In this paper we study the problem of generating all keys of a formal context as well as a hypergraph. We show that computing the maximum size of a key is NP-complete. Consequently, there is no polynomial time algorithm that decides if a hypergraph is k-conformal, unless P=NP. We also present an algorithmic framework based on decomposition to enumerates all keys of a hypergraph. As example we propose a decomposition of a hypergraph into conformal hypergraphs. Computing a minimal decomposition of an arbitrary hypergraph into conformal hypergraphs remains open in this paper.