Geometrical Algorithms and Cryptography
FSI-SAVCompulsory-optionalMaster's (2nd cycle)Acad. year: 2016/2017Summer semester2. year of study4 credits
Basic outline of computational geometry, commutative algebra and algebraic geometry with the emphasis on convexity, Groebner basis, Buchbereger algorithm and implicitization. Elliptic curves in cryptography, multivariate cryptosystems.
Learning outcomes of the course unit
The algoritmization of some geometric and cryptographic problems.
Mode of delivery
90 % face-to-face, 10 % distance learning
Basics of algebra. The craft of algoritmization.
Recommended optional programme components
Recommended or required reading
Bump, D., Algebraic Geometry, World Scientific 1998
Kureš, Miroslav: Geometrické algoritmy (rukopis, příprava k tisku)
Webster, R., Convexity, Oxford Science Publications, 1994
Bernstein, D., Buchmann, J., Dahmen, E., Post-Quantum Cryptography, Springer, 2009
Planned learning activities and teaching methods
The course is taught through lectures explaining the basic principles and theory of the discipline.
Assesment methods and criteria linked to learning outcomes
Language of instruction
The convergence of mathematician and computer scientist points of view.
Specification of controlled education, way of implementation and compensation for absences
Type of course unit
26 hours, optionally
Teacher / Lecturer
1. Convexity in euclidean spaces.
2. Voronoi diagrams.
3. Geodesic spaces.
4. Rings and fields.
5. Ideals and factorizations.
6. Polynomials, the ordering of polynomials.
7. Groebner basis.
8. Polynomial automorphisms.
9. Algebraic varieties, implicitization.
10. Elliptic and hyperelliptic curves.
11. Principles of asymmetric cryptography.
12. Cryptography based on elliptic curves.
13. Multivariate cryptosystems.