Can I create "private" index

I have two users USER1 and USER2 and two corresponding schemes USER1 USER2.
There is a table TABLE1 under schema USER1 with few indexes IND_N1, IND_N2, IND_N3.
USER2 has a "select" privilege for this table. I need to create an index for table USER1.TABLE1 which only USER2 can use. This index should not be visible, accessible or usable by USER1. Is it possible in Oracle 7.3.2 ? If yes, maybe someone know how to do it?

        Thanks.                Stan.