Lecture4

# Lecture4 - 1 IS 2150 / TEL 2810 Introduction to Security...

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Unformatted text preview: 1 IS 2150 / TEL 2810 Introduction to Security James Joshi Associate Professor, SIS Lecture 4 September 20, 2011 Access Control Model Foundational Results Objective Understand the basic results of the HRU model Saftey issue Turing machine Undecidability 2 3 Safety Problem: formally Given Initial state X = ( S , O , A ) Set of primitive commands c r is not in A [ s , o ] Can we reach a state X n where 5 s , o such that A n [ s , o ] includes a right r not in A [ s , o ]?- If so, the system is not safe- But is “ safe ” secure? 4 Undecidable Problems Decidable Problem A decision problem can be solved by an algorithm that halts on all inputs in a finite number of steps. Undecidable Problem A problem that cannot be solved for all cases by any algorithm whatsoever 5 Decidability Results (Harrison, Ruzzo, Ullman) Theorem : Given a system where each command consists of a single primitive command (mono-operational), there exists an algorithm that will determine if a protection system with initial state X is safe with respect to right r . 6 Decidability Results (Harrison, Ruzzo, Ullman) Proof: determine minimum commands k to leak Delete/destroy : Can’t leak Create/enter : new subjects/objects “equal”, so treat all new subjects as one No test for absence of right Tests on A[s 1 , o 1 ] and A[s 2 , o 2 ] have same result as the same tests on A[s 1 , o 1 ] and A[s 1 , o 2 ] = A[s 1 , o 2 ] ∪ A[s 2 , o 2 ] If n rights leak possible, must be able to leak k = n (| S | +1)(| O |+1)+1 commands Enumerate all possible states to decide 7 c 1 c 2 c i c j c m c n c x c y c i c n c y Delete/destroy REMOVE these c a c b c 2 c j c b Initial A Create Statements Create s 1 ; Create s 2 s 1 s 2 s 1 s 2 After execution of c b Discard these s 1 s 1 …… …… But the condition of But the condition of c c m needs to be changed needs to be changed c 1 c 2 c i c j c m c n c x c y c i c n c y Delete/destroy REMOVE these c a c b c 2 c j c b Initial A Create Statements Create s 1 s 1 s 2 s 1 s 2 Just use first create s 1 s 1 After two creates o 1 o 2 X Y Z Y ∪ Z X o 1 o 2 If Condition Condition Enter statement r ∈ A[ s 1 , o 1 ] r ∈ A[ s...
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## This note was uploaded on 12/01/2011 for the course INFSCI 2501 taught by Professor Jjoshi during the Spring '11 term at Pittsburgh.

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Lecture4 - 1 IS 2150 / TEL 2810 Introduction to Security...

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