2 releases

0.1.2 Jan 17, 2021
0.1.1 Jan 4, 2021


10K SLoC




bellperson is a crate for building zk-SNARK circuits. It provides circuit traits and and primitive structures, as well as basic gadget implementations such as booleans and number abstractions.

Example circuit

Say we want to write a circuit that proves we know the preimage to some hash computed using SHA-256d (calling SHA-256 twice). The preimage must have a fixed length known in advance (because the circuit parameters will depend on it), but can otherwise have any value. We take the following strategy:

  • Witness each bit of the preimage.
  • Compute hash = SHA-256d(preimage) inside the circuit.
  • Expose hash as a public input using multiscalar packing.
use bellperson::{
        boolean::{AllocatedBit, Boolean},
    groth16, Circuit, ConstraintSystem, SynthesisError,
use paired::{bls12_381::Bls12, Engine};
use rand::rngs::OsRng;
use sha2::{Digest, Sha256};

/// Our own SHA-256d gadget. Input and output are in little-endian bit order.
fn sha256d<E: Engine, CS: ConstraintSystem<E>>(
    mut cs: CS,
    data: &[Boolean],
) -> Result<Vec<Boolean>, SynthesisError> {
    // Flip endianness of each input byte
    let input: Vec<_> = data
        .map(|c| c.iter().rev())

    let mid = sha256(cs.namespace(|| "SHA-256(input)"), &input)?;
    let res = sha256(cs.namespace(|| "SHA-256(mid)"), &mid)?;

    // Flip endianness of each output byte
        .map(|c| c.iter().rev())

struct MyCircuit {
    /// The input to SHA-256d we are proving that we know. Set to `None` when we
    /// are verifying a proof (and do not have the witness data).
    preimage: Option<[u8; 80]>,

impl<E: Engine> Circuit<E> for MyCircuit {
    fn synthesize<CS: ConstraintSystem<E>>(self, cs: &mut CS) -> Result<(), SynthesisError> {
        // Compute the values for the bits of the preimage. If we are verifying a proof,
        // we still need to create the same constraints, so we return an equivalent-size
        // Vec of None (indicating that the value of each bit is unknown).
        let bit_values = if let Some(preimage) = self.preimage {
                .map(|byte| (0..8).map(move |i| (byte >> i) & 1u8 == 1u8))
                .map(|b| Some(b))
        } else {
            vec![None; 80 * 8]
        assert_eq!(bit_values.len(), 80 * 8);

        // Witness the bits of the preimage.
        let preimage_bits = bit_values
            // Allocate each bit.
            .map(|(i, b)| {
                AllocatedBit::alloc(cs.namespace(|| format!("preimage bit {}", i)), b)
            // Convert the AllocatedBits into Booleans (required for the sha256 gadget).
            .map(|b| b.map(Boolean::from))
            .collect::<Result<Vec<_>, _>>()?;

        // Compute hash = SHA-256d(preimage).
        let hash = sha256d(cs.namespace(|| "SHA-256d(preimage)"), &preimage_bits)?;

        // Expose the vector of 32 boolean variables as compact public inputs.
        multipack::pack_into_inputs(cs.namespace(|| "pack hash"), &hash)

// Create parameters for our circuit. In a production deployment these would
// be generated securely using a multiparty computation.
let params = {
    let c = MyCircuit { preimage: None };
    groth16::generate_random_parameters::<Bls12, _, _>(c, &mut OsRng).unwrap()

// Prepare the verification key (for proof verification).
let pvk = groth16::prepare_verifying_key(&params.vk);

// Pick a preimage and compute its hash.
let preimage = [42; 80];
let hash = Sha256::digest(&Sha256::digest(&preimage));

// Create an instance of our circuit (with the preimage as a witness).
let c = MyCircuit {
    preimage: Some(preimage),

// Create a Groth16 proof with our parameters.
let proof = groth16::create_random_proof(c, &params, &mut OsRng).unwrap();

// Pack the hash as inputs for proof verification.
let hash_bits = multipack::bytes_to_bits_le(&hash);
let inputs = multipack::compute_multipacking::<Bls12>(&hash_bits);

// Check the proof!
assert!(groth16::verify_proof(&pvk, &proof, &inputs).unwrap());


bellperson is being refactored into a generic proving library. Currently it is pairing-specific, and different types of proving systems need to be implemented as sub-modules. After the refactor, bellperson will be generic using the [ff] and group crates, while specific proving systems will be separate crates that pull in the dependencies they require.


~104K SLoC