Semigroup action based on skew polynomial evaluation with applications to Cryptography

Through this work we introduce an action of the skew polynomial ring ${\mathbb{F}}_q[X;\sigma ,\delta ]$ over ${\mathbb{F}}_q$ based on its polynomial valuation and the concept of left skew product of functions. This lead us to explore the construction of a certain subset $\mathcal{T}(X)\subset {\mathbb{F}}_q[X;\sigma ,\delta ]$ that allow us to control the non-commutativity of this ring, and exploit this fact in order to build a public key exchange protocol that is secure in Canetti and Krawczyk model.