Computer Security Confidentiality Policies 5/11/2019
Confidentiality Policies A confidentiality policy, or information flow policy prevents unauthorized disclosure of information. 5/11/2019
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). 5/11/2019
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). 5/11/2019
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. 5/11/2019
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 5/11/2019
An example of a lattice: the set of subsets of {a,b,c} {a,b} {b,c} {a,c} {a} {b} {c} 5/11/2019
A lattice for the categories NUC, EUR and US {NUC, EUR, US} {NUC, EUR} {EUR, US} {NUC, US} {NUC} {EUR} {US} 5/11/2019
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. 5/11/2019
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). 5/11/2019
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 48=32 nodes) 5/11/2019
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, 5/11/2019
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. 5/11/2019
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. 5/11/2019
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). 5/11/2019
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. 5/11/2019
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 = CK 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. 5/11/2019
Formal model Objects may be organized as a set of hierarchies (trees and single node). Let H = h: OP (O) represent the set of hierarchy functions. For oi, oj, ok O we require that: If oi h(oi) and ojh(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 5/11/2019
Formal model An example of a set of hierarchies: 5/11/2019
Formal model A state v V of the system is a 4-tuple (b,m,f,h), where b = (s,o,p) P (SOP) 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 5/11/2019
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 5/11/2019
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 5/11/2019
An example See textbook p.133 5/11/2019
The Bell-LaPadula model ss-property: (s,o,p) SOP 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. 5/11/2019
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. 5/11/2019
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 sS 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 5/11/2019
The Bell-LaPadula model *-propety: In other words, a state satisfies the *-property if for each sS: 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) 5/11/2019
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. 5/11/2019
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. 5/11/2019
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 5/11/2019
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) 5/11/2019
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. 5/11/2019
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. 5/11/2019