This paper presents a compact design of a multiplicative inverter for elliptic curve cryptosystems. Using a methodology based on the composite field arithmetic, we propose a combinatorial solution to mitigate the usage of look up tables as commonly adopted by the conventional software based approach. In particular, we perform further isomorphism in the subfield, such that the required arithmetic are constructed using logical AND and XOR gates only. In this work, we demonstrate our proposed methodology with the field GF((28)41) ≅ GF((((22)2)2)41) in optimal normal type II basis. The chosen field is both secure and results in efficient computation. An analysis of the resultant hardware complexity of our inverter is reported towards the end.