You are reading gnark development version documentation and some displayed features may not be available in the stable release. You can switch to stable version using the version box at screen bottom.

Updated on April 23, 2021

# Circuit

From a user perspective, a circuit is like a program, which can be written in a programming language like Go. However, internally a circuit is a constraint system; that is, a list of constraints which have an algebraic form.

For Groth16, a constraint looks like $(\sum_ia_ix_i)(\sum_ib_iy_i)=\sum_ic_iz_i$ where $a,b,c$ are constants and $x,y,z$ are variables which depend on the secret inputs known by a prover.

Translating a circuit, written with gnark API to such a constraint system is called the “arithmetization” of a circuit.

An important point is that every component of a constraint (variables, inputs and constants) live in $\mathbb{F}_p$, a finite field of characteristic $p$. To write a circuit which contains a reasonable number of constraints, it is important to work on the field $\mathbb{F}_p$, so that the field in which the circuits variables live is the same as the field on which the constraint system reasons.

On the other hand, a circuit reasoning on variables which live in $\mathbb{F}_r$ where $r\neq p$, has a high number of constraints because of the algebraic constraints needed to emulate the arithmetic modulo $r$ on a field of characteristic $p$.

Finally, the number of constraints in a circuit is limited; you cannot write arbitrarily large circuits. For example, using Groth16 on BN254, you cannot exceed ~$250M$ constraints.

Questions or feedback? You can discuss issues and obtain free support on gnark discussions channel.
For paid professional support by Consensys, contact us at [email protected]