The Polynomial Composition Problem in (Z/nZ)[X]

Let n be an RSA modulus and let $\mathcal {P},\mathcal{Q} \in (\mathbb{Z}/n\mathbb{Z})[X]$. This paper explores the following problem: Given polynomials $\mathcal{Q}$ and $\mathcal{Q}(\mathcal{P})$, find polynomial $\mathcal{P}$. We shed light on the connections between the above problem and the RSA problem and derive from it new zero-knowledge protocols suited to smart-card applications.