311.265 (21W) Selected Topics in Discrete Mathematics (Permutation Polynomials in Cryptography)
Overview
For further information regarding teaching on campus, please visit: https://www.aau.at/en/corona.
- Lecturer
- Course title german Selected Topics in Discrete Mathematics (Permutation Polynomials in Cryptography)
- Type Lecture
- Course model Attendance-based course
- Hours per Week 2.0
- ECTS credits 3.0
- Registrations 19
- Organisational unit
- Language of instruction Englisch
- possible language(s) of the assessment German , English , Spanish
- Course begins on 04.10.2021
- eLearning Go to Moodle course
Time and place
Course Information
Intended learning outcomes
Special polynomial functions play an essential role in modern cryptography. The participants of this course will be familiarized with properties of polynomial functions on finite fields and residue class rings. The discussed topics are important for applications and provide an insight into the current research in this field. The participants should be motivated to perform their own research in this area.
Teaching methodology
Elaboration and discussion of properties and applications of polynomial functions in cryptography.
Course content
1. Polynomial functions in modern cryptography
2. Algebraic properties of power functions
3. Fixed points of the power functions on GF(q) and Z_n
4. Chebyshev polynomials, Dickson polynomials and Lucas sequences
5. Dickson polynomial permutations on GF(q) and Z_n
6. Fixed points of Dickson polynomial permutations
7. Primality tests by Dickson polynomials
8. Pseudoprimes and Carmichael numbers
9. RSA-cryptosystems with wrong keys
10. Chains of permutable polynomials, Conjecture of Schur
Prior knowledge expected
Basic facts from algebra and elementary number theory.
Literature
Original papers on the topics of the lecture will be given during the course.
Some of the topics of this course are discussed on a high level in the book by Lausch, H. and W. Nöbauer: Algebra of Polynomials. North Holland Publishing Company, Amsterdam, 1973.
Examination information
Modified examination information (exceptional COVID-19 provisions)
In consideration of the Covid-19 situation the first examination on January 31 will be online. If somebody wishes a written exam I will arrange this too.
Examination methodology
Written exam at the end of the semester. Further dates in the following semester.
Examination topic(s)
Content of the course and examples similar to the exercises of the course.
Assessment criteria / Standards of assessment for examinations
The questions of the exam will be weighted with points. For a positive result one has to reach at least 50% of all possible points.
Grading scheme
Grade / Grade grading schemePosition in the curriculum
- Thematic Doctoral Programme Modeling-Analysis-Optimization of discrete, continuous and stochastic systems
(SKZ: ---, Version: 16W.1)
-
Subject: Modeling-Analysis-Optimization of discrete, continuous and stochastic systems
(Compulsory subject)
-
Modeling-Analysis - Optimization of discrete, continuous and stochastic systems (
0.0h XX / 0.0 ECTS)
- 311.265 Selected Topics in Discrete Mathematics (Permutation Polynomials in Cryptography) (2.0h VO / 3.0 ECTS)
-
Modeling-Analysis - Optimization of discrete, continuous and stochastic systems (
0.0h XX / 0.0 ECTS)
-
Subject: Modeling-Analysis-Optimization of discrete, continuous and stochastic systems
(Compulsory subject)
- Bachelorstudium Technische Mathematik
(SKZ: 201, Version: 17W.1)
-
Subject: Diskrete Mathematik
(Compulsory elective)
-
10.8 Ausgewählte Kapitel der Diskreten Mathematik (
2.0h VO / 3.0 ECTS)
- 311.265 Selected Topics in Discrete Mathematics (Permutation Polynomials in Cryptography) (2.0h VO / 3.0 ECTS) Absolvierung im 5., 6. Semester empfohlen
-
10.8 Ausgewählte Kapitel der Diskreten Mathematik (
2.0h VO / 3.0 ECTS)
-
Subject: Diskrete Mathematik
(Compulsory elective)
- Bachelor's degree programme Technical Mathematics
(SKZ: 201, Version: 12W.2)
-
Subject: Diskrete Mathematik
(Compulsory elective)
-
Ausgewählte Kapitel der Diskreten Mathematik (
3.0h VU / 5.0 ECTS)
- 311.265 Selected Topics in Discrete Mathematics (Permutation Polynomials in Cryptography) (2.0h VO / 3.0 ECTS)
-
Ausgewählte Kapitel der Diskreten Mathematik (
3.0h VU / 5.0 ECTS)
-
Subject: Diskrete Mathematik
(Compulsory elective)
- Master's degree programme Mathematics
(SKZ: 401, Version: 18W.1)
-
Subject: Discrete Mathematics
(Compulsory elective)
-
6.7 Selected Topics in Discrete Mathematics (
2.0h VO / 3.0 ECTS)
- 311.265 Selected Topics in Discrete Mathematics (Permutation Polynomials in Cryptography) (2.0h VO / 3.0 ECTS)
-
6.7 Selected Topics in Discrete Mathematics (
2.0h VO / 3.0 ECTS)
-
Subject: Discrete Mathematics
(Compulsory elective)
- Master's degree programme Technical Mathematics
(SKZ: 401, Version: 13W.1)
-
Subject: Diskrete Mathematik
(Compulsory elective)
-
Algebraic Methods in Discrete Optimization (
3.0h VU / 5.0 ECTS)
- 311.265 Selected Topics in Discrete Mathematics (Permutation Polynomials in Cryptography) (2.0h VO / 3.0 ECTS)
-
Algebraic Methods in Discrete Optimization (
3.0h VU / 5.0 ECTS)
-
Subject: Diskrete Mathematik
(Compulsory elective)
- Doctoral programme Doctoral programme in Technical Sciences
(SKZ: 786, Version: 12W.4)
-
Subject: Studienleistungen gem. § 3 Abs. 2a des Curriculums
(Compulsory subject)
-
Studienleistungen gem. § 3 Abs. 2a des Curriculums (
16.0h XX / 32.0 ECTS)
- 311.265 Selected Topics in Discrete Mathematics (Permutation Polynomials in Cryptography) (2.0h VO / 3.0 ECTS)
-
Studienleistungen gem. § 3 Abs. 2a des Curriculums (
16.0h XX / 32.0 ECTS)
-
Subject: Studienleistungen gem. § 3 Abs. 2a des Curriculums
(Compulsory subject)
Equivalent courses for counting the examination attempts
-
Wintersemester 2018/19
- 311.265 VO Ausgewählte Kapitel der Diskreten Mathematik (Permutationspolynome in der Kryptographie) (2.0h / 3.0ECTS)