Abstract: Multivariate cryptography belongs to post-quantum cryptography, which is the branch of cryptography that is supposed to remain secure even in the presence of a quantum computer. After introducing public-key cryptography and motivating the need for studying post-quantum cryptography, I will discuss the role played by commutative algebra techniques in multivariate cryptography. The security of multivariate cryptographic primitive relies on the hardness of computing the solutions of multivariate polynomial systems over finite fields. Since we can compute the solutions of a polynomial system from this Gröbner basis, bounds on the complexity of Gröbner bases computations provide bounds on the security of the corresponding multivariate cryptographic primitives. In this talk, I will introduce and discuss some algebraic invariants which play a role in these security estimates and motivate they importance in this applied setting.

Elisa Gorla, A native of Genoa Italy, received her Ph.D. in Mathematics in 2004 from the University of Notre Dame, USA, under the supervision of Juan Migliore. She became a Swiss National Science Foundation Professor at the University of Basel, Switzerland in 2009, and since 2012 she has been a Professor at the Mathematics Institute of the University of Neuchâtel, Switzerland, of which she is currently the Director.

Gorla’s research interests include coding theory, cryptography, Gröbner bases, as well as topics in commutative algebra and algebraic geometry. Since 2018, she has been a member of the Board of Trustees of the Swiss Mathematical Society. She has been on the Advisory Boards of MEGA (Effective Methods in Algebraic Geometry) since 2015 and serves on various Editorial Boards, such as for SIAM Journal on Applied Algebra and Geometry and the Journal of algebra, Combinatorics, Discrete Structures, and Applications. She was an invited research member at the Institute for Computation and Experimental Research in Mathematics (Providence, RI, USA), the Mathematical Science Research Institute (Berkeley, CA, USA), the Mittag-Leffler Institute (Stockholm Sweden), and the Max-Planck-Institute for Mathematics (Bonn, Germany).