Swapping Two Items in an Array in Circom This chapter shows how to swap two signals in a list of signals. This is an important subroutine for a sorting algorithm. More generally, lists are a...

Introduction to Stateful Computations in ZK When carrying out iterative computations such as powers, factorials, or computing the Fibonacci sequence, we need to “stop the computation” after a certain...

Conditional Statements in Circom Circom is very strict with the usage of if-statements. The following rules must be followed: Signals cannot be used to alter the behavior of an if-statement. A signal...

Public and Private Inputs A public input in Circom is a signal in the witness that will be revealed to the verifier. For example, suppose we want to create a ZK proof that states: “we know the input...

Symbolic Variables in Circom A symbolic variable in Circom is a variable that has been assigned values from a signal. When a signal is assigned to a variable (thereby turning it into a symbolic...

Quadratic Constraints Circom Constraints A Rank 1 Constraint System has at most one multiplication between signals per constraint. This is called a "quadratic" constraint. Any constraint containing...

Circom Template Parameters, Variables, Loops, If Statements, Assert This chapter covers essential syntax, which you'll see in most Circom programs. With Circom, we're able to define a Rank 1...

The Permutation Argument A permutation argument is a proof that two lists hold the same elements, but possibly in a different order. For example, is a permutation of and vice-versa. The permutation...

Quin Selector The Quin Selector is a design pattern that allows us to use a signal as an index for an array of signals. As a prerequisite, we assume the reader has read the chapter on Conditional...

Introduction to ZK Circuits with Circom Circom is a programming language for creating Rank 1 Constraint Systems (R1CS) and populating the witness vector of the R1CS. The R1CS format is of interest...

Circom Components in a Loop Circom does not allow for components to be directly instantiated in a loop. For example, compiling the following code results in the error below. The workaround is to...

Hacking Underconstrained Circom Circuits With Fake Proofs The operator in Circom can be dangerous because it assigns values to signals but does not constrain them. But how do you actually ~~exploit~~...