primitives/sharing/authenticated/pairwise/

share.rs

use std::{
    any::Any,
    iter::Sum,
    marker::PhantomData,
    mem::MaybeUninit,
    ops::{Add, AddAssign, Mul, MulAssign, Neg, Sub, SubAssign},
};

use itertools::{enumerate, izip, Itertools};
use rayon::prelude::IntoParallelIterator;
use serde::{de::DeserializeOwned, Deserialize, Serialize};
use subtle::{Choice, ConstantTimeEq};
use typenum::{PartialDiv, Prod, U1, U2, U3, U5};
use wincode::{
    io::{Reader, Writer},
    ReadResult,
    SchemaRead,
    SchemaWrite,
    WriteResult,
};

use crate::{
    algebra::{
        elliptic_curve::{BaseField, Curve, Point, ScalarAsExtension, ScalarField},
        field::{
            binary::Gf2_128,
            mersenne::Mersenne107,
            FieldElement,
            FieldExtension,
            SubfieldElement,
        },
        ops::transpose::transpose,
    },
    errors::PrimitiveError,
    izip_eq,
    random::{CryptoRngCore, Random, RandomWith},
    sharing::{
        authenticated::{GlobalKey, PairwiseAuthKey, PairwiseAuthOpenShare},
        unauthenticated::AdditiveShares,
        PairwiseAuthenticated,
        PlaintextOps,
        Reconstructible,
        Verifiable,
    },
    types::{
        heap_array::{CurvePoints, FieldElements, SubfieldElements},
        Batched,
        CollectAll,
        ConditionallySelectable,
        HeapArray,
        PeerIndex,
        Positive,
        TryFoldAll,
    },
    utils::IntoExactSizeIterator,
};

/// Generic base for pairwise authenticated shares, analogous to [`PairwiseAuthKey`].
///
/// The three type parameters are:
/// - `V`: value type.
/// - `B`: MAC and local key (Beta) type, an additive Group.
/// - `A`: global key (Alpha) type.
///
/// The authenticated shares fulfill this relation:
///
/// ```MAC(x_i)_j = α_ji · x_i + β_ji  ∀i∈[1..n]  ∀j∈[1..n]∖{i}```
/// 
/// where `β_ji` and `α_ji` are the (local and global) keys of value `x_i` held by `P_j`.
///
/// As such, the share of party `P_i` contains:
/// - `x_i`, the unauthenticated share value (s.t. `x = Σ x_i`)
/// - `{MAC(x_i)_j} ∀j∈[1..n]∖{i}`, the MACs of `x_i` for each of the other n-1 parties.
/// - `{β_ij} ∀j∈[1..n]∖{i}` and `{α_ij} ∀j∈[1..n]∖{i}`, the (local and global) keys tied to the values&MACs of the other n-1 parties.
#[derive(Debug, Clone, Default, PartialEq, Eq, Serialize, Deserialize)]
#[serde(
    bound = "V: Serialize + DeserializeOwned, A: Serialize + DeserializeOwned, B: Serialize + DeserializeOwned"
)]
#[repr(C)]
pub struct PairwiseAuthShare<V, A, B> {
    pub(crate) value: V,
    pub(crate) macs: Box<[B]>,
    pub(crate) keys: Box<[PairwiseAuthKey<A, B>]>,
}

impl<V, A, B> SchemaWrite for PairwiseAuthShare<V, A, B>
where
    V: SchemaWrite<Src = V>,
    B: SchemaWrite<Src = B>,
    PairwiseAuthKey<A, B>: SchemaWrite<Src = PairwiseAuthKey<A, B>>,
{
    type Src = Self;

    fn size_of(src: &Self) -> WriteResult<usize> {
        Ok(V::size_of(&src.value)?
            + <Box<[B]> as SchemaWrite>::size_of(&src.macs)?
            + <Box<[PairwiseAuthKey<A, B>]> as SchemaWrite>::size_of(&src.keys)?)
    }

    fn write(writer: &mut impl Writer, src: &Self) -> WriteResult<()> {
        V::write(writer, &src.value)?;
        <Box<[B]> as SchemaWrite>::write(writer, &src.macs)?;
        <Box<[PairwiseAuthKey<A, B>]> as SchemaWrite>::write(writer, &src.keys)
    }
}

impl<'de, V, A, B> SchemaRead<'de> for PairwiseAuthShare<V, A, B>
where
    V: SchemaRead<'de, Dst = V>,
    B: SchemaRead<'de, Dst = B>,
    PairwiseAuthKey<A, B>: SchemaRead<'de, Dst = PairwiseAuthKey<A, B>>,
{
    type Dst = Self;

