Information Flow
BOTTOM: Masters, I am to discourse wonders: but ask me not what; for if I tell you, I am no true Athenian. I will tell you every thing, right as it fell out.
—A Midsummer Night's Dream, IV, ii, 30–33.
Although access controls can constrain the rights of a user, they cannot constrain the flow of information about a system. In particular, when a system has a security policy regulating information flow, the system must ensure that the information flows do not violate the constraints of the policy. Both compiletime mechanisms and runtime mechanisms support the checking of information flows. Several systems implementing these mechanisms demonstrate their effectiveness.
15.1 Basics and Background
Information flow policies define the way information moves throughout a system. Typically, these policies are designed to preserve confidentiality of data or integrity of data. In the former, the policy's goal is to prevent information from flowing to a user not authorized to receive it. In the latter, information may flow only to processes that are no more trustworthy than the data.
Any confidentiality and integrity policy embodies an information flow policy.
EXAMPLE: The BellLaPadula Model describes a latticebased information flow policy. Given two compartments A and B, information can flow from an object in A to a subject in B if and only if B dominates A.
Let x be a variable in a program. The notation x refers to the information flow class of x.
EXAMPLE: Consider a system that uses the BellLaPadula Model. The variable x, which holds data in the compartment (TS, { NUC, EUR }), is set to 3. Then x = 3 and x = (TS, { NUC, EUR }).
Intuitively, information flows from an object x to an object y if the application of a sequence of commands c causes the information initially in x to affect the information in y.

Definition 15–1. The command sequence c causes a flow of information from x to y if, after execution of c, some information about the value of x before c was executed can be deduced from the value of y after c was executed.
This definition views information flow in terms of the information that the value of y allows one to deduce about the value in x. For example, the statement
y := x;
reveals the value of x in the initial state, so information about the value of x in the initial state can be deduced from the value of y after the statement is executed. The statement
y := x / z;
reveals some information about x, but not as much as the first statement.
The final result of the sequence c must reveal information about the initial value of x for information to flow. The sequence
tmp := x; y := tmp;
has information flowing from x to y because the (unknown) value of x at the beginning of the sequence is revealed when the value of y is determined at the end of the sequence. However, no information flow occurs from tmp to x, because the initial value of tmp cannot be determined at the end of the sequence.
EXAMPLE: Consider the statement
x := y + z;
Let y take any of the integer values from 0 to 7, inclusive, with equal probability, and let z take the value 1 with probability 0.5 and the values 2 and 3 with probability 0.25 each. Once the resulting value of x is known,the initial value of y can assume at most three values. Thus, information flows from y to x. Similar results hold for z.
EXAMPLE: Consider a program in which x and y are integers that may be either 0 or 1. The statement
if x = 1 then y := 0; else y := 1;
does not explicitly assign the value of x to y.
Assume that x is equally likely to be 0 or 1. Then H(x_{s}) = 1. But H(x_{s}  y_{t}) = 0, because if y is 0, x is 1, and vice versa. Hence, H(x_{s}  y_{t}) = 0 < H(x_{s}  y_{s}) = H(x_{s}) = 1. Thus, information flows from x to y.

Definition 15–2. An implicit flow of information occurs when information flows from x to y without an explicit assignment of the form y := f(x), where f(x) is an arithmetic expression with the variable x.
The flow of information occurs, not because of an assignment of the value of x, but because of a flow of control based on the value of x. This demonstrates that analyzing programs for assignments to detect information flows is not enough. To detect all flows of information, implicit flows must be examined.
15.1.1 Information Flow Models and Mechanisms
An information flow policy is a security policy that describes the authorized paths along which that information can flow. Each model associates a label, representing a security class, with information and with entities containing that information. Each model has rules about the conditions under which information can move throughout the system.
In this chapter, we use the notation x ≤ y to mean that information can flow from an element of class x to an element of class y. Equivalently, this says that information with a label placing it in class x can flow into class y.
Earlier chapters usually assumed that the models of information flow policies were lattices. We first consider nonlattice information flow policies and how their structures affect the analysis of information flow. We then turn to compilerbased information flow mechanisms and runtime mechanisms. We conclude with a look at flow controls in practice.