Detecting Behaviorally Equivalent Functions via Symbolic Execution

Software bugs are a reality of programming. They can be di cult to identify and resolve, even for the most experienced programmers. Certain bugs may even be impossible to remove because they provide some desired functionality. For this reason, designers of modern security-critical applications must accept the inevitable existence of bugs and find ways to detect and recover from the errors they cause. One approach to error detection involves running multiple implementations of a single program at the same time, on the same input, and comparing the results. Divergence of the behavior of the di↵erent implementations indicates the existence of a bug. The question we consider in this paper is how to construct these diverse implementations of security-critical programs in a cost-e↵ective way. The solution we propose is to first find existing diverse function implementations and then use these function implementations as building blocks for diverse program implementations. To find diverse function implementations, we use a technique we call adaptor synthesis to compare arbitrary functions for behavioral equivalence. To account for di↵erences in input argument structure between arbitrary functions we allow for adaptor functions, or adaptors, that convert from one argument structure to another. Using adaptors, the problem of determining whether two arbitrary functions are behaviorally equivalent becomes the problem of synthesizing an adaptor between the two functions that makes their output equivalent on all inputs in a specified domain. Along with presenting our adaptor synthesis technique, we describe an implementation for comparing functions for behavioral equivalence at the binary level on the Linux x86-64 platform using a family of adaptors that allows arithmetic combinations of integer values.