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SIAM SAGA - Seminar on Applied Geometry and Algebra
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Date: Tuesday, September 14 at 11:00am Eastern time zone

Speaker: Elisa Gorla, University of Neuchâtel

Title: Multivariate cryptography and the complexity of polynomial system solving

Abstract: The security of multivariate cryptographic primitives 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 its Groebner basis, bounds on the complexity of Groebner bases computations provide bounds on the security of the corresponding multivariate cryptographic primitives. After introducing multivariate cryptography, I will discuss linear-algebra-based methods for computing Groebner bases, which are currently considered the most efficient algorithms available. I will introduce some invariants which control this complexity and try to answer the question of how hard it is to solve a "random" polynomial system.

Moderator: Jose Israel Rodriguez, University of Wisconsin Madison
Oct 12, 2021 11:00 AM
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Elisa Gorla
@University of Neuchâtel
Elisa Gorla received a Ph.D. degrees in Mathematics from the University of Notre Dame, USA in 2004. In the same year, she joined the Department of Mathematics of the University of Zurich, Switzerland, and in 2009 she was awarded a Swiss National Science Foundation Professorship at the University of Basel, Switzerland. Since 2012, she has been a Professor at the Department of Mathematics of the University of Neuchatel, Switzerland. Her research focuses on the applications of commutative algebra and algebraic geometry, especially to coding theory and cryptography. She is a life member of the Swiss Mathematical Society, the American Mathematical Society, and the Society for Industrial and Applied Mathematics. She is on the Board of Trustees of the Swiss Mathematical Society and on the Steering Committee of the University of Genoa (Italy). During the period 2014-15 she was Vice Chair of the SIAM Activity Group on Algebraic Geometry SI(AG)^2.