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Merge main and auxiliary Paillier key and ring-Pedersen parameters #42

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Nov 5, 2023
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Merge main and auxiliary Paillier key and ring-Pedersen parameters #42

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75 changes: 9 additions & 66 deletions synedrion/src/cggmp21/protocols/auxiliary.rs
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Original file line number Diff line number Diff line change
Expand Up @@ -62,16 +62,13 @@ enum KeyRefreshErrorEnum<P: SchemeParams> {
#[serde(bound(serialize = "PrmProof<P>: Serialize"))]
#[serde(bound(deserialize = "PrmProof<P>: for<'x> Deserialize<'x>"))]
pub struct FullData<P: SchemeParams> {
xs_public: Vec<Point>, // $\bm{X}_i$
sch_commitments_x: Vec<SchCommitment>, // $\bm{A}_i$
el_gamal_pk: Point, // $Y_i$,
el_gamal_commitment: SchCommitment, // $B_i$
paillier_pk: PublicKeyPaillier<P::Paillier>, // $N_i$
aux_paillier_pk: PublicKeyPaillier<P::Paillier>, // $\hat{N}_i$
rp_params: RPParams<P::Paillier>, // $s_i$ and $t_i$
prm_proof: PrmProof<P>, // $\hat{\psi}_i$
aux_rp_params: RPParams<P::Paillier>, // setup parameters($s_i$ and $t_i$ for $\hat{N}$)
aux_prm_proof: PrmProof<P>, // a proof for the setup parameters
xs_public: Vec<Point>, // $\bm{X}_i$
sch_commitments_x: Vec<SchCommitment>, // $\bm{A}_i$
el_gamal_pk: Point, // $Y_i$,
el_gamal_commitment: SchCommitment, // $B_i$
paillier_pk: PublicKeyPaillier<P::Paillier>, // $N_i$
rp_params: RPParams<P::Paillier>, // $s_i$ and $t_i$
prm_proof: PrmProof<P>, // $\hat{\psi}_i$
#[serde(with = "serde_bytes::as_base64")]
rho_bits: Box<[u8]>, // $\rho_i$
#[serde(with = "serde_bytes::as_base64")]
Expand All @@ -83,14 +80,11 @@ pub struct FullData<P: SchemeParams> {
pub struct FullDataPrecomp<P: SchemeParams> {
data: FullData<P>,
paillier_pk: PublicKeyPaillierPrecomputed<P::Paillier>, // $N_i$
aux_paillier_pk: PublicKeyPaillierPrecomputed<P::Paillier>, // $\hat{N}_i$
rp_params: RPParamsMod<P::Paillier>, // $s_i$ and $t_i$
aux_rp_params: RPParamsMod<P::Paillier>, // setup parameters($s_i$ and $t_i$ for $\hat{N}$)
}

struct Context<P: SchemeParams> {
paillier_sk: SecretKeyPaillierPrecomputed<P::Paillier>,
aux_paillier_sk: SecretKeyPaillierPrecomputed<P::Paillier>,
el_gamal_sk: Scalar,
xs_secret: Vec<Scalar>,
el_gamal_proof_secret: SchSecret,
Expand All @@ -109,11 +103,8 @@ impl<P: SchemeParams> Hashable for FullData<P> {
.chain(&self.el_gamal_pk)
.chain(&self.el_gamal_commitment)
.chain(&self.paillier_pk)
.chain(&self.aux_paillier_pk)
.chain(&self.rp_params)
.chain(&self.prm_proof)
.chain(&self.aux_rp_params)
.chain(&self.aux_prm_proof)
.chain(&self.rho_bits)
.chain(&self.u_bits)
}
Expand Down Expand Up @@ -160,21 +151,9 @@ impl<P: SchemeParams> FirstRound for Round1<P> {
let rp_secret = RPSecret::random(rng, &paillier_sk);
let rp_params = RPParamsMod::random_with_secret(rng, &rp_secret, paillier_pk);

// CHECK: This is not a part of the KeyRefresh/Aux protocol in Fig.6, but according to
// "Generating the Setup Parameter for the Range Proofs" in Section 2.3,
// the verifier generates the auxiliary RP params (and the corresponding
// P^{mod} and P^{prm} proofs), so this seems like the right place to do it.
let aux_paillier_sk = SecretKeyPaillier::<P::Paillier>::random(rng).to_precomputed();
let aux_paillier_pk = aux_paillier_sk.public_key();
let aux_rp_secret = RPSecret::random(rng, &aux_paillier_sk);
let aux_rp_params = RPParamsMod::random_with_secret(rng, &aux_rp_secret, aux_paillier_pk);

let aux = (&shared_randomness, &party_idx);
let prm_proof = PrmProof::<P>::random(rng, &paillier_sk, &rp_secret, &rp_params, &aux);

let aux_prm_proof =
PrmProof::<P>::random(rng, &aux_paillier_sk, &aux_rp_secret, &aux_rp_params, &aux);

