We address the inference control problem in data cubes with some data known to users through external knowledge. The goal of inference controls is to prevent exact values of sensitive data from being inferred through answers to online analytical processing (OLAP) queries. We present an information theoretic approach for cardinalitybased inference control, which simply counts the number of cells that all queries have covered thus far to determine whether a new query should be answered. Compared to previous approaches in sum-only data cubes, our new approach has a more general framework (applies to MIN, MAX and SUM) and is more effective. Categories and Subject Descriptors H.2.8 [Information Systems]: Database Applications—Data Mining; H.2.7 [Information Systems]: Database Administration—Data warehouse and repository, Security, integrity, and protection General Terms Algorithms, Security Keywords Data Mining, OLAP, Inference Control, Information Theory