Modul: MAT076 Arbeitsgemeinschaft in Codierungstheorie und Kryptographie

## The Finite Field Isomorphism Problem and its Cryptographic Applications.

Pascal Christinat talk

**Date:** 03.10.18 **Time:** 16.00 - 17.00 **Room:** Y27H12

Any finite field has cardinality p^n, where p is prime and n a positive integer. Conversely, for any prime power p^n we can construct isomorphic finite fields X and Y. The elements of these fields can be seen as polynomials with coefficients mod p.

Doröz et al. observed that the images of polynomials from X appear to be uniformly distributed in Y. If this observation is true, it can be made arbitrarily hard to distinguish between the image of a collection of polynomials from X and a randomly chosen collection of polynomials from Y. They made use of this new problem to set up a homomorphic encryption scheme and we use this observation to build a pseudorandom number generator.