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**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.