Cryptography
Kryptographie
8 CPSummerEN
Prerequisites
Recommended, as written
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)
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
Learning outcomes
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
Assessment
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.
Literature (4)
- 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
- V. Diekert, M. Kufleitner, G. Rosenberger: Diskrete Algebraische Methoden, De Gruyter 2013
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" • Study programme Mathematics M.Sc.: Compulsory elective module in complex „Analysis / Algebra / Combinatorics“ • Study programme Mathematical Data Science M.Sc.: Compulsory elective module in complex „Fundamentals of Data Science“
Source: BTU's module description · retrieved 19 Oct 2026Original