19.06.2025 –, ZKM Vortragssaal
Sprache: English
Tropical geometry is a recently named branch in mathematics. Some of those tropical structures are now discussed in regards of cryptography. In the talk I will give an overview about currently discussed protocols and pros and cons of tropical math in computer science. The tropical automorphism protocol suggested by Grigoriev and Shpilrain, 2014, will be discussed in further detail.
A tropical semiring has two operators, plus and min (some people also use max). To have an identity element for the min operation, the infinity element is added to whichever set (from Z to R) is used. It's a semiring because you could define a minus, but no inverse of min, making it a structure similar to a ring, missing the invertability of one operator. Using the information loss caused by min, some people thought of using it for cryptography. Whether using the tropical semiring safes resources or lowers compexity is still being discussed.
Multiple papers were released discussing attacks and variations of different protocols, such as the Stickel protocol, and a tropical matrix protocol similar to Diffie-Hellman, both proposed by Dima Grigoriev and Vladimir Shpilrain. Another one, which is also the protocol I work with the most, is based on automorphisms. Automorphisms are easily invertible if you know what they are made of, in this case monomial and triangular automorphisms. It's used for key transferring. I'll show an analysis on my implementation of that protocol.
I am Toni, currently writing my thesis about tropical cryptography, and how to use tropical structures in computer science. I will turn 23 soon, which is my favorite prime number. I usually wear at least one "something" rainbow and pants with pockets. I like photography, one on one conversations and love math.