11859 - Cryptography Modulübersicht

Module Number: 11859
Module Title:Cryptography
  Kryptographie
Department: Faculty 1 - Mathematics, Computer Science, Physics, Electrical Engineering and Information Technology
Responsible Staff Member:
  • Prof. Dr. rer. nat. habil Meer, Klaus
  • Prof. Dr. rer. nat. Averkov, Gennadiy
Language of Teaching / Examination:English
Duration:1 semester
Frequency of Offer: Every summer semester
Credits: 8
Learning Outcome:The students should
  • know relevant symmetric and asymmetric crypto systems
  • understand the mathematics relevant for desgining and analyzing crypto systems
  • be able to explain and use the most important approaches to cryptography
  • gain the ability to understand state-of-the-art scientific work in the area of cryptography
Contents:
  • Mathematical Foundations relevant in the context of cryptography, including basic number theory, finite fields, polynomial rings, factorization
  • elementary crypto systems
  • Symmetric Cryptosystems DES and AES
  • public key cryptography, RSA - discrete logarithm, elliptic curve systems
  • secure signature and authentication methods
  • security of crypto systems
  • zero knowledge proofs
  • complexity theoretic aspects
Recommended Prerequisites:Basic knowledge about discrete mathematics and linear algebra, for example as covered by the modules
  • 11101: Lineare Algebra und analytische Geometrie I
  • 11102: Lineare Algebra und analytische Geometrie II
or
  • 11112: Mathematik IT-1 (Diskrete Mathematik)
  • 11113: Mathematik IT-2 (Lineare Algebra)
Mandatory Prerequisites:None
Forms of Teaching and Proportion:
  • Lecture / 4 Hours per Week per Semester
  • Exercise / 2 Hours per Week per Semester
  • Self organised studies / 150 Hours
Teaching Materials and Literature:Books in English 
  • G. Baumslag, B. Fine, M. Kreuzer, G. Rosenberger: A Course in Mathematical Cryptography, De Gruyter, 2015
  • J. Hoffstein, J. Pipher, J.H. Silverman: An Introduction to Mathematical Cryptography, 2nd Edition, Springer 2014.
  • D.R. Stinson: Cryptography: Theory and Practice, CRC, 1995
Books in German
  • V. Diekert, M. Kufleitner, G. Rosenberger: Diskrete Algebraische Methoden, De Gruyter 2013
Module Examination:Prerequisite + Final Module Examination (MAP)
Assessment Mode for Module Examination:Prerequisite:
  • Successful completion of homework (fortnightly) and/or successful completion of tests (approx. 4 tests of 15-30 minutes each, written during the lecture period)
Final module examination:
  • Written examination, 90 minutes, OR
  • Oral examination, 30 - 45 minutes, (in case of a small number of participants)
In the first lecture it will be anounced, if the examination will be offered in written or oral form.
Evaluation of Module Examination:Performance Verification – graded
Limited Number of Participants:80
Part of the Study Programme:
  • Master (research-oriented) / Angewandte Mathematik / PO 2008
  • Master (research-oriented) / Angewandte Mathematik / PO 2019
  • Master (research-oriented) / Artificial Intelligence / PO 2022
  • Abschluss im Ausland / Cyber Security / keine PO
  • Master (research-oriented) / Cyber Security / PO 2017
  • Abschluss im Ausland / Informatik / keine PO
  • Bachelor (research-oriented) / Informatik / PO 2008 - 1. SÄ 2017
  • Master (research-oriented) / Informatik / PO 2008 - 2. SÄ 2017
  • Master (research-oriented) / Informations- und Medientechnik / PO 2017
  • Bachelor (research-oriented) / Mathematik / PO 2023
  • Bachelor (research-oriented) - Co-Op Programme with Practical Placement / Mathematik - dual / PO 2023
  • Master (research-oriented) / Physics / PO 2021
  • Bachelor (research-oriented) / Wirtschaftsmathematik / PO 2007
  • Bachelor (research-oriented) / Wirtschaftsmathematik / PO 2023
  • Bachelor (research-oriented) - Co-Op Programme with Practical Placement / Wirtschaftsmathematik - dual / PO 2023
Remarks:
  • Study programme Cyber Security M.Sc.: Mandatory module in complex „Cyber Security Basics“
  • Study programme Informatik M.Sc.: Compulsory elective module in complex „Mathematik“ or in field of application „Mathematik“
  • Study programme Artificial Intelligence M.Sc.: Compulsory elective module in complex „Advanced Methods“
  • Study programme Angewandte Mathematik M.Sc.: Compulsory elective module in complex „Analysis / Algebra / Kombinatorik“
  • Study programme Mathematik B.Sc.: Compulsory elective module in complex „Vertiefung“, in limited extend
  • Study programme Wirtschaftsmathematik B.Sc.: Compulsory elective module in complex „Vertiefung“, in limited extend
  • Study programme Physics M. Sc.: Compulsory elective module in complex „Minor Subject
Module Components:
  • Lecture: Cryptography
  • Accompanying exercises
  • Related examination
Components to be offered in the Current Semester: