A zero-knowledge (ZK) proof guarantees that the result of a computation is correct while keeping part of the computation details private. Some ZK proofs are tiny and can be verified in short time, which makes them one of the most promising technologies for solving two key aspects: the challenge of enabling privacy to public and transparent distributed ledgers and enhancing their scalability limitations. Most practical ZK systems require the computation to be expressed as an arithmetic circuit that is encoded as a set of equations called rank-1 constraint system (R1CS). In this paper, we presentCircom, a programming language and a compiler for designing arithmetic circuits that are compiled to R1CS. More precisely, withCircom, programmers can design arithmetic circuits at a constraint level, and the compiler outputs a file with the R1CS description, and WebAssembly andC++programs to efficiently compute all values of the circuit. We also provide an open-source library calledcircomlibwith multiple circuit templates.Circomcan be complemented withsnarkjs, a library for generating and validating ZK proofs from R1CS. Altogether, our software tools abstract the complexity of ZK proving mechanisms and provide a unique and friendly interface to model low-level descriptions of arithmetic circuits.

Abstract The most widely used Zero-Knowledge (ZK) protocols require provers to prove they know a solution to a computational problem expressed as a Rank-1 Constraint System (R1CS). An R1CS is essentially a system of non-linear arithmetic constraints over a set of signals, whose security level depends on its non-linear part only, as the linear (additive) constraints can be easily solved by an attacker. Distilling the essential constraints from an R1CS by removing the part that does not contribute to its security is important, not only to reduce costs (time and space) of producing the ZK proofs, but also to reveal to cryptographic programmers the real hardness of their proofs. In this paper, we formulate the problem of distilling constraints from an R1CS as the (hard) problem of simplifying constraints in the realm of non-linearity. To the best of our knowledge, it is the first time that constraint-based techniques developed in the context of formal methods are applied to the challenging problem of analysing and optimizing ZK protocols.