The numerous and huge operations involved in homomorphic encryption applications require fast arithmetic. RNS arithmetic is popular in their software implementations. In this context, we proposed a hierarchical approach for RNS base extension. It leads to 50-60 % reduction of both computation time and constant storage requirements for large homomorphic parameters in our experimental setup. When state-of-the-art parameters are not suitable for our approach, we propose to use equivalent parameters leading to similar reductions.