Tropical Varieties of Cryptography by Jian Lu ’19, Mathematics Senior Thesis Defense, Wednesday, May 1, 1 – 1:45 pm, Stetson Court Classroom 101
Abstract: Imagine you are some Hungarian-born Brazilian mathematician working on expanding an interesting section of algebraic geometry, but suddenly some French mathematicians decide to meme you and label your entire field “Tropical Algebra” despite the fact that you do not even live in the tropics.
In this talk we will continue the legacy of Imre Simon and study the max tropical semiring where it is the reals union negative infinity with addition redefined as the maximum, and multiplication defined as normal addition. More specifically we will show that it is possible to “tropicalize” a cryptographic system that is not secure in classical arithmetic, but is secure in the tropical world. We will also explore the group law on tropical elliptic curves in 3D.