Course detail
Geometrical Algorithms and Cryptography
FSI-SAV-AAcad. year: 2023/2024
Basic outline of the lattice theory in vector spaces, Voronoi tesselation, computational geometry, commutative algebra and algebraic geometry with the emphasis on convexity, Groebner basis, Buchbereger algorithm and implicitization. Elliptic curves in cryptography, multivariate cryptosystems.
Language of instruction
Number of ECTS credits
Mode of study
Guarantor
Department
Entry knowledge
Rules for evaluation and completion of the course
Lectures: recommended
Aims
The algoritmization of some geometric and cryptographic problems.
Study aids
Prerequisites and corequisites
Basic literature
Bump, D., Algebraic Geometry, World Scientific 1998 (EN)
Webster, R., Convexity, Oxford Science Publications, 1994 (EN)
Recommended reading
Classification of course in study plans
Type of course unit
Lecture
Teacher / Lecturer
Syllabus
2. Delone sets.
3. k-lattices, Gram matrix, dual lattice.
4. Orders of quaternion algebras.
5. Voronoi cells. Facet vectors.
6. Fedorov solids. Lattice problems.
7. Principles of asymmetric cryptography. RSA system.
8. Elliptic and hypereliptic curves. Elliptic curve cryptography.
9. Polynomial rings, polynomial automorphisms.
10. Gröbner bases. Multivariate cryptosystems.
11. Algebraic varieties, implicitization. Multivariate cryptosystems.
12. Convexity in Euclidean and pseudoeucleidic spaces.
13. Reserve.