# Applications of Polynomial System Solving in Cryptology

### From SIAG-AG

The security of many cryptosystems is strongly related to the hardness of solving polynomial systems over finite fields. These systems often have specific algebraic properties, which may be leveraged by specialized methods. The goal of this minisymposium is to bring together experts in cryptology and in computational algebraic geometry to discuss the interaction of recent developments in polynomial system solving and related problems arising in cryptology.

Speakers:

- Elisa Gorla (University of Neuchâtel, Switzerland): Optimal representations for trace zero subgroups
- Tim Hodges (University of Cincinnati, USA): Weil-descent, first-fall degree and complexity of Grobner basis algorithms
- Sebastian Kochinke (University of Leipzig, Germany): The Discrete Logarithm Problem on non-hyperelliptic Curves of Genus g>3
- Koh-ichi Nagao (Kanto Gakuin University, Japan): Equation systems coming from Weil descent and the elliptic curve discrete logarithm problem
- Pablo Parrilo (Massachusetts Institute of Technology, USA): Chordal Structure and Polynomial Systems
- Igor Semaev (University of Bergen, Norway): New results in the linear cryptanalysis of DES
- Bo-Yin Yang (Academia Sinica, Taiwan): Enumerations and Groebner bases methods on generic multivariate polynomial systems