# 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 systemsunderstand the mathematics relevant for desgining and analyzing crypto systemsbe able to explain and use the most important approaches to cryptographygain 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, factorizationelementary crypto systemsSymmetric Cryptosystems DES and AESpublic key cryptography, RSA - discrete logarithm, elliptic curve systemssecure signature and authentication methodssecurity of crypto systemszero knowledge proofscomplexity theoretic aspects Recommended Prerequisites: Basic knowledge about discrete mathematics and linear algebra, for example as covered by the modules11101: Lineare Algebra und analytische Geometrie I11102: Lineare Algebra und analytische Geometrie II or11112: 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, 2015J. Hoffstein, J. Pipher, J.H. Silverman: An Introduction to Mathematical Cryptography, 2nd Edition, Springer 2014.D.R. Stinson: Cryptography: Theory and Practice, CRC, 1995Books in GermanV. Diekert, M. Kufleitner, G. Rosenberger: Diskrete Algebraische Methoden, De Gruyter 2013 Module Examination: Final Module Examination (MAP) Assessment Mode for Module Examination: Written examination, 90 minutes, OROral 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: None Part of the Study Programme: Master (research-oriented) / Angewandte Mathematik / PO 2008 Master (research-oriented) / Angewandte Mathematik / PO 2019 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 Master (research-oriented) / Künstliche Intelligenz Technologie / PO 2022 Bachelor (research-oriented) / Mathematik / PO 2019 Master (research-oriented) / Physics / PO 2021 Bachelor (research-oriented) / Wirtschaftsmathematik / PO 2007 Bachelor (research-oriented) / Wirtschaftsmathematik / PO 2019 - SÄ 2021 Remarks: Study programme Cyber Security M.Sc.: Mandatory module in complex „Cyber Security Basics“Study programme Informations- und Medientechnik M.Sc.: Compulsory elective module in complex „Methodische Grundlagen“Study programme Informatik M.Sc.: Compulsory elective module in complex „Mathematik“ or in field of application „Mathematik“Study programme Künstliche Intelligenz Technologie B.Sc.: Compulsory elective module in complex „Software-basierte Systeme“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 extendStudy programme Wirtschaftsmathematik B.Sc.: Compulsory elective module in complex „Vertiefung“, in limited extendStudy programme Physics M. Sc.: Compulsory elective module in complex „Minor Subject Module Components: Lecture: CryptographyAccompanying exercisesRelated examination Components to be offered in the Current Semester: 130250 Examination Cryptography Phase-out Module: Follow-up Module since: 18.01.2020 11439 Kryptographie (Methoden)