MATH783 POINT LATTICES AND THEIR APPLICATIONS
| Course Code: | 2360783 |
| METU Credit (Theoretical-Laboratory hours/week): | 3 (3.00 - 0.00) |
| ECTS Credit: | 8.0 |
| Department: | Mathematics |
| Language of Instruction: | English |
| Level of Study: | Graduate |
| Course Coordinator: | Prof.Dr. GÜLİN ERCAN |
| Offered Semester: | Fall and Spring Semesters. |
Course Objectives
To study mathematical properties of lattices, discuss several lattice problems which we believe are hard (even against quantum computers), and use these hard problems to construct cryptographic applications with a particular emphasis on recent results.
Course Content
The definition of a lattice, lattice basis, fundamental region, lattice scaling, lattice cosets, lattice determinant, minimum distance, Minkowski and Blichfeldt theorems, successive minima, dual lattice, shortest vector problem, closest vector problem, covering radius, lattice reduction algoritms, lattice-based cryptosystems with attacks.
Course Learning Outcomes
At the end of the course students are expected to:
- understand basic properties and the geometry of lattices,
- be familiar with the fundamental lattice problems such as SVP, CVP and their approximations
- use algorithms for solving computational problems on lattices and their applications to lattice based cryptography.
Program Outcomes Matrix
| Level of Contribution | |||||
| # | Program Outcomes | 0 | 1 | 2 | 3 |
| 1 | Acquires mathematical thinking skills (problem solving, generating ways of thinking, forming correspondence, generalizing etc.) and can use them in related fields. | ✔ | |||
| 2 | Gains academic maturity through self-study. | ✔ | |||
| 3 | Can design mathematics related problems, devise solution methods and apply them when appropriate. | ✔ | |||
| 4 | Carries out parts of a mathematical research program independently. | ✔ | |||
| 5 | Has a command of Turkish and English languages so that he/she can actively communicate (read, write, listen and speak). | ✔ | |||
| 6 | Contributes to solving global, environmental and social problems either individually or as being part of a social group. | ✔ | |||
| 7 | Respects ethical values and rules; applies them in professional and social issues. | ✔ | |||
| 8 | Can work cooperatively in a team and also individually. | ✔ | |||
| 9 | Gets exposed to academic culture through interaction with others. | ✔ | |||
| 10 | Comprehends necessity of knowledge, can define it and acquires it; uses knowledge effectively and shares it with others. | ✔ | |||
0: No Contribution 1: Little Contribution 2: Partial Contribution 3: Full Contribution