Loading Events

« All Events

  • This event has passed.

Ramachandran CHITTUR ANANTHARAMAN (University of Namur)

March 9, 2023 @ 13:00 - 14:00

Title: Inverses of polynomials over finite fields – A Koopman operator based approach

Abstract: Any map (linear or non-linear) from a finite field to itself can be represented as a polynomial with coefficients over the finite field. When the map is invertible (under composition), the inverse map will also have a polynomial representation. Verifying invertibility and computing the inverse of the non-linear maps over finite fields have significant applications in cryptography and coding theory. In this talk, I discuss a Koopman operator-based approach to test invertibility, compute the inverse of polynomials, and define a linear representation for non-linear maps. This approach can be extended to a parametric family of maps over finite fields (such as Dickson polynomials), and the parametric inverse is computed (when the parametric map is invertible). Further, I shall discuss how this linear representation defined through the Koopman operator leads to a group representation for a group generated by multiple invertible maps under composition.

The seminar will take place in Room S08 at the Faculty of Sciences.


March 9, 2023
13:00 - 14:00
Event Category: