ZK

Circuit

A circuit can be represented as follows:

$$C(x: \{ \dots \},\ w: \{ \dots \})$$

Here, $x$ denotes the public input, and $w$ denotes the witness (i.e., private input).

The circuit outputs $C(x, w) = 1$ if the conditions are satisfied; otherwise, it returns $0$.

Example

Suppose you want to create a circuit that checks whether you know the square root of a value $X$ without revealing the square root itself. The circuit can be expressed as:

$$C(x: \{ X \},\ w: \{ y \}):\quad y^2 \stackrel{?}{=} X$$

This verifies that $y$ is a valid square root of the public input $X$.