Function full_mta_proved 

pub fn full_mta_proved(
    i_keypair: &PaillierKeypair,
    ck_i: &CommitmentKey,
    ck_j: &CommitmentKey,
    q: &BigUint,
    k_i: &BigUint,
    x_j: &BigUint,
) -> Result<(BigUint, BigUint), MtaProofError>

Run the full proved MtA protocol between party i and party j, in-process (one coordinator holding i’s keypair).

i_keypair is the INITIATOR’s Paillier keypair — the exchange runs under it end to end. ck_i/ck_j are the parties’ commitment keys (each proves against the OTHER’s). Returns (α, β′) with α − β′ = k_i·x_j exactly (hence also mod q and mod N) — honest shares never wrap.