Circuits

Arithmetic circuits

Circuit is like a program , which can be written in a programming language like Circom. However, internally a circuit is a constraint system; that is, a list of constraints which have a algebric forms;

Constraints:

In order to use zk-SNARK protocols, we need to describe the relation between signals as a system of equations that relate variables with gates. The equations that describe the circuit is called constraints.

Constraints must be quadratic, linear or constant equations. In general, circuits will have several constraints (typically, one per multiplicative gate). The set of constraints describing the circuit is called rank-1 constraint system (R1CS).

• Since circuits are bit difficult for developers, we have programming languages (called DSL) for writing circuit logic. Domain specific language (DSL) : Circom, ZoKrates, Leo, Zinc, Cairo etc

• Once you written your program, it goes for compilation which converts the DSL into SNARK friendly format (R1CS, AIR, plonk-CG etc)

• Once we convert into SNARK friendly format (constraint system), we generate public parameters (Sp, Sv) which is feeded into SNARK prover function to generate zk-proof.

Circom

circom allows programmers to define the constraints that define the arithmetic circuit. All constraints must be of the form A*B + C = 0, where A, B and C are linear combinations of signals. The arithmetic circuits built using circom operate on signals (inputs and outputs).

Zero-knowledge permits proving circuit satisfiability. What this means is, that you can prove that you know a set of signals that satisfy the circuit, or in other words, that you know a solution to the R1CS. This set of signals is called the witness.