# Crate phase2 [−] [src]

Grab the `bellman` and `pairing` crates. Bellman provides a trait called `Circuit`, which you must implement for your computation.

Here's a silly example: proving you know the cube root of a field element.

```extern crate pairing;
extern crate bellman;

use pairing::{Engine, Field};
use bellman::{
Circuit,
ConstraintSystem,
SynthesisError,
};

struct CubeRoot<E: Engine> {
cube_root: Option<E::Fr>
}

impl<E: Engine> Circuit<E> for CubeRoot<E> {
fn synthesize<CS: ConstraintSystem<E>>(
self,
cs: &mut CS
) -> Result<(), SynthesisError>
{
// Witness the cube root
let root = cs.alloc(|| "root", || {
self.cube_root.ok_or(SynthesisError::AssignmentMissing)
})?;

// Witness the square of the cube root
let square = cs.alloc(|| "square", || {
self.cube_root
.ok_or(SynthesisError::AssignmentMissing)
.map(|mut root| {root.square(); root })
})?;

// Enforce that `square` is root^2
cs.enforce(
|| "squaring",
|lc| lc + root,
|lc| lc + root,
|lc| lc + square
);

// Witness the cube, as a public input
let cube = cs.alloc_input(|| "cube", || {
self.cube_root
.ok_or(SynthesisError::AssignmentMissing)
.map(|root| {
let mut tmp = root;
tmp.square();
tmp.mul_assign(&root);
tmp
})
})?;

// Enforce that `cube` is root^3
// i.e. that `cube` is `root` * `square`
cs.enforce(
|| "cubing",
|lc| lc + root,
|lc| lc + square,
|lc| lc + cube
);

Ok(())
}
}```

## Create some proofs

Now that we have `CubeRoot<E>` implementing `Circuit`, let's create some parameters and make some proofs.

```extern crate rand;

use pairing::bls12_381::{Bls12, Fr};
use bellman::groth16::{
generate_random_parameters,
create_random_proof,
prepare_verifying_key,
verify_proof
};
use rand::{OsRng, Rand};

let rng = &mut OsRng::new();

// Create public parameters for our circuit
let params = {
let circuit = CubeRoot::<Bls12> {
cube_root: None
};

generate_random_parameters::<Bls12, _, _>(
circuit,
rng
).unwrap()
};

// Prepare the verifying key for verification
let pvk = prepare_verifying_key(&params.vk);

// Let's start making proofs!
for _ in 0..50 {
// Verifier picks a cube in the field.
// Let's just make a random one.
let root = Fr::rand(rng);
let mut cube = root;
cube.square();
cube.mul_assign(&root);

// Prover gets the cube, figures out the cube
// root, and makes the proof:
let proof = create_random_proof(
CubeRoot::<Bls12> {
cube_root: Some(root)
}, &params, rng
).unwrap();

// Verifier checks the proof against the cube
assert!(verify_proof(&pvk, &proof, &[cube]).unwrap());
}```

## Creating parameters

Notice in the previous example that we created our zk-SNARK parameters by calling `generate_random_parameters`. However, if you wanted you could have called `generate_parameters` with some secret numbers you chose, and kept them for yourself. Given those numbers, you can create false proofs.

In order to convince others you didn't, a multi-party computation (MPC) can be used. The MPC has the property that only one participant needs to be honest for the parameters to be secure. This crate (`phase2`) is about creating parameters securely using such an MPC.

Let's start by using `phase2` to create some base parameters for our circuit:

```extern crate phase2;

let mut params = phase2::MPCParameters::new(CubeRoot {
cube_root: None
}).unwrap();```

The first time you try this, it will try to read a file like `phase1radix2m2` from the current directory. You need to grab that from the Powers of Tau.

These parameters are not safe to use; false proofs can be created for them. Let's contribute some randomness to these parameters.

```// Contribute randomness to the parameters. Remember this hash,
// it's how we know our contribution is in the parameters!
let hash = params.contribute(rng);```

These parameters are now secure to use, so long as you weren't malicious. That may not be convincing to others, so let them contribute randomness too! `params` can be serialized and sent elsewhere, where they can do the same thing and send new parameters back to you. Only one person needs to be honest for the final parameters to be secure.

Once you're done setting up the parameters, you can verify the parameters:

```let contributions = params.verify(CubeRoot {
cube_root: None
}).expect("parameters should be valid!");

// We need to check the `contributions` to see if our `hash`
// is in it (see above, when we first contributed)
assert!(phase2::contains_contribution(&contributions, &hash));```

Great, now if you're happy, grab the Groth16 `Parameters` with `params.params()`, so that you can interact with the bellman APIs just as before.

## Structs

 MPCParameters MPC parameters are just like bellman `Parameters` except, when serialized, they contain a transcript of contributions at the end, which can be verified.

## Functions

 contains_contribution This is a cheap helper utility that exists purely because Rust still doesn't have type-level integers and so doesn't implement `PartialEq` for `[T; 64]` verify_contribution Verify a contribution, given the old parameters and the new parameters. Returns the hash of the contribution.