## Module Handbook

• Dynamischer Default-Fachbereich geändert auf MAT

# Course MAT-40-14-K-4

## Course Type

SWS Type Course Form CP (Effort) Presence-Time / Self-Study
- K Lecture with exercise classes (V/U)
4 V Lecture 6.0 CP 56 h 124 h
2 U Exercise class (in small groups) 3.0 CP 28 h 62 h
(4V+2U) 9.0 CP 84 h 186 h

## Basedata

SWS 4V+2U 9.0 CP = 270 h 1 Sem. in SuSe [4] Bachelor (Specialization) [EN] English 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 [NORM] Active

## Notice

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

## Possible Study achievement

• Verification of study performance: proof of successful participation in the exercise classes (ungraded)
• Examination number (Study achievement): 84013 ("Exercise Class Cryptography")
• Details of the examination (type, duration, criteria) will be announced at the beginning of the course.

## 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

The students will understand 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.

## 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.

## Materials

Further literature will be announced in the lecture(s); exercise material is provided.

## Registration

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

None

## References to Course [MAT-40-14-K-4]

Module Name Context
[MAT-30-10L-M-5] Specialisation Module (Teachers Training Programme Mathematics) WP: Obligation to choose in Obligatory-Modulteil #A (Lectures) 4V, 6.0 LP
[MAT-40-14-M-4] Cryptography P: Obligatory 4V+2U, 9.0 LP
Course-Pool Name
[MAT-40-4V-KPOOL-4] Elective Courses Algebra, Geometry and Computeralgebra (4V, B.Sc.)
[MAT-40-KPOOL-4] Specialisation Algebra, Geometry and Computer Algebra (B.Sc.)