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DTSTART;TZID=Europe/Brussels:20230309T130000
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SUMMARY:Ramachandran CHITTUR ANANTHARAMAN (University of Namur)
DESCRIPTION:Title: Inverses of polynomials over finite fields – A Koopman operator based approach \nAbstract: 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. \nThe seminar will take place in Room S08 at the Faculty of Sciences.
URL:https://www.naxys.be/event/ramachandran-chittur-anantharaman-university-of-namur/
CATEGORIES:NAXYS Seminar
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