Applying the stuff we like: blocking semiovals and cryptology
In 2000, a cryptographic protocol relying on ideas from design theory was
patented and gave rise to a whole new set of problems for researchers. The key
ingredient was that of a ``determining set,'' something that can be defined
completely synthetically. In the case of finite projective planes, the
extremal example of a determining set is called a ``blocking semioval.'' In
this talk, I will describe the cryptographic protocol from 2000 in detail,
providing a firm motivation for the study of blocking semiovals. I will then
survey some known results on blocking semiovals and talk about some of my
recent work in this area. The techniques involved are a healthy blend of
incidence geometry, combinatorics, and algebraic geometry over finite fields.
This talk is recommended for undergrads.