Share commitments should be vectors

[upbqdn]

Description

The field share_commitment

redjubjub/src/messages.rs

Line 189 in 3db05e2

share_commitment: BTreeMap<ParticipantId, Commitment>,

should contain a vector of commitments instead of just one commitment.

In our tests, we also consider only the zeroth commitment, which is a commitment to the shared secret, and we don't consider the remaining commitments:

redjubjub/src/messages/tests/integration.rs

Line 783 in 3db05e2

Commitment::from(share.share.commitment.0[0].clone()),

Rationale

The field share_commitment, as defined above, should represent the struct ShareCommitment in the FROST implementation:

redjubjub/src/frost.rs

Line 93 in 3db05e2

pub struct ShareCommitment(pub(crate) Vec<Commitment>);

The struct ShareCommitment is a vector, and represents a public commitment C⃗_i as defined in step 3, Round 1 of Figure 1 of the FROST paper. This public commitment contains commitments to the individual coefficients of the secret polynomial.