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# 16 - Chapter 16 Information Flow Entropy and analysis...

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July 1, 2004 Computer Security: Art and Science ©2002-2004 Matt Bishop Slide #16-1 Chapter 16: Information Flow Entropy and analysis Non-lattice information flow policies Compiler-based mechanisms Execution-based mechanisms Examples

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July 1, 2004 Computer Security: Art and Science ©2002-2004 Matt Bishop Slide #16-2 Overview Basics and background Entropy Nonlattice flow policies Compiler-based mechanisms Execution-based mechanisms Examples Security Pipeline Interface Secure Network Server Mail Guard
July 1, 2004 Computer Security: Art and Science ©2002-2004 Matt Bishop Slide #16-3 Basics Bell-LaPadula Model embodies information flow policy Given compartments A , B , info can flow from A to B iff B dom A Variables x , y assigned compartments x , y as well as values If x = A and y = B, and A dom B , then y := x allowed but not x := y

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July 1, 2004 Computer Security: Art and Science ©2002-2004 Matt Bishop Slide #16-4 Entropy and Information Flow Idea: info flows from x to y as a result of a sequence of commands c if you can deduce information about x before c from the value in y after c Formally: s time before execution of c , t time after H ( x s | y t ) < H ( x s | y s ) – If no y at time s , then H ( x s | y t ) < H ( x s )
July 1, 2004 Computer Security: Art and Science ©2002-2004 Matt Bishop Slide #16-5 Example 1 Command is x := y + z ; where: 0 y 7, equal probability z = 1 with prob. 1/2, z = 2 or 3 with prob. 1/4 each s state before command executed; t , after; so – H( y s ) = H( y t ) = –8(1/8) lg (1/8) = 3 – H( z s ) = H( z t ) = –(1/2) lg (1/2) –2(1/4) lg (1/4) = 1.5 If you know x t , y s can have at most 3 values, so H ( y s | x t ) = –3(1/3) lg (1/3) = lg 3

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July 1, 2004 Computer Security: Art and Science ©2002-2004 Matt Bishop Slide #16-6 Example 2 Command is if x = 1 then y := 0 else y := 1; where: x , y equally likely to be either 0 or 1 H ( x s ) = 1 as x can be either 0 or 1 with equal probability H ( x s | y t ) = 0 as if y t = 1 then x s = 0 and vice versa – Thus, H ( x s | y t ) = 0 < 1 = H ( x s ) So information flowed from x to y
July 1, 2004 Computer Security: Art and Science ©2002-2004 Matt Bishop Slide #16-7 Implicit Flow of Information Information flows from x to y without an explicit assignment of the form y := f ( x ) f ( x ) an arithmetic expression with variable x Example from previous slide: if x = 1 then y := 0 else y := 1; So must look for implicit flows of information to analyze program

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July 1, 2004 Computer Security: Art and Science ©2002-2004 Matt Bishop Slide #16-8 Notation x means class of x In Bell-LaPadula based system, same as “label of security compartment to which x belongs” x y means “information can flow from an element in class of x to an element in class of y Or, “information with a label placing it in class x can flow into class y
July 1, 2004 Computer Security: Art and Science ©2002-2004 Matt Bishop Slide #16-9 Information Flow Policies Information flow policies are usually: reflexive So information can flow freely among members of a single class transitive So if information can flow from class 1 to class 2, and from class 2 to class 3, then information can flow from class 1 to class 3

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