// $\tau_j$
let sch_secrets_x: Vec<SchSecret> =
(0..num_parties).map(|_| SchSecret::random(rng)).collect();
Expand All @@ -191,26 +170,20 @@ impl<P: SchemeParams> FirstRound for Round1<P> {
el_gamal_pk,
el_gamal_commitment,
paillier_pk: paillier_pk.to_minimal(),
aux_paillier_pk: aux_paillier_pk.to_minimal(),
rp_params: rp_params.retrieve(),
aux_rp_params: aux_rp_params.retrieve(),
prm_proof,
aux_prm_proof,
rho_bits: rho_bits.clone(),
u_bits: u_bits.clone(),
};

let data_precomp = FullDataPrecomp {
data,
paillier_pk: paillier_pk.clone(),
aux_paillier_pk: aux_paillier_pk.clone(),
rp_params,
aux_rp_params,
};

let context = Context {
paillier_sk,
aux_paillier_sk,
el_gamal_sk,
xs_secret,
sch_secrets_x,
Expand Down Expand Up @@ -378,20 +351,10 @@ impl<P: SchemeParams> BroadcastRound for Round2<P> {
)));
}

let aux_paillier_pk = msg.data.aux_paillier_pk.to_precomputed();
let aux_rp_params = msg.data.aux_rp_params.to_mod(&aux_paillier_pk);
if !msg.data.aux_prm_proof.verify(&aux_rp_params, &aux) {
return Err(ReceiveError::Provable(KeyRefreshError(
KeyRefreshErrorEnum::Round2("PRM verification (setup parameters) failed".into()),
)));
}

Ok(FullDataPrecomp {
data: msg.data,
paillier_pk,
aux_paillier_pk,
rp_params,
aux_rp_params,
})
}
}
Expand Down Expand Up @@ -426,7 +389,6 @@ pub struct Round3<P: SchemeParams> {
rho: Box<[u8]>,
datas: HoleVec<FullDataPrecomp<P>>,
mod_proof: ModProof<P>,
aux_mod_proof: ModProof<P>,
sch_proof_y: SchProof,
}

Expand All @@ -439,7 +401,6 @@ pub struct Round3<P: SchemeParams> {
Ciphertext<P::Paillier>: for<'x> Deserialize<'x>"))]
pub struct FullData2<P: SchemeParams> {
mod_proof: ModProof<P>, // `psi_j`
aux_mod_proof: ModProof<P>, // $P^{mod}$ for the setup parameters
fac_proof: FacProof<P>, // `phi_j,i`
sch_proof_y: SchProof, // `pi_i`
paillier_enc_x: Ciphertext<P::Paillier>, // `C_j,i`
Expand All @@ -463,8 +424,6 @@ impl<P: SchemeParams> Round3<P> {
let aux = (&context.shared_randomness, &rho, &context.party_idx);
let mod_proof = ModProof::random(rng, &context.paillier_sk, &aux);

let aux_mod_proof = ModProof::random(rng, &context.aux_paillier_sk, &aux);

let sch_proof_y = SchProof::new(
&context.el_gamal_proof_secret,
&context.el_gamal_sk,
Expand All @@ -478,7 +437,6 @@ impl<P: SchemeParams> Round3<P> {
datas,
rho,
mod_proof,
aux_mod_proof,
sch_proof_y,
}
}
Expand Down Expand Up @@ -525,7 +483,7 @@ impl<P: SchemeParams> DirectRound for Round3<P> {
let fac_proof = FacProof::random(
rng,
&self.context.paillier_sk,
&self.datas.get(idx).unwrap().aux_rp_params,
&self.datas.get(idx).unwrap().rp_params,
&aux,
);

