Syllabus
1. Factorization of polynomials over finite fields, factorization of integral polynomials 2.
Gröbner bases, applications, solving of systems of polynomial equation 3. Algorithm LLL, applications (factorization of polynomials over Z, cryptography).
Annotation
The main topics of the course are algorithms for polynomial factorization, Gröbner bases and Lenstra-Lenstra-
Lovasz Algorithm. All the algorithms find many applications in computer algebra, geometry, cryptoanalysis, and in design of new cryptosystems.