Databases Reference
In-Depth Information
Shifting the Center
Shifting the center of the area returned by a sensing technology is another
way of obfuscating a location measurement. The obfuscated area is derived
from the original area by calculating the distance
d
between the two centers
and the shifting angle
θ
.Let
Area
(
r, x
c
+
Δx, y
c
+
Δy
) be the obfuscated
area. Note that, since LBAC applications cannot deal with false information
to provide a service, obfuscated areas with no intersection with the original
location measurement are considered not acceptable. The reason is that, since
location measurements contain users positions with probability 1, all the areas
disjoint with a location measurement have probability 0 of including the real
user location, and then are indiscernible using the relevance metric. Therefore,
these areas must be simply considered as false location information.
The privacy gain can be measured by considering the intersection of the
original and obfuscated areas, denoted
Area
Tech∩Priv
. Intuitively, the degree
of privacy is inversely proportional to the intersection of the two areas and
therefore it is directly proportional to the distance
d
[0
,
2
r
] between the
two centers. In particular, if
d
= 0, there is no privacy gain and
P
((
x
u
,y
u
)
∈
∈
Area
(
r, x
c
+
Δx, y
c
+
Δy
)) =
P
((
x
u
,y
u
)
∈
Area
(
r, x
c
,y
c
)) = 1. If
d
=2
r
,
there is maximum privacy and
P
((
x
u
,y
u
)
Area
(
r, x
c
+
Δx, y
c
+
Δy
)) tends
to 0; and if 0
<d<
2
r
, there is an increment of privacy and 0
<P
((
x
u
,y
u
)
∈
∈
Area
(
r, x
c
+
Δx, y
c
+
Δy
))
<
1.
Angle
θ
(see Fig. 1(b)) is assumed to be randomly chosen, since all values
of
θ
are equivalent with respect to the privacy preferences of users.
To measure the obfuscation effect and define the relation between rele-
vances, two probabilities must be composed:
i)
the probability that the real
user's position belongs to the intersection
Area
Tech∩Priv
,and
ii)
the proba-
bility that a random point selected from the whole obfuscated area belongs
to the intersection. Then, the relation between relevances
R
Tech
and
R
Priv
is
represented by:
R
Priv
=
P
((
x
u
,y
u
)
∈ Area
Tech∩Priv
)
· P
((
x, y
)
∈ Area
Tech∩Priv
)
·R
Tech
=
Area
Tech
∩
Priv
Area
(
r, x
c
,y
c
)
·
Area
Tech
∩
Priv
Area
(
r, x
c
,y
c
)
2
·R
Tech
Area
Tech∩Priv
Area
(
r, x
c
+
Δx, y
c
+
Δy
)
·R
Tech
=
(3)
0, the distance
d
between
the centers of the original and obfuscated area is calculated from (1) and (3)
as follows:
Given the privacy preference expressed by
λ
≥
Area
2
Tech∩Priv
Area
(
r, x
c
,y
c
)
2
(
λ
+1)
−
1
=
(4)
The distance
d
between the centers is the unknown variable to be derived
to obtain the obfuscated area. It can be calculated by expanding the term
Area
Tech∩Priv
as a function of
d
and by solving the following system of equa-
tions, whose variables are
d
,
σ
and
γ
.
σ
and
γ
are the central angles of circular