Expand All @@ -543,7 +501,6 @@ impl<P: SchemeParams> DirectRound for Round3<P> {

let data2 = FullData2 {
mod_proof: self.mod_proof.clone(),
aux_mod_proof: self.aux_mod_proof.clone(),
fac_proof,
sch_proof_y: self.sch_proof_y.clone(),
paillier_enc_x: ciphertext,
Expand Down Expand Up @@ -590,21 +547,9 @@ impl<P: SchemeParams> DirectRound for Round3<P> {
)));
}

if !msg
.data2
.aux_mod_proof
.verify(&sender_data.aux_paillier_pk, &aux)
{
return Err(ReceiveError::Provable(KeyRefreshError(
KeyRefreshErrorEnum::Round3(
"Mod proof (setup parameters) verification failed".into(),
),
)));
}

if !msg.data2.fac_proof.verify(
&sender_data.paillier_pk,
&self.context.data_precomp.aux_rp_params,
&self.context.data_precomp.rp_params,
&aux,
) {
return Err(ReceiveError::Provable(KeyRefreshError(
Expand Down Expand Up @@ -665,9 +610,7 @@ impl<P: SchemeParams> FinalizableToResult for Round3<P> {
.map(|data| PublicAuxInfo {
el_gamal_pk: data.data.el_gamal_pk,
paillier_pk: data.paillier_pk.to_minimal(),
aux_paillier_pk: data.aux_paillier_pk.to_minimal(),
rp_params: data.rp_params.retrieve(),
aux_rp_params: data.aux_rp_params.retrieve(),
})
.collect();

Expand Down
10 changes: 0 additions & 10 deletions synedrion/src/cggmp21/protocols/common.rs
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Original file line number Diff line number Diff line change
Expand Up @@ -90,9 +90,6 @@ pub(crate) struct PublicAuxInfo<P: SchemeParams> {
pub(crate) el_gamal_pk: Point, // `Y_i`
/// The Paillier public key.
pub(crate) paillier_pk: PublicKeyPaillier<P::Paillier>,
/// Auxiliary public key and ring-Pedersen parameters (for ZK proofs).
pub(crate) aux_paillier_pk: PublicKeyPaillier<P::Paillier>,
pub(crate) aux_rp_params: RPParams<P::Paillier>,
/// The ring-Pedersen parameters.
pub(crate) rp_params: RPParams<P::Paillier>, // `s_i` and `t_i`
}
Expand All @@ -118,8 +115,6 @@ pub(crate) struct PublicAuxInfoPrecomputed<P: SchemeParams> {
#[allow(dead_code)]
pub(crate) el_gamal_pk: Point,
pub(crate) paillier_pk: PublicKeyPaillierPrecomputed<P::Paillier>,
pub(crate) aux_rp_params: RPParamsMod<P::Paillier>,
#[allow(dead_code)]
pub(crate) rp_params: RPParamsMod<P::Paillier>,
}

Expand Down Expand Up @@ -243,12 +238,10 @@ impl<P: SchemeParams> KeyShare<P> {
.iter()
.map(|public_aux| {
let paillier_pk = public_aux.paillier_pk.to_precomputed();
let aux_paillier_pk = public_aux.aux_paillier_pk.to_precomputed();
PublicAuxInfoPrecomputed {
el_gamal_pk: public_aux.el_gamal_pk,
paillier_pk: paillier_pk.clone(),
rp_params: public_aux.rp_params.to_mod(&paillier_pk),
aux_rp_params: public_aux.aux_rp_params.to_mod(&aux_paillier_pk),
}
})
.collect(),
Expand Down Expand Up @@ -454,11 +447,8 @@ pub(crate) fn make_aux_info<P: SchemeParams>(
.iter()
.map(|secret| {
let sk = secret.paillier_sk.to_precomputed();
let aux_sk = SecretKeyPaillier::<P::Paillier>::random(rng).to_precomputed();
PublicAuxInfo {
paillier_pk: sk.public_key().to_minimal(),
aux_paillier_pk: aux_sk.public_key().to_minimal(),
aux_rp_params: RPParamsMod::random(rng, &aux_sk).retrieve(),
el_gamal_pk: secret.el_gamal_sk.mul_by_generator(),
rp_params: RPParamsMod::random(rng, &sk).retrieve(),
}
Expand Down
32 changes: 16 additions & 16 deletions synedrion/src/cggmp21/protocols/presigning.rs
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Original file line number Diff line number Diff line change
Expand Up @@ -179,7 +179,7 @@ impl<P: SchemeParams> DirectRound for Round1<P> {
&Signed::from_scalar(&self.context.ephemeral_scalar_share),
&self.context.rho,
&self.context.key_share.secret_aux.paillier_sk,
&self.context.key_share.public_aux[destination.as_usize()].aux_rp_params,
&self.context.key_share.public_aux[destination.as_usize()].rp_params,
&aux,
);
Ok((Round1Direct(proof), ()))
Expand Down Expand Up @@ -218,7 +218,7 @@ impl<P: SchemeParams> FinalizableToNextRound for Round1<P> {
if !proof.0.verify(
&self.context.key_share.public_aux[from].paillier_pk,
&ciphertexts.k_ciphertext,
&public_aux.aux_rp_params,
&public_aux.rp_params,
&aux,
) {
return Err(FinalizeError::Provable {
Expand Down Expand Up @@ -353,7 +353,7 @@ impl<P: SchemeParams> DirectRound for Round2<P> {
let f_hat = Ciphertext::new_with_randomizer_signed(pk, &beta_hat, &r_hat.retrieve());

