- plane projective cubics over arbitrary fields, rational points,
- endomorphisms of elliptic curves, isogenies, complex multiplication, moduli,
- counting of rational points, Hasse bound, Weil conjectures, Schoof's algorithm,
- constructions of elliptic curves, quadratic twist, good/bad reduction,
- special algorithms, discrete logarithm for elliptic curves, factorisation.
Elliptic Curves in Positive Characteristics (M, 3.0 LP)
|Module Number||Module Name||CP (Effort)|
|MAT-40-27-M-6||Elliptic Curves in Positive Characteristics||3.0 CP (90 h)|
|CP, Effort||3.0 CP = 90 h|
|Position of the semester||1 Sem. irreg.|
|Level|| Master (General)|
|Area of study||[MAT-AGCA] Algebra, Geometry and Computer Algebra|
|Reference course of study||[MAT-88.105-SG] M.Sc. Mathematics|
|Type/SWS||Course Number||Title||Choice in |
|SL||SL is |
required for exa.
Elliptic Curves in Positive Characteristics
|P||28 h||62 h||-||-||PL1||3.0||irreg.|
- About [MAT-40-27-K-6]: Title: "Elliptic Curves in Positive Characteristics"; Presence-Time: 28 h; Self-Study: 62 h
Examination achievement PL1
- Form of examination: oral examination (20-30 Min.)
- Examination Frequency: irregular (by arrangement)
- Examination number: 86199 ("Elliptic Curves in Positive Characteristics")
Evaluation of grades
The grade of the module examination is also the module grade.
Competencies / intended learning achievements
Using the example of elliptic curves over arbitrary fields, the students have enlarged their abilities to work on interdisciplinary mathematics (in particular, the triangle between geometry, algebraic number theory, and cryptography). They have studied the theoretical principles of cryptographic algorithms and are able to apply these concepts and techniques successfully. They understand the proofs presented in the lecture and are able to comprehend and explain them.
- J .Silverman, The Arithmetic of Elliptic Curves.
Requirements for attendance of the module (informal)
Requirements for attendance of the module (formal)None
References to Module / Module Number [MAT-40-27-M-6]
|Course of Study||Section||Choice/Obligation|
|[MAT-88.105-SG] M.Sc. Mathematics||[Core Modules (non specialised)] Pure Mathematics||[WP] Compulsory Elective|
|[MAT-88.706-SG] M.Sc. Mathematics International||[Core Modules (non specialised)] Pure Mathematics||[WP] Compulsory Elective|
|[MAT-GM-MPOOL-5]||General Mathematics (Introductory Modules M.Sc.)|