CirC: Compiler infrastructure for proof systems, software verification, and more

Cryptographic tools like proof systems, multi-party computation, and fully homomorphic encryption are usually applied to computations expressed as systems of arithmetic constraints. In practice, this means that these applications rely on compilers from high-level programming languages (like C) to such constraints. This compilation task is challenging, but not entirely new: the software verification community has a rich literature on compiling programs to logical constraints (like SAT or SMT). In this work, we show that building shared compiler infrastructure for compiling to constraint representations is possible, because these representations share a common abstraction: stateless, non-uniform, non-deterministic computations that we call existentially quantified circuits, or EQCs. Moreover, we show that this shared infrastructure is useful, because it allows compilers for proof systems to benefit from decades of work on constraint compilation techniques for software verification. To make our approach concrete we create CirC, an infrastructure for building compilers to EQCs. CirC makes it easy to compile to new EQCs: we build support for three, R1CS (used for proof systems), SMT (used for verification and bug-finding), and ILP (used for optimization), in approximate to 2000 LOC. It's also easy to extend CirC to support new source languages: we build a feature-complete compiler for a cryptographic language in one week and approximate to 900 LOC, whereas the reference compiler for the same language took years to write, comprises approximate to 24000 LOC, and produces worse-performing output than our compiler. Finally, CirC enables novel applications that combine multiple EQCs. For example, we build the first pipeline that (1) automatically identifies bugs in programs, then (2) automatically constructs cryptographic proofs of the bugs' existence.