ZK proof cleanup (#99)

synedrion/src/cggmp21/params.rs

@@ -1,45 +1,57 @@
+use crate::curve::Scalar;
 use crate::curve::ORDER;
 use crate::paillier::PaillierParams;
 use crate::uint::{
-    upcast_uint, U1024Mod, U2048Mod, U4096Mod, U512Mod, U1024, U2048, U4096, U512, U8192,
+    subtle::ConditionallySelectable, upcast_uint, Bounded, Encoding, NonZero, Signed, U1024Mod,
+    U2048Mod, U4096Mod, U512Mod, Zero, U1024, U2048, U4096, U512, U8192,
 };
 
 #[derive(Debug, Copy, Clone, PartialEq, Eq)]
 pub struct PaillierTest;
 
 impl PaillierParams for PaillierTest {
-    // We need 257-bit primes because we need MODULUS_BITS to accommodate all the possible
-    // values of curve scalar squared, which is 512 bits.
-
     /*
     The prime size is chosen to be minimal for which the `TestSchemeParams` still work.
     In the presigning, we are effectively constructing a ciphertext of
+
         d = x * sum(j=1..P) y_i + sum(j=1..2*(P-1)) z_j
+
     where
+
         0 < x, y_i < q < 2^L, and
         -2^LP < z < 2^LP
+
     (`q` is the curve order, `L` and `LP` are constants in `TestSchemeParams`,
     `P` is the number of parties).
-    This is `delta_i`, an additive share of the product of two secret values.
+    This is `delta_i` or `chi_i`.
+
+    During signing `chi_i` gets additionally multiplied by `r` (nonce, a scalar).
 
     We need the final result to be `-N/2 < d < N/2`
-    (that is, it may be negative, and it cannot wrap around modulo N).
+    (that is, it may be negative, and it cannot wrap around modulo N),
+    so that it could fit in a Paillier ciphertext without wrapping around.
+    This is needed for ZK proofs to work.
 
     `N` is a product of two primes of the size `PRIME_BITS`, so `N > 2^(2 * PRIME_BITS - 2)`.
-    The upper bound on `log2(d)` is
-        max(2 * L, LP + 2) + ceil(log2(P))
+    The upper bound on `log2(d * r)` is
+
+        max(2 * L, LP + 2) + ceil(log2(CURVE_ORDER)) + ceil(log2(P))
 
     (note that in reality, due to numbers being random, the distribution will have a distinct peak,
     and the upper bound will have a low probability of being reached)
 
-    Therefore we require `max(2 * L, LP + 2) + ceil(log2(P)) < 2 * PRIME_BITS - 2`.
+    Therefore we require
+
+        max(2 * L, LP + 2) + ceil(log2(CURVE_ORDER)) + ceil(log2(P)) < 2 * PRIME_BITS - 2`
+
     For tests we assume `ceil(log2(P)) = 5` (we won't run tests with more than 32 nodes),
-    and since in `TestSchemeParams` `L = LP = 256`, this leads to `PRIME_BITS >= L + 4`.
+    and since in `TestSchemeParams` `L = LP = 256`, this leads to `PRIME_BITS >= 397`.
 
-    For production it does not matter since both 2*L and LP are much smaller than 2*PRIME_BITS.
+    For production it does not matter since 2*L, LP, and log2(CURVE_ORDER)
+    are much smaller than 2*PRIME_BITS.
     */
 
