Decomposition Instead of Self-Composition for k-Safety

We describe a novel technique for proving k-safety properties (non-interference, determinism, etc.) via a decomposition that enables one to leverage non-relational reasoning techniques. The key is the inter-operation of the following principles. First, we observe that many k-safety properties of interest have a particular structure that we call ψ-quotient partitionability where ψ is a k-ary formula. Second, we develop a partitioning strategy of execution traces based on the k-safety property Φ of interest such that if ψ holds for k traces then they must be in the same partition. Finally, within a partition component Ti, we observe that we can prove k-safety by instead proving a universal property: all traces within the partition satisfy some common property Pi, chosen to be strong enough that it implies the k-safety property Φ of any k-tuple of traces in components Ti. We apply this strategy to the task of discovering timing side channels. A key feature of our approach is a demanddriven partitioning strategy that uses high/low-annotated regex-like trails to reason about one partition component of execution traces at a time. We have applied our technique in a prototype implementation tool called Blazer, based on WALA, PPL, Z3, and the brics automaton library. We have proved non-interference of (or synthesized an attack specification for) 25 programs written in Java bytecode, including 7 classic examples from the literature, and 6 examples extracted from the DARPA STAC challenge problems.