Hi, In http://issues.apache.org/jira/browse/HARMONY-2091 there is an optimization for modInverse. The issue includes a patch and two html files showing the performance of the method before and after the patch.
In order to obtain this optimized version algorithms from the articles "The Montgomery Modular Inverse - Revisited" (by Savas, E; Koc, C) and "New Algorithm for Classical Modular Inverse" (by Lórencz, R) were implemented. Also some ad-hoc combination of arithmetic operations were introduced in order to avoid unnecessary creation of intermediate data. Thanks, Daniel