Crate gennaro_dkg

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Gennaro’s Distributed Key Generation Algorithm.

The algorithm uses participants with unique identifiers and each party communicates broadcast data and peer-to-peer data depending on the round. Round 1 generates secret_participant key shares which are checked for correctness in round 2. Any secret_participant that fails in round 2 is dropped from the valid set which is communicated in round 3. Round 4 communicates only with the remaining valid participants and computes the secret share and verification key. Round 5 checks that all participants computed the same verification key.

The idea is that Rounds 3 and 5 serve as echo broadcasts to check the state of all valid participants. If an error occurs in any round, then participants either drop invalid participants or abort.

The full paper can be found https://link.springer.com/content/pdf/10.1007/s00145-006-0347-3.pdf.

The interface has been written to work with anything that implements the elliptic-curve::Group trait.

An example for generating a secret key on the Secp256k1 curve with 2 out of 3 participants.

use gennaro_dkg::*;
use k256::{ProjectivePoint, Scalar};
use maplit::btreemap;
use std::{
    collections::BTreeMap,
    num::NonZeroUsize,
};
use vsss_rs::{Share, combine_shares, elliptic_curve::{Group, PrimeField}};

let parameters = Parameters::new(NonZeroUsize::new(2).unwrap(), NonZeroUsize::new(3).unwrap());

let mut participant1 = SecretParticipant::<ProjectivePoint>::new(NonZeroUsize::new(1).unwrap(), parameters).unwrap();
let mut participant2 = SecretParticipant::<ProjectivePoint>::new(NonZeroUsize::new(2).unwrap(), parameters).unwrap();
let mut participant3 = SecretParticipant::<ProjectivePoint>::new(NonZeroUsize::new(3).unwrap(), parameters).unwrap();

// Round 1
let (b1data1, p2p1data) = participant1.round1().unwrap();
let (b2data1, p2p2data) = participant2.round1().unwrap();
let (b3data1, p2p3data) = participant3.round1().unwrap();

// Can't call the same round twice
assert!(participant1.round1().is_err());
assert!(participant2.round1().is_err());
assert!(participant3.round1().is_err());

// Send b1data1 to secret_participant 2 and 3
// Send b2data1 to secret_participant 1 and 3
// Send b3data1 to secret_participant 1 and 2

// Send p2p1data[&2] to secret_participant 2
// Send p2p1data[&3] to secret_participant 3

// Send p2p2data[&1] to secret_participant 1
// Send p2p2data[&3] to secret_participant 3

// Send p2p3data[&1] to secret_participant 1
// Send p2p3data[&2] to secret_participant 2

let p1bdata1 = btreemap! {
    2 => b2data1.clone(),
    3 => b3data1.clone(),
};
let p1pdata = btreemap! {
    2 => p2p2data[&1].clone(),
    3 => p2p3data[&1].clone(),
};
let b1data2 = participant1.round2(p1bdata1, p1pdata).unwrap();

let p2bdata1 = btreemap! {
    1 => b1data1.clone(),
    3 => b3data1.clone(),
};
let p2pdata = btreemap! {
    1 => p2p1data[&2].clone(),
    3 => p2p3data[&2].clone(),
};
let b2data2 = participant2.round2(p2bdata1, p2pdata).unwrap();

let p3bdata1 = btreemap! {
    1 => b1data1.clone(),
    2 => b2data1.clone(),
};
let p3pdata = btreemap! {
    1 => p2p1data[&3].clone(),
    2 => p2p2data[&3].clone(),
};
let b3data2 = participant3.round2(p3bdata1, p3pdata).unwrap();

// Send b1data2 to participants 2 and 3
// Send b2data2 to participants 1 and 3
// Send b3data2 to participants 1 and 2

// This is an optimization for the example in reality each secret_participant computes this
let bdata2 = btreemap! {
    1 => b1data2,
    2 => b2data2,
    3 => b3data2,
};

let b1data3 = participant1.round3(&bdata2).unwrap();
let b2data3 = participant2.round3(&bdata2).unwrap();
let b3data3 = participant3.round3(&bdata2).unwrap();

// Send b1data3 to participants 2 and 3
// Send b2data3 to participants 1 and 3
// Send b3data3 to participants 1 and 2

// This is an optimization for the example in reality each secret_participant computes this
let bdata3 = btreemap! {
    1 => b1data3,
    2 => b2data3,
    3 => b3data3,
};

let b1data4 = participant1.round4(&bdata3).unwrap();
let b2data4 = participant2.round4(&bdata3).unwrap();
let b3data4 = participant3.round4(&bdata3).unwrap();

// Send b1data4 to participants 2 and 3
// Send b2data4 to participants 1 and 3
// Send b3data4 to participants 1 and 2

// Verify that the same key is computed then done

// This is an optimization for the example in reality each secret_participant computes this
let bdata4 = btreemap! {
    1 => b1data4,
    2 => b2data4,
    3 => b3data4,
};

assert!(participant1.round5(&bdata4).is_ok());
assert!(participant2.round5(&bdata4).is_ok());
assert!(participant3.round5(&bdata4).is_ok());

// Get the verification key
let pk1 = participant1.get_public_key().unwrap();
// Get the secret share
let share1 = participant1.get_secret_share().unwrap();

assert_eq!(pk1.is_identity().unwrap_u8(), 0u8);
assert_eq!(share1.is_zero().unwrap_u8(), 0u8);

let pk2 = participant2.get_public_key().unwrap();
let share2 = participant2.get_secret_share().unwrap();

assert_eq!(pk2.is_identity().unwrap_u8(), 0u8);
assert_eq!(share2.is_zero().unwrap_u8(), 0u8);

let pk3 = participant3.get_public_key().unwrap();
let share3 = participant3.get_secret_share().unwrap();

assert_eq!(pk3.is_identity().unwrap_u8(), 0u8);
assert_eq!(share3.is_zero().unwrap_u8(), 0u8);

// Public keys will be equal
assert_eq!(pk1, pk2);
assert_eq!(pk2, pk3);
// Shares should not be
assert_ne!(share1, share2);
assert_ne!(share1, share3);
assert_ne!(share2, share3);

// For demonstration purposes, the shares if collected can be combined to recreate
// the computed secret

let s1 = <Vec<u8> as Share>::from_field_element(1u8, share1).unwrap();
let s2 = <Vec<u8> as Share>::from_field_element(2u8, share2).unwrap();
let s3 = <Vec<u8> as Share>::from_field_element(3u8, share3).unwrap();

let sk: Scalar = combine_shares(&[s1, s2, s3]).unwrap();
let computed_pk = ProjectivePoint::GENERATOR * sk;
assert_eq!(computed_pk, pk1);

The output of the DKG is the same as if shamir secret sharing had been run on the secret and sent to separate parties.

Re-exports

Structs

Enums

  • Error
    Errors produced by the gennaro DKG
  • ParticipantError
    Detailed errors to describe problems that occurred with specific participants
  • Round
    Valid rounds

Traits

Type Aliases