    fn read(reader: &mut impl Reader<'de>, dst: &mut MaybeUninit<Self>) -> ReadResult<()> {
        let mut value = MaybeUninit::<V>::uninit();
        let mut macs = MaybeUninit::<Box<[B]>>::uninit();
        let mut keys = MaybeUninit::<Box<[PairwiseAuthKey<A, B>]>>::uninit();
        V::read(reader, &mut value)?;
        <Box<[B]> as SchemaRead>::read(reader, &mut macs)?;
        <Box<[PairwiseAuthKey<A, B>]> as SchemaRead>::read(reader, &mut keys)?;
        // SAFETY: all fields were initialised by the reads above
        let value = unsafe { value.assume_init() };
        let macs = unsafe { macs.assume_init() };
        let keys = unsafe { keys.assume_init() };
        dst.write(PairwiseAuthShare { value, macs, keys });
        Ok(())
    }
}

impl<V, A, B> PairwiseAuthShare<V, A, B> {
    /// Constructs a new share, returning an error if the MAC and key slices are
    /// inconsistent (empty or length-mismatched).
    pub fn try_new(
        value: V,
        macs: Box<[B]>,
        keys: Box<[PairwiseAuthKey<A, B>]>,
    ) -> Result<Self, PrimitiveError> {
        if macs.is_empty() {
            return Err(PrimitiveError::MinimumLength(2, 0));
        }
        if macs.len() != keys.len() {
            return Err(PrimitiveError::InvalidSize(keys.len(), macs.len()));
        }
        Ok(Self { value, macs, keys })
    }

    /// Returns a reference to the share value.
    #[inline]
    pub fn get_value(&self) -> &V {
        &self.value
    }

    /// Returns a mutable reference to the share value.
    #[inline]
    pub fn get_value_mut(&mut self) -> &mut V {
        &mut self.value
    }

    /// Returns a slice of all MACs (one per distant peer).
    #[inline]
    pub fn get_macs(&self) -> &[B] {
        &self.macs
    }

    /// Returns the MAC for the given peer index, or `None` if out of bounds.
    #[inline]
    pub fn get_mac(&self, peer_index: PeerIndex) -> Option<&B> {
        self.macs.get(peer_index)
    }

    /// Returns a slice of all keys (one per distant peer).
    #[inline]
    pub fn get_keys(&self) -> &[PairwiseAuthKey<A, B>] {
        &self.keys
    }

    /// Returns a mutable slice of all keys.
    #[inline]
    pub fn get_keys_mut(&mut self) -> &mut [PairwiseAuthKey<A, B>] {
        &mut self.keys
    }

    /// Returns the key for the given peer index, or `None` if out of bounds.
    #[inline]
    pub fn get_key(&self, peer_index: PeerIndex) -> Option<&PairwiseAuthKey<A, B>> {
        self.keys.get(peer_index)
    }

    /// Consumes the share, returning the value.
    #[inline]
    pub fn into_value(self) -> V {
        self.value
    }

    #[allow(clippy::type_complexity)]
    /// Consumes the share, returning all the internal data (value, MACs, and keys).
    #[inline]
    pub fn into_inner(self) -> (V, Box<[B]>, Box<[PairwiseAuthKey<A, B>]>) {
        (self.value, self.macs, self.keys)
    }

    /// Total number of parties (including the local party).
    #[inline]
    pub fn n_parties(&self) -> usize {
        self.macs.len() + 1
    }

    /// Number of distant parties (excludes the local party).
    #[inline]
    pub fn n_distant_parties(&self) -> usize {
        self.macs.len()
    }

    /// Returns an iterator over the global keys (alpha values) for each distant peer.
    #[inline]
    pub fn get_alphas(&self) -> impl ExactSizeIterator<Item = GlobalKey<A>> + '_ {
        self.keys.iter().map(|key| key.alpha())
    }

    /// Returns an iterator over the local keys (beta values) for each distant peer.
    #[inline]
    pub fn get_betas(&self) -> impl ExactSizeIterator<Item = &B> + '_ {
        self.keys.iter().map(|key| key.get_beta())
    }
}

/// Alias for batched shares using `HeapArray`-based value/MAC/key types, with the same structure as
/// [`PairwiseAuthShare`].
pub type BatchedShare<V, A, B, M> = PairwiseAuthShare<HeapArray<V, M>, A, HeapArray<B, M>>;

