Databases Reference
In-Depth Information
5 Securing OLAP Data Cubes
The data cube is a natural data model for OLAP systems and underlying
data warehouses. This section reviews several methods in safeguarding OLAP
data cubes against both unauthorized accesses and indirect inferences.
5.1 SUM-only Data Cubes
This section describes two efforts inspired by previous inference control meth-
ods in statistical databases. As an inherited limitation, only SUMs are con-
sidered. Moreover, only the core cuboid is considered as sensitive. We show
that improved results can be obtained by exploring the unique structures of
data cubes.
Cardinality-Based Method
The
cardinality-based
method by Dobkin et. al [13] determines the existence
of inferences based on the number of answered queries. In a data cube, aggre-
gations are pre-defined based on the dimension hierarchy, and what may vary
is the number of empty cells, that is previously known values. Recall that
in Section 3.1, Example 1 illustrated a straightforward connection between
1-d inferences and the number of empty cells in a data cube. That is, an 1-d
inference is present when an adversary can access any cell that has exactly
one ancestor in the core cuboid. A similar but less straightforward connection
also exists between m-d inferences and the number of empty cells, as we shall
show in this here.
The model for inferences in this case is similar to that given by Chin et.
al [8], but the queries are limited to data cube cells. Here we only consider one-
level dimension hierarchy where each dimension can only have two attributes,
that is the attribute in core cuboid and the
all
. For each attribute of the core
cuboid, we assume an arbitrary but fixed order on its domain. Although an
attribute may have infinitely many values, we shall only consider the values
that appear in at least one non-empty cell in the given data cube instance. The
number of such values is thus fixed. From the point of view of an adversary,
the value in any non-empty cell is unknown, and hence the cell is denoted by
an unknown variable. The central tabulation in Table 1 rephrases part of the
core cuboid in Figure 1.
Table 1 also includes cells in descendants of the core cuboid, namely, the
aggregation cuboids
. These are
,as
we only consider one-level dimension hierarchy. For SUM-only data cubes, the
dependency relation can be modeled as linear equations. At the left side of
those equations are the unknown variables in the core cuboid, and at the left
side the values in the aggregation cuboids. Table 2 shows a system of nine
equations corresponding to the nine cells in the aggregation cuboids.
Next we obtain the reduced row echelon form (RREF)
M
rref
of the coe
-
cients matrix through a sequence of elementary row operations [19], as shown
all, employee
,
quarter, all
,and
all, all