-    const PRIME_BITS: usize = 260;
+    const PRIME_BITS: usize = 397;
     type HalfUint = U512;
     type HalfUintMod = U512Mod;
     type Uint = U1024;
@@ -68,7 +80,9 @@ impl PaillierParams for PaillierProduction {
 // but for now they are hardcoded to `k256`.
 pub trait SchemeParams: Clone + Send + PartialEq + Eq + core::fmt::Debug + 'static {
     /// The order of the curve.
-    const CURVE_ORDER: <Self::Paillier as PaillierParams>::Uint; // $q$
+    const CURVE_ORDER: NonZero<<Self::Paillier as PaillierParams>::Uint>; // $q$
+    /// The order of the curve as a wide integer.
+    const CURVE_ORDER_WIDE: NonZero<<Self::Paillier as PaillierParams>::WideUint>;
     /// The sheme's statistical security parameter.
     const SECURITY_PARAMETER: usize; // $\kappa$
     /// The bound for secret values.
@@ -79,6 +93,68 @@ pub trait SchemeParams: Clone + Send + PartialEq + Eq + core::fmt::Debug + 'stat
     const EPS_BOUND: usize; // $\eps$, in paper $= 2 \ell$ (see Table 2)
     /// The parameters of the Paillier encryption.
     type Paillier: PaillierParams;
+
+    /// Converts a curve scalar to the associated integer type.
+    fn uint_from_scalar(value: &Scalar) -> <Self::Paillier as PaillierParams>::Uint {
+        let scalar_bytes = value.to_bytes();
+        let mut repr = <Self::Paillier as PaillierParams>::Uint::ZERO.to_be_bytes();
+
+        let uint_len = repr.as_ref().len();
+        let scalar_len = scalar_bytes.len();
+
+        debug_assert!(uint_len >= scalar_len);
+        repr.as_mut()[uint_len - scalar_len..].copy_from_slice(&scalar_bytes);
+        <Self::Paillier as PaillierParams>::Uint::from_be_bytes(repr)
+    }
+
+    /// Converts a curve scalar to the associated integer type, wrapped in `Bounded`.
+    fn bounded_from_scalar(value: &Scalar) -> Bounded<<Self::Paillier as PaillierParams>::Uint> {
+        const ORDER_BITS: usize = ORDER.bits_vartime();
+        Bounded::new(Self::uint_from_scalar(value), ORDER_BITS as u32).unwrap()
+    }
+
+    /// Converts a curve scalar to the associated integer type, wrapped in `Signed`.
+    fn signed_from_scalar(value: &Scalar) -> Signed<<Self::Paillier as PaillierParams>::Uint> {
+        Self::bounded_from_scalar(value).into_signed().unwrap()
+    }
+
+    /// Converts an integer to the associated curve scalar type.
+    fn scalar_from_uint(value: &<Self::Paillier as PaillierParams>::Uint) -> Scalar {
+        let r = *value % Self::CURVE_ORDER;
+
+        let repr = r.to_be_bytes();
+        let uint_len = repr.as_ref().len();
+        let scalar_len = Scalar::repr_len();
+
+        // Can unwrap here since the value is within the Scalar range
+        Scalar::try_from_bytes(&repr.as_ref()[uint_len - scalar_len..]).unwrap()
+    }
+
+    /// Converts a `Signed`-wrapped integer to the associated curve scalar type.
+    fn scalar_from_signed(value: &Signed<<Self::Paillier as PaillierParams>::Uint>) -> Scalar {
+        let abs_value = Self::scalar_from_uint(&value.abs());
+        Scalar::conditional_select(&abs_value, &-abs_value, value.is_negative())
+    }
+
+    /// Converts a wide integer to the associated curve scalar type.
+    fn scalar_from_wide_uint(value: &<Self::Paillier as PaillierParams>::WideUint) -> Scalar {
+        let r = *value % Self::CURVE_ORDER_WIDE;
+
+        let repr = r.to_be_bytes();
+        let uint_len = repr.as_ref().len();
+        let scalar_len = Scalar::repr_len();
+
+        // Can unwrap here since the value is within the Scalar range
+        Scalar::try_from_bytes(&repr.as_ref()[uint_len - scalar_len..]).unwrap()
+    }
+
+    /// Converts a `Signed`-wrapped wide integer to the associated curve scalar type.
+    fn scalar_from_wide_signed(
+        value: &Signed<<Self::Paillier as PaillierParams>::WideUint>,
+    ) -> Scalar {
+        let abs_value = Self::scalar_from_wide_uint(&value.abs());
+        Scalar::conditional_select(&abs_value, &-abs_value, value.is_negative())
+    }
 }
 
 /// Scheme parameters **for testing purposes only**.
@@ -100,7 +176,10 @@ impl SchemeParams for TestParams {
     const LP_BOUND: usize = 256;
     const EPS_BOUND: usize = 320;
     type Paillier = PaillierTest;
-    const CURVE_ORDER: <Self::Paillier as PaillierParams>::Uint = upcast_uint(ORDER);
+    const CURVE_ORDER: NonZero<<Self::Paillier as PaillierParams>::Uint> =
+        NonZero::<<Self::Paillier as PaillierParams>::Uint>::const_new(upcast_uint(ORDER)).0;
+    const CURVE_ORDER_WIDE: NonZero<<Self::Paillier as PaillierParams>::WideUint> =
+        NonZero::<<Self::Paillier as PaillierParams>::WideUint>::const_new(upcast_uint(ORDER)).0;
 }
 
 /// Production strength parameters.
@@ -113,5 +192,8 @@ impl SchemeParams for ProductionParams {
     const LP_BOUND: usize = Self::L_BOUND * 5;
     const EPS_BOUND: usize = Self::L_BOUND * 2;
     type Paillier = PaillierProduction;
-    const CURVE_ORDER: <Self::Paillier as PaillierParams>::Uint = upcast_uint(ORDER);
+    const CURVE_ORDER: NonZero<<Self::Paillier as PaillierParams>::Uint> =
+        NonZero::<<Self::Paillier as PaillierParams>::Uint>::const_new(upcast_uint(ORDER)).0;
+    const CURVE_ORDER_WIDE: NonZero<<Self::Paillier as PaillierParams>::WideUint> =
+        NonZero::<<Self::Paillier as PaillierParams>::WideUint>::const_new(upcast_uint(ORDER)).0;
 }

