Latticies, algorithms, number theory and modern cryptography.
Course objective is to acquaint students with the most important modern tools to build cryptosystems using the methods of number theory and algebraic geometry. Special attention is given to the methods that use lattice in Euclidean space. The basis for this approach are the assumptions on the complexity of some problems on lattices. The important fact here is principal for cryptography is the result of Ajtai that the complexity of closest vector problem on lattices should the complexity of the average of such a problem. The course provides a rigorous mathematical definition of the necessary concepts of algebra and number theory, and evidence essential claims.