1. Computer Security Confidentiality Policies
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2. Confidentiality Policies
A confidentiality policy, or information flow policy
prevents unauthorized disclosure of information.
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3. The Bell-LaPadula model
Top secret (TS)
Personnel files
Alice, Bob
Secret (S)
Electronic mail files
Sally, Cindy
Confidential (C)
Activity log files
Claire, David
Unclassified (UC)
Telephone list files
Joe Bloggs
Confidentiality, in its simplest form, can be achieved by using a set of security clearances, arranged, say linearly (hierarchically).
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4. The Bell-LaPadula model
Let L(S) = lS be the security clearance of subject S and
L(O) = lO be the security classification of object O.
Simple Security Property (ss- Property), Preliminary version :
S can read O iff
.lO ≤ lS (MAC) and
S has discretionary read access to O (DAC).
*- Property (star Property), Preliminary version :
S can write O iff
.lS ≤ lO (MAC) and
S has discretionary write access to O (DAC).
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5. Secure Systems
A system S is secure if all its states satisfy the ss-property
and the *-property.
Theorem. Basic Security Theorem, Preliminary version.
Let S be a system with secure initial state s0, and let T
be the set of its state transformations. If every element of
T preserves the ss- and *-properties then S is secure.
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6. Extending the model
Extend the structure of the security clearances by using
a lattice instead of a hierarchical (linear) structure.
This model uses categories.
Objects are placed in multiple categories
Sets of category are added to each security classification.
Categories arise from the “need-to-know ” principle
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7. An example of a lattice: the set of subsets of {a,b,c}
{a,b} {b,c}
{a,c}
{a} {b} {c} 
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8. A lattice for the categories NUC, EUR and US
{NUC, EUR, US}
{NUC, EUR} {EUR, US}
{NUC, US}
{NUC} {EUR} {US} 
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9. An example, continued
Let H = TS, S, SC, UC be a set of classifications with hierarchical ordering
Take a set of categories NUC, EUR, US
A compartment is a set of categories.
A security label is a pair (L,C), where L in H is
the security level and C is a compartment.
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10. An example, continued The partial ordering is defined by:
(L,C) dom (L,C ) if and only if L L and C C .
We say that (L,C) dominates (L,C ).
Example:
(S, NUC,EUR) dom (UC, NUC).
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11. A sublattice of a partial ordering
{TS; NUC,EUR, US} .
{S; NUC, EUR}
{S; NUC, US} {S; EUR, US}
{UC;NUC} {UC;EUR} {UC; US} 
(the full lattice has 48=32 nodes)
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12. Examples
Suppose
George is cleared into security level (S, NUC,EUR)
DocA is classified (UC, NUC)
DocB is classified (UC, EUR,US)
DocC is classified (S, EUR)
Then
George dom DocA, George dom DocC,
George dom DocB,
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13. Bell-LaPadula (BLP) Model
BLP Structure
Combines,
.access permission matrices for access control,
a security lattice, for security levels,
an automaton, for access operations.
Security policies are reduced to relations in the BLP
structure.
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14. BLP Model A set of subjects S A set of objects O
A set of access operations
A = {execute,read,append,write}
A set L of security levels, with a partial ordering.
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15. The Bell-LaPadula model (general case)
Simple Security Condition (ss-Condition):
S can read O iff
S dom O (MAC) and
S has discretionary read access to O (DAC).
*- Condition (star Condition), Preliminary version :
S can write O iff
O dom S (MAC) and
S has discretionary write access to O (DAC).
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16. Secure Systems Theorem. Basic Security Theorem
Let S be a system with secure initial state s0, and let T
be the set of its state transformations. If every element of
T preserves the ss and * conditions then S is secure.
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17. Formal model S = set of subjects O = set of objects
P = set of rights: r (read), a (write), w (read/write),
e (empty) (= execute in BLP)
M = set of possible ACMs
L = CK lattice of security levels, where:
C = set of clearances, K = set of categories
F = set of triples (fs, fo, fc,) where
fs and fc, associate to each subject a maximum/current security level and
fo associates with each object a security level.
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18. Formal model
Objects may be organized as a set of hierarchies (trees and
single node).
Let H =  h: OP (O) represent the set of hierarchy
functions.
