Docs

AssertZero

AssertZero is the main opcode in almost any circuit: it allows arithmetic operations over an arbitrary set of variables. This arithmetic operations are represented through equations that must hold throughout the program. For example, if we want to say

x := y*y + z - 2

we should express it like an equation

y*y + z - x - 2 == 0

that ultimately will translate into an AssertZero opcode of the form

#![allow(unused)]
fn main() {
{
    quadratic_terms: [(1,y,y)]
    linear_combinations: [(1,z), (-1, x)]
    constant: -2
}
}

Any assignment of a variable done in Noir, or any comparison by equality will end up being an AssertZero opcode.

Equivalence in Plonky2

Plonky2 has an ArithmeticGate that we can access through the CircuitBuilder API. There are some methods that we can use to facilitate the translation without the need of using the gate directly:

• add(t1: Target, t2: Target)
• mul(t1: Target, t2: Target)
• mul_const(t1: Target, c: FieldElement)
• assert_zero(t: Target) -> Restricts the value being held by the target to equal 0.

The ArithmeticGate accepts equations of the form

k_0 * x * y + k_1 * z

so to translate a single AssertZero we need to generate a Plonky2 circuit that potentially uses many Arithmetic Gates. So, to sum it up, a single AssertZero opcode might be translated to many arithmetic operations.