It is well known that security policies for programs (such as noninterference) are not properties of a single run, but rather of properties about sets of runs. For example, the following program uses a so-called implicit flow to exfiltrate the value of its secret input:

if (secret == 0) then

This program is bad because it leaks something (one bit of knowledge) about its input: whether or not it is zero. Informally, a program that consumes a secret output and produces a publicly observable output is only secure if that ouput is a constant. Because most programs that produce constant outputs are not useful, this definition is often upgraded to a program that takes a public and private input. The program is then secure if — for any fixed public input iᵖ — and all secret inputs iˢ, the program produces a fixed output o. Simple batch programs are boring and unrealistic, so there are a number of ways in which we can upgrade these definitions to more realistic programs. This is called noninterference, and it is not a property of single executions, but rather a property of a set of executions.

My intention with this post is to make the argument that we are not being as systematic as we could be about constructing program analyses based on our security definitions.

Hyperproperties offer a general framework for discussing these properties on sets of program exectuions. But hyperproperties only give us the means to define what it means for a program to be secure, they don’t give us a tractable mechanism for checking program security. It’s also worth noting that hyperproperties do have some applications beyond merely security properties. They can reason about, e.g., properties of concurrent executions or program refinement. Clearly, the idea of checking sets of program executions is not radical, but doing so has proved difficult and impractical.

To check programs for security definitions like noninterference, a variety of mechanisms have been proposed. Perhaps the most popular in the literature has been security-typed languages, where types encode which information can flow to which sources and whose type systems enforce the security gaurentee. Jif and lio are notable examples that fall into this category.

Checking properties about programs has a rich history in programming languages, that have established a variety of fields: static analysis, type theory, and model checking to name a few. Most of these techniques were originally developed with the intention of checking facts about single-run program properties (e.g., pointer analysis, taint analysis, etc..). Applying them to security is often nonobvious, because they have to be adapted to talk about sets of program runs.

Figuring out how to upgrade our single-run techniques to reason about sets of runs has been the theme of a lot of security research:

  • Security type systems (like the ones in Jif) use type-based techniques to give a composable way to reason about security of a program from smaller components, just as type systems have done for traditional properties like type correctness and resource usage (linear logic).

  • Faceted execution (as seen in languages like Jeeves) is a method of enforcing program security dynamically. It uses an upgraded form of taint tracking to reason about what information has influenced computation of variables. Then it uses this to show observers a view of the computation that ensures they don’t learn secret inputs. This is analogous to inline reference monitors for policies like “the network can never be accessed after the file is read.”

  • Relational program verifiection reasons about pairs of program components (like functions that manipulate heaps) in isolation and glues them together using composition. An example of this is Relational F*, which uses dependent types to specify program behavior on pairs of input states and relates their output states.

  • Hyper temporal logics levels up standard notions of model checking to apply them to checking temporal logic hyperproperties. That work includes a notion of model checking that begins by taking the program and modeling it as a state space of a single execution, and then runs a product semantics for it, showing how to systematically use this semantics to check hyper properties about temporal assertions on state sets. This allows a rich encoding for many trace-based hyperoproperties such as generalized noninterference and observational determinism.

The Future: Push Button Security Checking

One thing that I think is lacking in security currently is that our analyses are only tenuously tied to the properties we want to check. There’s no systematic way to go from a semantics and fact to a way to check facts about those properties for programs. Instead, we see lots of one-off security definitions, and lots of tools for checking definitions, but we rarely see security statements along with a systematically derived mechanism to check facts about those programs. This is an area I think we as a field could improve on.

Within PL, the abstracting abstracting machines technique to deriving abstract interpreters has this flavor. You find the semantics you want to check, bake in the facts you want to check, and then systematically derive an abstract interpreter in a cookbook style. But we have no such bushbutton methodology for checking security properties of programs. As a designer of a system for security today, you have to read the vast literature on the set of security properties you might want to check, find one that suits you, and then dream up an enforcement technique for whatever language you want to work with.

I’m not sure exactly what this would look like. But I think it’s going to be something like this: write down the semantics for the program you want, and then manipulate the semantics in some way to get a state space representing what you want. Then, perform a simple abstraction over that state space to get the properties you want to check.

Here’s how I think this might work. First, you could imagine taking your semantics and simply running it in parallel with another version of the program, so that the concrete state space is now a product space. Hyperproperties that rely on program pairs can be specified using sets of concrete runs. Now abstract the program using our AAM trick and get an abstract state space that is lifted to each component of the pair. Abstract states concretize to pairs of concrete runs, and now checking properties of executions means extending these properties to work on our abstract domain, however they are represented. E.g., if they are represented as symbolic states in a symbolic executor, you would write symbolic formulas asserting noninterference, though certainly other forms are possible. It’s also worth noting that this works for more than just pairs, you could also imagine doing it for triples to check properties like generalized noninterference.

The abstraction technique I proposed is running a product program and then doing the abstraction pointwise over each pair component. I think this is a good first cut because it is easier to see how it relates to the extensional property we want to check: simply check the property by concretizing each point in the abstract state product and running it through the formula. I’m not sure whether or not this technique will scale to larger programs.

One thing that’s missing from this technique is that the abstraction doesn’t know anything about the property we want to check, the abstraction is simply pointwise and the abstract domain hasn’t been efficiently engineered to be tailored to semantic knowlege about the program. But I think this is the right place to start, because it gives us an intuitive baseline for our abstraction.

Let’s say that we want to level this technique up. We would want an abstraction that does know things about how the program is operating. Here’s how I think we might do that for the specific case of noninterference checking: run the original program under a faceted execution semantics with faceted values for the inputs we care about. The faceted semantics is implicitly unrolling this product program when it needs to to gaurentee that our security needs are met. If we want to check whether the program is secure, we simply need to look at the output and ask whether or not it is a faceted value. If it is, we still might be able to do something. Let’s say, for example, that we can prove the faceted value produces the same result no matter what the principle. If we can do this, we can still gaurentee the program doesn’t leak any information.

I’m not sure why this intuition holds, but I have a feeling that it’s because the facet refines the “dumb” product semantics so that it does the product behavior only when necessary. Frankly, I’m not sure if this single case generalizes to the intuition about other sorts of hyperproperties. But I this story of systematically deriving abstract interpreters for security properties is very appealing, and one that we should continue to push on.