Algebra and Number Theory (M.Sc.)
[MAT-AM-MPOOL-7] Applied Mathematics (Advanced Modules M.Sc.)
[MAT-RM-MPOOL-7] Pure Mathematics (Advanced Modules M.Sc.)