halo2-tutorial VS tornado-core

As another example, you could define a circuit for proving the N-th Fibonacci number, where row i of the matrix has the values x[i-2], x[i-1], x[i]. This means you'd need three advice columns to begin with, let's call them a, b, c. Then, you'd constrain c to be equal to a + b in the same row using a gate, which requires adding a selector column for controlling it. And you'd have to set up equality constraints so that a and b are equal to b and c from the previous row. Last, in order to expose the N-th number as a public value, you'd need an instance column, constrained to equal the value of c at the last row.

This is the repo we’re going to look at: Tornado core.

The method that I’m using is the same as what is used by Tornado Cash. Tornado Cash is a non-custodial Ethereum and ERC20 privacy solution based on zkSNARKs.

Tornado Cash is a great learning resource on how to build a real-world zk-app with Circom circuits. I strongly recommend going through the 3-page-long white paper, as well as Gubsheep's breaking down Tornado Cash session from the 0xparc course, plus Porter's overview of the white paper.

This was my very short tutorial on using zk-SNARK in JavaScript. It’s not a full course, and you probably have many questions, but I hope I helped you to start your journey. Circom and snarkjs are well documented, and you can also learn a lot from existing projects like Tornado Cash.

This is the MerkleTree contract, and the problem is on lines 58 and 59, I cannot understand why would you need to veryfy that the hash of a number has to be less than FIELD_SIZE.