It trusted database administrator monitors queries and introduces noise to the responses with the goal of maintaining data privacy. Under a rigorous definition of breach of privacy, it proved that the total number of queries is sub-linear in the size of the database, a substantial amount of noise is required to avoid a breach, rendering the database almost useless. The positive datamining results in the extensions to the model of described while maintaining the strengthened privacy requirement : 1. Multi-attribute SuLQ databases : The statistics for every k-ary Boolean func- tion can be learned. Since the queries here are powerful (any function), it is not surprising that statistics for any function can be learned. The strength of the result is that statistics are learned while maintaining privacy. 2. Multiple single-attribute SuLQ databases : It how to learn the statistics of any 2-ary Boolean function. For example, we can learn the fraction of records having neither attribute 1 nor attribute 2, or the conditional proba- bility of having attribute 2 given that one has attribute 1. 3. Vertically Partitioned k-attribute SuLQ Databases : The constructions here are a combination of the results for the first two cases: the k attributes are partitioned into (possibly overlapping) sets of size k1 and k2, respectively, where k1 +k2 >= k; each of the two sets of attributes is managed by a multi- attribute SuLQ database. A single-attribute database can be simulated in all of the above settings; hence, in order to preserve privacy, the sub-linear upper bound on queries must be enforced. How this bound is enforced is beyond the scope of this work. Data mining on Published Statistics : Our technique for testing implication in probability yields surprising results in the real life model in which confidential information is gathered by a trusted party, such as the census bureau, who pub- lishes aggregate statistics.