Semigroup action based on skew polynomial evaluation with applications to Cryptography

Abstract: Through this work we introduce an action of the skew polynomial ring $\mathbb{F}<em>{q}\left[X; σ, δ\right]$ over $\mathbb{F}</em>{q}$ 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 $$\mathcal{T}(X)\subset\mathbb{F}_{q}\left[X; σ, δ\right]$$ 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.