synedrion/src/cggmp21/protocols/interactive_signing.rs

@@ -259,3 +259,67 @@ impl<P: SchemeParams> FinalizableToResult for Round4<P> {
             .map_err(wrap_finalize_error)
     }
 }
+
+#[cfg(test)]
+mod tests {
+    use k256::ecdsa::{signature::hazmat::PrehashVerifier, VerifyingKey};
+    use rand_core::{OsRng, RngCore};
+
+    use super::{Context, Round1};
+    use crate::cggmp21::TestParams;
+    use crate::common::KeyShare;
+    use crate::curve::Scalar;
+    use crate::rounds::{
+        test_utils::{step_next_round, step_result, step_round},
+        FirstRound, PartyIdx,
+    };
+
+    #[test]
+    fn execute_interactive_signing() {
+        let mut shared_randomness = [0u8; 32];
+        OsRng.fill_bytes(&mut shared_randomness);
+
+        let message = Scalar::random(&mut OsRng);
+
+        let num_parties = 3;
+        let key_shares = KeyShare::new_centralized(&mut OsRng, num_parties, None);
+        let r1 = (0..num_parties)
+            .map(|idx| {
+                Round1::<TestParams>::new(
+                    &mut OsRng,
+                    &shared_randomness,
+                    num_parties,
+                    PartyIdx::from_usize(idx),
+                    Context {
+                        message,
+                        key_share: key_shares[idx].clone(),
+                    },
+                )
+                .unwrap()
+            })
+            .collect();
+
+        let r1a = step_round(&mut OsRng, r1).unwrap();
+        let r2 = step_next_round(&mut OsRng, r1a).unwrap();
+        let r2a = step_round(&mut OsRng, r2).unwrap();
+        let r3 = step_next_round(&mut OsRng, r2a).unwrap();
+        let r3a = step_round(&mut OsRng, r3).unwrap();
+        let r4 = step_next_round(&mut OsRng, r3a).unwrap();
+        let r4a = step_round(&mut OsRng, r4).unwrap();
+        let signatures = step_result(&mut OsRng, r4a).unwrap();
+
+        for signature in signatures {
+            let (sig, rec_id) = signature.to_backend();
+
+            let vkey = key_shares[0].verifying_key();
+
+            // Check that the signature can be verified
+            vkey.verify_prehash(&message.to_bytes(), &sig).unwrap();
+
+            // Check that the key can be recovered
+            let recovered_key =
+                VerifyingKey::recover_from_prehash(&message.to_bytes(), &sig, rec_id).unwrap();
+            assert_eq!(recovered_key, vkey);
+        }
+    }
+}

synedrion/src/cggmp21/protocols/key_refresh.rs

@@ -18,8 +18,8 @@ use crate::cggmp21::{
 use crate::common::{KeyShareChange, PublicAuxInfo, SecretAuxInfo};
 use crate::curve::{Point, Scalar};
 use crate::paillier::{
-    Ciphertext, PaillierParams, PublicKeyPaillier, PublicKeyPaillierPrecomputed, RPParams,
-    RPParamsMod, RPSecret, Randomizer, SecretKeyPaillier, SecretKeyPaillierPrecomputed,
+    Ciphertext, PublicKeyPaillier, PublicKeyPaillierPrecomputed, RPParams, RPParamsMod, RPSecret,
+    Randomizer, SecretKeyPaillier, SecretKeyPaillierPrecomputed,
 };
 use crate::rounds::{
     all_parties_except, try_to_holevec, BaseRound, BroadcastRound, DirectRound, Finalizable,
@@ -30,13 +30,7 @@ use crate::tools::collections::HoleVec;
 use crate::tools::hashing::{Chain, Hash, HashOutput, Hashable};
 use crate::tools::random::random_bits;
 use crate::tools::serde_bytes;
-use crate::uint::{FromScalar, UintLike};
-
-fn uint_from_scalar<P: SchemeParams>(
-    x: &Scalar,
-) -> <<P as SchemeParams>::Paillier as PaillierParams>::Uint {
-    <<P as SchemeParams>::Paillier as PaillierParams>::Uint::from_scalar(x)
-}
+use crate::uint::UintLike;
 
 /// Possible results of the KeyRefresh protocol.
 #[derive(Debug, Clone, Copy)]
@@ -528,7 +522,7 @@ impl<P: SchemeParams> DirectRound for Round3<P> {
 
         let x_secret = self.context.xs_secret[idx];
         let x_public = self.context.data_precomp.data.xs_public[idx];
-        let ciphertext = Ciphertext::new(rng, &data.paillier_pk, &uint_from_scalar::<P>(&x_secret));
+        let ciphertext = Ciphertext::new(rng, &data.paillier_pk, &P::uint_from_scalar(&x_secret));
 
         let sch_proof_x = SchProof::new(
             &self.context.sch_secrets_x[idx],
@@ -556,11 +550,8 @@ impl<P: SchemeParams> DirectRound for Round3<P> {
     ) -> Result<Self::Payload, ReceiveError<Self::Result>> {
         let sender_data = &self.datas.get(from.as_usize()).unwrap();
 
-        let x_secret = msg
-            .data2
-            .paillier_enc_x
-            .decrypt(&self.context.paillier_sk)
-            .to_scalar();
+        let x_secret =
+            P::scalar_from_uint(&msg.data2.paillier_enc_x.decrypt(&self.context.paillier_sk));
 
         if x_secret.mul_by_generator()
             != sender_data.data.xs_public[self.context.party_idx.as_usize()]