1. 1/15/20161 Computer Security Confidentiality Policies

2. 1/15/20162 Confidentiality Policies A confidentiality policy, or information flow policy prevents unauthorized disclosure of information.

3. 1/15/20163 The Bell-LaPadula model Confidentiality, in its simplest form, can be achieved by using a set of security clearances, arranged, say linearly ( hierarchically ). 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

4. 1/15/20164 The Bell-LaPadula model Let L ( S ) = l S be the security clearance of subject S and L ( O ) = l O be the security classification of object O. Simple Security Property (ss- Property), Preliminary version : S can read O iff. l O ≤ l S (MAC) and S has discretionary read access to O (DAC). *- Property (star Property), Preliminary version : S can write O iff. l S ≤ l O (MAC) and S has discretionary write access to O (DAC).

5. 1/15/20165 Secure Systems A system  is secure if all its states satisfy the ss- property and the *-property. Theorem. Basic Security Theorem, Preliminary version. Let  be a system with secure initial state  0, and let T be the set of its state transformations. If every element of T preserves the ss- and *-properties then  is secure.

6. 1/15/20166 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

7. 1/15/20167 An example of a lattice: the set of subsets of {a,b,c} {a,b,c} {a,b} {b,c} {a,c} {a} {b} {c} 

8. 1/15/20168 A lattice for the categories NUC, EUR and US {NUC, EUR, US} {NUC, EUR} {EUR, US} {NUC, US} {NUC} {EUR} {US} 

9. 1/15/20169 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.

10. 1/15/201610 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  ).

11. 1/15/201611 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)

12. 1/15/201612 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,

13. 1/15/201613 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.

14. 1/15/201614 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.

15. 1/15/201615 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).

16. 1/15/201616 Secure Systems Theorem. Basic Security Theorem Let  be a system with secure initial state  0, and let T be the set of its state transformations. If every element of T preserves the ss and * conditions then  is secure.

17. 1/15/201617 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 ( f s, f o, f c,) where – f s and f c, associate to each subject a maximum/current security level and – f o associates with each object a security level.

18. 1/15/201618 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 o i, o j, o k  O we require that: 1.If o i,≠ o j, then h ( o i )∩ h ( o i ) =  2.There is no set  o 1, o 2,…, o k   O such that for each i = 1,2,…, k, o i +1  h ( o i  and o k +1 = o 1

19. 1/15/201619 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, m  M is the ACM for the current state, f is the triple indicating the current subject and object clearances and categories, h  H is the hierarchy of objects for the current state.

20. 1/15/201620 Formal model 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. The history of a system as it executes. Let N be the set of +ve integers (representing time) X = R N are sequences of requests x (a tuple) Y = D N are sequences of decisions y (a tuple) Z = V N are sequences of states z (a tuple) We interpret this as follows: at some point in time t  N: The system is in state v t-1 A subject makes a request x i The system makes a decision y i The system transitions into a possibly new state z i

21. 1/15/201621 Formal model A system  is represented by an initial state and a sequence of requests, decisions and corresponding states. Formally:  R,D,W,z 0  X  Y  Z, with z 0 the initial state. Furthermore, (x,y,z)   R,D,W,z 0  iff ( x t, y t, z t, z t-1 )  W  for all t  N

22. 1/15/201622 An example See textbook p.133

23. 1/15/201623 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: a.p = e or p = a b.p = r or p = w and f c ( s ) dom f o ( o ). A system satisfies the ss-property if all its states satisfy it.

24. 1/15/201624 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.

25. 1/15/201625 The Bell-LaPadula model Define b ( s : p 1,…, p n ) to be the set of objects that s has access to. *-propety : A state satisfies the *-property iff for each s  S the following hold: a.b ( s : a ) ≠   [  o  b ( s : a ) [ f o ( o ) dom f c ( s )] ] (write-up) b.b ( s : w ) ≠   [  o  b ( s : w ) [ f o ( o ) = f c ( s )] ] (equality for read) c.b ( s : r ) ≠   [  o  b ( s : r ) [ f c ( s ) dom f o ( o )] ] (read-down)

26. 1/15/201626 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 o if its classification is the same as the clearance level (equality for read)

27. 1/15/201627 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 the ss-property, the *-property and the ds-property.

28. 1/15/201628 The Bell-LaPadula model Basic Security Theorem  R,D,W,z 0  is a secure system if it satisfies the ss- property, the *-property and the ds-property.

29. 1/15/201629 Example model instantiation Multics The Multics system There are five groups of rules 1.A set of requests R 1 : to request & release access 2.A set of requests R 2 : to give access & remove access from a different subject 3.A set of requests R 3 : to create and reclassify objects 4.A set of requests R 4 : to remove objects 5.A set of requests R 5 : to change a subjects security level

30. 1/15/201630 Tranquility Principle of 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 & *)

31. 1/15/201631 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  satisfies these properties if: given a state of  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  that would violate the initial state.

32. 1/15/201632 McLean’s system Z Theorem  is secure if its initial state is secure and if each action satisfies the alternative versions of ss, * and ds.