Péter Kutas:
Lattice reduction and its application to cryptography
A (full) lattice is a discrete subgroup of ℝn, or alternatively the integer linear combination of a basis of ℝn. Due to their simplicity lattices appear in many different areas of mathematics such as number theory, combinatorial geometry or algebraic geometry. This course will take a glimpse into lattice reduction, i.e., how to find short vectors in lattices and will present several applications. One major application concerns the cryptanalysis of RSA variants through a method introduced by Coppersmith to find small roots of univariate polynomials modulo N. If time permits we will also show how lattices allow one to build cryptographic schemes resistant to quantum attacks.