Why you cannot even hope to use Ore algebras in Cryptography

Abstract

We adapt tag-variables and Buchberger reduction in order, given two elements, $$pg\in R$$ into an effective ring R, to express g as the evaluation of a polynomial $$f(X)\in R[X]$$ at p, $$g=f(p)$$ . As a by-product, we present also an attack to a couple of Cryptographical protocols.