## Module Handbook

• Dynamischer Default-Fachbereich geändert auf MAT

# Module MAT-40-14-M-4

## Module Identification

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

## Basedata

CP, Effort 9.0 CP = 270 h 1 Sem. in SuSe [4] Bachelor (Specialization) [EN] English Fieker, Claus, Prof. Dr. (PROF | DEPT: MAT) Fieker, Claus, Prof. Dr. (PROF | DEPT: MAT) Horn, Max, Prof. Dr. (PROF | DEPT: MAT) Malle, Gunter, Prof. Dr. (PROF | DEPT: MAT) [MAT-AGCA] Algebra, Geometry and Computer Algebra [MAT-88.105-SG] M.Sc. Mathematics [NORM] Active

## Notice

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

## Courses

Type/SWS Course Number Title Choice in
Module-Part
Presence-Time /
Self-Study
SL SL is
required for exa.
PL CP Sem.
4V+2U MAT-40-14-K-4
Cryptography
P 84 h 186 h
U-Schein
- 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")

## Contents

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.

## Literature

• 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

Registration for the exercise classes via the online administration system URM (https://urm.mathematik.uni-kl.de).

None

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

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