Information Technology Reference
In-Depth Information
Table 1.
Protection state
∆
A
o
0
o
1
s
0
{r
1
,r
2
}
{r
0
,r
1
,r
2
}
s
1
{r
0
,r
1
,r
2
}
{r
1
,r
2
}
s
2
{r
1
,r
2
}
{r
1
,r
2
}
2
Protection States
Let
R
be a finite set with typical member denoted
r
,
r
etc, possibly with sub-
scripts. Its elements are called rights. The rights of our abstract model corre-
spond, for instance, to those of the Unix system:
read
,
write
,etc.Let
SC
be a
countable set of individuals of type subject with typical member denoted
s
,
s
etc, possibly with subscripts, and
OC
be a countable set of individuals of type
object with typical member denoted
o
,
o
etc, possibly with subscripts. Indi-
viduals will also be denoted by the letters
a
,
a
, etc, possibly with subscripts.
Elements of
SC
will also be called subjects and elements of
OC
will also be called
objects. The set of subjects is the set of active entities, such as human beings.
The set of objects is the set of passive entities, such as files. To characterize the
connection between subjects and objects, we present the concept of protection
state. A protection state (
S, O, A
) has three components: a finite subset
S
of
SC
, a finite subset
O
of
OC
, and a function
A
assigning to each subject
s
in
S
and each object
o
in
O
a subset
A
(
s, o
)of
R
. With each finite subset
S
or
O
we associate its cardinality, denoted by
be the cardinality of
the finite set
R
. For subject
s
in
S
and object
o
in
O
, the relationship “
r
is in
A
(
s, o
)” means that subject
s
has right
r
on object
o
. Protection states will be
denoted by the letters
∆
,
∆
, etc, possibly with subscripts. Table 1 illustrates a
simple protection state
∆
presented in a matrix form. The entries in the matrix
specify the rights that each subject has on each object. Seeing that entities such
as processes can be treated as both subjects and objects, we will assume that for
all protection states (
S, O, A
),
S
is included in
O
.Let
SV
be a countable set of
variables of type subject with typical member denoted
σ
,
σ
etc, possibly with
subscripts, and
OV
be a countable set of variables of type object with typical
member denoted
ω
,
ω
etc, possibly with subscripts. Variables will also be de-
noted by the letters
X
,
X
, etc, possibly with subscripts. There are 6 primitive
operations which are used to modify protection states:
|
S
|
or
|
O
|
.Let
|
R
|
-
“
create subject
σ
”and“
destroy subject
σ
”,
-
“
create object
ω
”and“
destroy object
ω
”,
-
“
enter
r
into
A
(
σ, ω
)” and “
delete
r
from
A
(
σ, ω
)”.
Primitive operations will be denoted by the letters
π
,
π
, etc, possibly with
subscripts. Substitutions replace individuals for variables. Hence they are finite
sets of the form
where each
X
i
is a variable, each
a
i
is an
individual, and the variables
X
1
,
...
,
X
n
are pairwise distinct. We will always
consider that substitutions are balanced, i.e. for all
i
in
{
X
1
/a
1
,...,X
n
/a
n
}
,
X
i
and
a
i
are
of the same type. Substitutions will be denoted by the letters
θ
,
θ
, etc, possibly
{
1
,...,n
}
