# Tutorial¶

## circom and snarkjs tutorial¶

This tutorial will guide you in creating your first Zero Knowledge zkSnark circuit. It will navegate across the various techniques to write circuits and it will show you how to create proofs and verify them off-chain and on-chain on Ethereum.

### 1. Installing the tools¶

#### 1.1 Pre-requisites¶

If you don’t have it installed yet, you need to install Node.js in your laptop.

Last stable version of Node.js (Or 8.12.0) works just fine. But if you install the latest current version Node.js (10.12.0) you will see significant performance increase. This is because last versions of node includes Big Integer Libraries nativelly. The snarkjs library makes use of this feature if available, and this improves the performance x10 (!).

#### 1.2 Install circom and snarkjs¶

Just run:

npm install -g circom
npm install -g snarkjs


### 2. Working with a circuit¶

Let’s create a circuit that tries to prove that you are able to factor a number!

#### 2.1 Create a circuit in a new directory¶

1. Create an empty directory called factor where you will put all the files that you will use in this tutorial.
mkdir factor
cd factor

In a real circuit, you will probably want to create a git repository with a circuits directory and a test directory with all your tests, and the needed scripts to build all the circuits.
1. Create a new file named circuit.circom with the following content:
template Multiplier() {
signal private input a;
signal private input b;
signal output c;

c <== a*b;
}

component main = Multiplier();


This circuit has 2 private input signals named a and b and one output named c.

The only thing that the circuit does is forcing the signal c to be the value of a*b

After declaring the Multiplier template, we instantiate it with a component namedmain.

Note: When compiling a circuit a component named main must always exist.

#### 2.2 Compile the circuit¶

We are now ready to compile the circuit. Run the following command:

circom circuit.circom -o circuit.json


to compile the circuit to a file named circuit.json

### 3. Taking the compiled circuit to snarkjs¶

Now that the circuit is compiled, we will continue with snarkjs. Please note that you can always access the help of snarkjs by typing:

snarkjs --help


#### 3.1 View information and stats regarding a circuit¶

To show general statistics of this circuit, you can run:

snarkjs info -c circuit.json


You can also print the constraints of the circuit by running:

snarkjs printconstraints -c circuit.json


#### 3.2 Setting up using snarkjs¶

Ok, let’s run a setup for our circuit:

snarkjs setup

By default snarkjs will look for and use circuit.json. You can always specify a different circuit file by adding -c <circuit JSON file name>

The output of the setup will in the form of 2 files: proving_key.json and verification_key.json

#### 3.3. Calculating a witness¶

Before creating any proof, we need to calculate all the signals of the circuit that match (all) the constrains of the circuit.

snarkjs calculates these for you. You need to provide a file with the inputs and it will execute the circuit and calculate all the intermediate signals and the output. This set of signals is the witness.

The zero knowledge proofs prove that you know a set of signals (witness) that match all the constraints but without revealing any of the signals except the public inputs plus the outputs.

For example, Imagine that you want to prove that you are able to factor 33 that means that you know two numbers a and b that when you multiply them, it results in 33.

Of course you can always use one and the same number as a and b. We will deal with this problem later.

So you want to prove that you know 3 and 11.

Let’s create a file named input.json

{"a": 3, "b": 11}


And now let’s calculate the witness:

snarkjs calculatewitness


You may want to take a look at witness.json file with all the signals.

#### Create the proof¶

Now that we have the witness generated, we can create the proof.

snarkjs proof


This command will use the prooving_key.json and the witness.json files by default to generate proof.json and public.json

The proof.json file will contain the actual proof. And the public.json file will contain just the values of the public inputs and the outputs.

#### Verifying the proof¶

To verify the proof run:

snarkjs verify


This command will use verification_key.json, proof.json and public.json to verify that is valid.

Here we are veifying that we know a witness that the public inputs and the outputs matches the ones in the public.json file.

If the proof is ok, you will see an OK in the screen or INVALID otherwise.

#### Generate the solidity verifier¶

snarkjs generateverifier


This command will take the verification_key.json and generate a solidity code in verifier.sol file.

You can take the code in verifier.sol and cut and paste in remix.

This code contains two contracts: Pairings and Verifier. You just need to deploy the Verifier contract.

You may want to use a test net like Rinkeby, Kovan or Ropsten. You can also use the Javascript VM, but in some browsers, the verification takes long and it may hang the page.

#### Verifying the proof on-chain¶

The verifier contract deployed in the last step has a view function called verifyProof.

This function will return true if the proof and the inputs are valid.

To facilitiate the call, you can use snarkjs to generate the parameters of the call by typing:

snarkjs generatecall


Just cut and paste the output to the parameters field of the verifyProof method in Remix.

If every thing works ok, this method should return true.

If you just change any bit in the parameters, you can check that the result will be false.

### Bonus track¶

We can fix the circuit to not accept one as any of the values by adding some extra constraints.

Here the trick is that we use the property that 0 has no inverse. so (a-1) should not have an inverse.

that means that (a-1)*inv = 1 will be inpossible to match if a is one.

We just calculate inv by 1/(a-1)

So let’s modify the circuit:

template Multiplier() {
signal private input a;
signal private input b;
signal output c;
signal inva;
signal invb;

inva <-- 1/(a-1);
(a-1)*inva === 1;

invb <-- 1/(b-1);
(b-1)*invb === 1;

c <== a*b;
}

component main = Multiplier();


A nice thing of circom language is that you can split a <== into two independent acions: <– and ===

The <– and –> operators Just assign a value to a signal without creating any constraints.

The === operator just adds a constraint without assigning any value to any signal.

The circuit has also another problem and it’s that the operation works in Zr, so we need to guarantee too that the multiplication does not overflow. This can be done by binarizing the inputs and checking the ranges, but we will reserve it for future tutorials.