SubjectsSubjects(version: 845)
Course, academic year 2018/2019
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Elliptic Curves - NMIB015
Title in English: Eliptické křivky
Guaranteed by: Department of Algebra (32-KA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2018
Semester: winter
E-Credits: 6
Hours per week, examination: winter s.:4/0 Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: cancelled
Language: Czech
Teaching methods: full-time
Guarantor: prof. RNDr. Aleš Drápal, CSc., DSc.
Classification: Mathematics > Algebra
Interchangeability : NMMB538
Is incompatible with: NMMB538
Is interchangeable with: NMMB538
Annotation -
Last update: prof. RNDr. Aleš Drápal, CSc., DSc. (22.04.2011)
The course introduces into arithmetics of elliptic curves, to its implementation and to concrete algorithms and cryptosystems based on elliptic curves. It is assumed that the student is familiar with basic concepts of algebraic geometry (say, in the extent of the course "Algebraic geometry in positive characteristic").
Literature - Czech
Last update: T_KA (23.05.2003)

Silverman: The arithmetic of elliptic curves, Springer Verlag 1986;

Blake, Seroussi, Smart: Elliptic curves in cryptography, Cambridge Univ. Press 1999;

Cremona: Algorithms for modular elliptic curves, Cambridge Univ. Press 1992.

Syllabus -
Last update: T_KA (23.05.2003)

Arithmetic of elliptic curves (Weierstrass equation, isomorphisms and endomorphisms, invariants, chord and tangent process), influence of characteristics, division polynomials, Weil pairing). Effective implementation (addition and multiplication of points, Frobenius expansion, compression of points). Algorithmic complexity of elliptic curves. Schoof algorithm and its extensions.

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