Hades252

Implementation of Hades252 permutation algorithm over the Bls12-381 Scalar field.

Documentation

To generate the Hades252 documentation:

make doc
make doc-internal

Use

To import Hades252, add the following to the dependencies section of your project's Cargo.toml:

dusk-hades = "0.16.0"

Hades252 has a width equals to 5; it's possible to use a different value, see How to generate the assets.

Parameters

• p = 0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001

• Security level is 117 -120 bits of security [NCCG] bits.

• width = 5

• Number of full rounds = 8 . There are four full rounds at the beginning and four full rounds at the end, where each full round has WIDTH quintic S-Boxes.

• Number of partial rounds = 59, where each partial round has one quintic S-Box and (width-1) identity functions.

• Number of round constants = 960

Example for ScalarStrategy

use dusk_bls12_381::BlsScalar;
use dusk_hades::{ScalarStrategy, Strategy, WIDTH};

// Generate the inputs that will permute.
// The number of values we can input is equivalent to `WIDTH`

let input = vec![BlsScalar::from(1u64); dusk_hades::WIDTH];
let mut output = input.clone();

let mut strategy = ScalarStrategy::new();
strategy.perm(output.as_mut_slice());

assert_ne!(&input, &output);
assert_eq!(input.len(), output.len());

Example for GadgetStrategy

// Proving that we know the pre-image of a hades-252 hash.
use dusk_hades::{GadgetStrategy, Strategy, WIDTH};
use dusk_plonk::prelude::*;

// Setup OG params.
const CAPACITY: usize = 1 << 10;

let public_parameters = PublicParameters::setup(CAPACITY, &mut rand::thread_rng()).unwrap();
let (ck, vk) = public_parameters.trim(CAPACITY).unwrap();;

// Gen inputs
let mut inputs = [BlsScalar::one(); WIDTH];

let mut prover = Prover::new(b"Hades_Testing");

// Generate the witness data
let mut composer = prover.composer_mut();
let zero = TurboComposer::constant_zero();

let mut witness = [zero; WIDTH];
witness.iter_mut()
    .zip(inputs.iter())
    .for_each(|(w, i)| *w = composer.append_witness(*i));

// Perform the permutation in the circuit
GadgetStrategy::gadget(prover.composer_mut(), &mut witness);

// Now your composer has been filled with a hades permutation
// inside.
// Now you can build your proof or keep extending your circuit.

Deviations

• Round constants for the full rounds are generated following: https://extgit.iaik.tugraz.at/krypto/hadesmimc/blob/master/code/calc_round_numbers.py

• The MDS matrix is a cauchy matrix, the method used to generate it, is noted in section "Concrete Instantiations Poseidon and Starkad"

Reference

https://eprint.iacr.org/2019/458.pdf