circom/TUTORIAL.md

circom and snarkjs tutorial

This tutorial will guide you in creating your first Zero Knowledge zkSnark circuit. It will take you through the various techniques to write circuits, and 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.

The 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 a significant increase in performance. 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

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.

2. 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 those 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, without revealing any of the signals except the public inputs plus the outputs.

For example, imagine you want to prove you are able to factor 33. It means that you know two numbers a and b and 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}

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 proving_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 verifying 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 OK or INVALID if not ok.

Generate the solidity verifier

snarkjs generateverifier

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

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

This code contains two contracts: Pairings and Verifier. You only 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 facilitate 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 change any bit in the parameters, the result will be verifiably 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 1.

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 the circom language is that you can split a <== into two independent actions: <-- and ===

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

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

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

Where to go from here:

You may want to read the README to learn more features about circom.

You can also check a library with many basic circuits lib binarizations, comparators, eddsa, hashes, merkle trees etc here (Work in progress).

Or a exponentiation in the Baby Jub curve here (Work in progress).

Final note

There is nothing worse for a dev than working with a buggy compiler. This is a very early stage of the compiler, so there are many bugs and lots of work needs to be done. Please have it present if you are doing anything serious with it.

And please contact us for any isue you have. In general, a github issue with a small piece of code with the bug is very useful to us.

Enjoy zero knowledge proving!