let public_aux = &self.context.key_share.public_aux[idx];
let aux_rp = &public_aux.aux_rp_params;
let rp = &public_aux.rp_params;

let psi = AffGProof::random(
rng,
Expand All @@ -364,7 +364,7 @@ impl<P: SchemeParams> DirectRound for Round2<P> {
target_pk,
pk,
&self.k_ciphertexts[idx],
aux_rp,
rp,
&aux,
);

Expand All @@ -377,7 +377,7 @@ impl<P: SchemeParams> DirectRound for Round2<P> {
target_pk,
pk,
&self.k_ciphertexts[idx],
aux_rp,
rp,
&aux,
);

Expand All @@ -387,7 +387,7 @@ impl<P: SchemeParams> DirectRound for Round2<P> {
&self.context.nu,
pk,
&Point::GENERATOR,
aux_rp,
rp,
&aux,
);

Expand Down Expand Up @@ -429,7 +429,7 @@ impl<P: SchemeParams> DirectRound for Round2<P> {

let public_aux =
&self.context.key_share.public_aux[self.context.key_share.party_index().as_usize()];
let aux_rp = &public_aux.aux_rp_params;
let rp = &public_aux.rp_params;

if !msg.psi.verify(
pk,
Expand All @@ -438,7 +438,7 @@ impl<P: SchemeParams> DirectRound for Round2<P> {
&msg.d,
&msg.f,
&msg.gamma,
aux_rp,
rp,
&aux,
) {
return Err(ReceiveError::Provable(PresigningError::Round2(
Expand All @@ -453,7 +453,7 @@ impl<P: SchemeParams> DirectRound for Round2<P> {
&msg.d_hat,
&msg.f_hat,
&big_x,
aux_rp,
rp,
&aux,
) {
return Err(ReceiveError::Provable(PresigningError::Round2(
Expand All @@ -466,7 +466,7 @@ impl<P: SchemeParams> DirectRound for Round2<P> {
&self.g_ciphertexts[from.as_usize()],
&Point::GENERATOR,
&msg.gamma,
aux_rp,
rp,
&aux,
) {
return Err(ReceiveError::Provable(PresigningError::Round2(
Expand Down Expand Up @@ -612,15 +612,15 @@ impl<P: SchemeParams> DirectRound for Round3<P> {
let idx = destination.as_usize();

let public_aux = &self.context.key_share.public_aux[idx];
let aux_rp = &public_aux.aux_rp_params;
let rp = &public_aux.rp_params;

let psi_hat_pprime = LogStarProof::random(
rng,
&Signed::from_scalar(&self.context.ephemeral_scalar_share),
&self.context.rho,
pk,
&self.big_gamma,
aux_rp,
rp,
&aux,
);
let message = Round3Direct {
Expand All @@ -642,14 +642,14 @@ impl<P: SchemeParams> DirectRound for Round3<P> {

let public_aux =
&self.context.key_share.public_aux[self.context.key_share.party_index().as_usize()];
let aux_rp = &public_aux.aux_rp_params;
let rp = &public_aux.rp_params;

if !msg.psi_hat_pprime.verify(
from_pk,
&self.k_ciphertexts[from.as_usize()],
&self.big_gamma,
&msg.big_delta,
aux_rp,
rp,
&aux,
) {
return Err(ReceiveError::Provable(PresigningError::Round3(
Expand Down Expand Up @@ -746,7 +746,7 @@ impl<P: SchemeParams> FinalizableToResult for Round3<P> {
// Should we have a "double hole vec" for that?
for l in HoleRange::new(num_parties, my_idx) {
let target_pk = &self.context.key_share.public_aux[j].paillier_pk;
let aux_rp = &self.context.key_share.public_aux[l].aux_rp_params;
let rp = &self.context.key_share.public_aux[l].rp_params;

let p_aff_g = AffGProof::<P>::random(
rng,
Expand All @@ -757,7 +757,7 @@ impl<P: SchemeParams> FinalizableToResult for Round3<P> {
target_pk,
pk,
&self.k_ciphertexts[j],
aux_rp,
rp,
&aux,
);

Expand Down
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