For oi, oj, ok  O we require that:
If oi h(oi) and ojh(oi) , then h(oi)∩ h(oi) =
There is no set o1, o2,…,ok  O such that for each i = 1,2,…, k, oi+1 h(oi) and ok+1= o1
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19. Formal model
An example of a set of hierarchies:
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20. Formal model A state v  V of the system is a 4-tuple (b,m,f,h), where
b = (s,o,p) P (SOP) indicates which subjects have access to which objects and what the rights are
m  M is the ACM for the current state
f  F is the triple indicating the current subject and object clearances and categories
h  H is the hierarchy of objects for the current state
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21. Formal model The history of a system as it executes.
R denotes the set of requests.
D denotes the set of outcomes (decisions).
W = (r,d,v,v’)  R D V V the set of actions of the system moving the system from one state (in V) to the next one
The history of a system as it executes.
Let N be the set of +ve integers (representing time)
X = RN are sequences of requests x (a tuple)
Y = DN are sequences of decisions y (a tuple)
Z = VN are sequences of states z (a tuple)
We interpret this as follows: at some point in time t N:
The system is in state vt-1
A subject makes a request xi
The system makes a decision yi
The system transitions into a possibly new state zt
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22. Formal model S = S (R,D,W,z0)  X Y  Z , with z0 the initial state.
A system S is represented by an initial state and a sequence of requests, decisions and corresponding states.
Formally:
S = S (R,D,W,z0)  X Y  Z ,
with z0 the initial state.
Furthermore,
(x,y,z)  S (R,D,W,z0) iff (xt, yt, zt , zt-1)  W
for all t  N
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23. An example
See textbook p.133
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24. The Bell-LaPadula model
ss-property:
(s,o,p) SOP satisfies the ss-property relative
to the security level f iff one of the following holds:
p = e or p = a
p = r or p = w and fc(s) dom fo(o).
A system satisfies the ss-property if all its states satisfy it.
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25. The Bell-LaPadula model
ss-property:
In other words, a subject can read an object or read
and write to it, only if it dominates it.
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26. The Bell-LaPadula model
Define b(s: p1,…,pn) to be the set of objects that s
has access to.
*-property:
A state satisfies the *-property iff for each sS the following hold:
b(s:a) ≠   [o b(s:a) [fo(o) dom fc(s)] ] “write-up”1
b(s:w) ≠   [o b(s:w) [fo(o) = fc(s)] ] “equality for read/write”
b(s:r) ≠   [o b(s:r) [fc(s) dom fo(o)] ] “read-down”
1 N.B. Should be write-same-or-up, or better, not-write-down
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27. The Bell-LaPadula model
*-propety:
In other words, a state satisfies the *-property if for
each sS:
s can write to an object o only if the objects classification dominates the subjects clearance (write-up)
s can also read (read/write) o if its classification is the same as the clearance level (equality for read/write)
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28. The Bell-LaPadula model
ds-property
A state v = (b,m,f,h) satisfies the discretionary security property (ds-property) iff:
 (s,o,p)  b we have p  m[s,o].
A system is secure if it satisfies (all its states) the ss-property, the *-property and the ds-property.
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29. The Bell-LaPadula model
Basic Security Theorem
S(R,D,W,z0) is a secure system if it satisfies the ss- property, the *-property and the ds-property.
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30. Example model instantiation Multics
The Multics system
There are five groups of rules
A set of requests R1: to request & release access
A set of requests R2 : to give access & remove access from a different subject
A set of requests R3 : to create and reclassify objects
A set of requests R4 : to remove objects
A set of requests R5 : to change a subjects security level
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31. Tranquility Principle of tranquility Principle of strong tranquility
Subjects and objects may not change their security
levels once they have been instantiated.
Principle of strong tranquility
No change during the lifetime of the system.
Principle of weak tranquility
Security levels do not change in a way that violates the
rules of a given security policy. (for BLP: ss, *- and ds)
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32. McLean’s system Z
Mc Lean reformulated the notion of a secure action and
defined an alternative version of ss, * and ds
Roughly,
A system S satisfies these properties if:
given a state of S that satisfies them, the action transforms
the state into a possibly new state that also satisfies them and
eliminates any accesses present in the transformed state
of S that would violate the initial state.
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33. McLean’s system Z Theorem
S is secure if its initial state is secure and if each
action satisfies the alternative versions of ss, *- and ds.
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