impl<V, A, B, M: Positive> BatchedShare<V, A, B, M>
where
    V: Copy + for<'a> Add<&'a V, Output = V>,
    B: Copy + for<'a> Add<&'a B, Output = B>,
{
    /// Sum the columns at the positions listed in `indices` into a single [`PairwiseAuthShare`],
    /// reducing the `M`-wide batch by summing the value, MACs, and key betas at those positions
    /// (the shared `alpha`s are copied). Returns `None` if `indices` is empty.
    ///
    /// Equivalent to materializing the per-element shares and summing the selected ones —
    /// `indices.iter().map(|&i| self.get(i)).reduce(|a, b| a + &b)` — but it reads only the
    /// selected columns by index (no scan or per-column branch over the whole batch) and allocates
    /// a single output share instead of one share object per element. Indices must be in `0..M`.
    pub fn indexed_sum(&self, indices: &[usize]) -> Option<PairwiseAuthShare<V, A, B>> {
        let (&first, rest) = indices.split_first()?;

        let mut value = self.get_value()[first];
        let mut macs: Box<[B]> = self.get_macs().iter().map(|mac| mac[first]).collect();
        let mut keys: Box<[PairwiseAuthKey<A, B>]> = self
            .get_keys()
            .iter()
            .map(|key| PairwiseAuthKey::new(key.alpha(), key.get_beta()[first]))
            .collect();

        for &i in rest {
            value = value + &self.get_value()[i];
            for (acc, mac) in izip_eq!(&mut macs, self.get_macs()) {
                *acc = *acc + &mac[i];
            }
            for (key, src) in izip_eq!(&mut keys, self.get_keys()) {
                key.beta = key.beta + &src.get_beta()[i];
            }
        }

        Some(PairwiseAuthShare { value, macs, keys })
    }
}

/// Broadcast a single (non-batched) plaintext to every column of a batched share.
///
/// This is the batched counterpart of the blanket [`PlaintextOps`] impl: where that one adds a
/// full-width `HeapArray<V, M>` plaintext, this adds a single `V` to all `M` columns at once.
impl<V, A, B, M: Positive> PlaintextOps<V> for BatchedShare<V, A, B, M>
where
    BatchedShare<V, A, B, M>: Reconstructible<Value = HeapArray<V, M>> + Clone,
    V: Copy,
    HeapArray<V, M>: for<'a> AddAssign<&'a V> + for<'a> SubAssign<&'a V>,
    HeapArray<B, M>: for<'b> AddAssign<&'b B> + for<'b> SubAssign<&'b B>,
    for<'a> V: Mul<&'a A, Output = B>,
{
    /// Add a single scalar to every column of the batch.
    fn add_plaintext(mut self, scalar: &V, is_first_peer: bool) -> Self {
        if is_first_peer {
            self.value += scalar;
        } else {
            let key0 = self.keys.get_mut(0).expect("Missing key 0");
            key0.beta -= &(*scalar * &key0.alpha);
        }
        self
    }

    /// Subtract a single scalar from every column of the batch.
    fn sub_plaintext(mut self, scalar: &V, is_first_peer: bool) -> Self {
        if is_first_peer {
            self.value -= scalar;
        } else {
            let key0 = self.keys.get_mut(0).expect("Missing key 0");
            key0.beta += &(*scalar * &key0.alpha);
        }
        self
    }
}

/// Pairwise authenticated share `<x_i>` of secret shared `<x>` over a field F.
/// Alias for [`PairwiseAuthShare<SubfieldElement<F>, FieldElement<F>, FieldElement<F>>`].
/// See also [`FieldShares<F, M>`] for the batched variant.
pub type FieldShare<F> = PairwiseAuthShare<SubfieldElement<F>, FieldElement<F>, FieldElement<F>>;
/// Pairwise authenticated share over F_{2^107-1}. See [`FieldShare<F>`].
pub type Mersenne107Share = FieldShare<Mersenne107>;

/// Alias for [`PairwiseAuthShare<FieldElement<F>, FieldElement<F>, FieldElement<F>>`], using values
/// in F_p^r instead of F_p. See [`FieldShare<F>`] for the (more commonly used) subfield variant.
pub type FieldExtShare<F> = PairwiseAuthShare<FieldElement<F>, FieldElement<F>, FieldElement<F>>;

/// A share of a single point on a curve, with its associated MACs and the keys for all
/// other parties' shares.
///
/// Alias for [`PairwiseAuthShare<Point<C>, ScalarAsExtension<C>, Point<C>>`].
/// See also [`PointShares<C, M>`] for the batched variant.
pub type PointShare<C> = PairwiseAuthShare<Point<C>, ScalarAsExtension<C>, Point<C>>;

/// Authenticated batch share `<x_i>` of `M` secret-shared field elements held by `P_i`.
///
/// A vectorised counterpart of [`FieldShare<F>`]: same MAC/key structure, but all slots
/// are stored as fixed-length [`HeapArray`]s of size `M`.
///
/// Alias for [`PairwiseAuthShare<SubfieldElements<F,M>, FieldElement<F>, FieldElements<F,M>>`].
/// See also [`FieldShare<F>`] for the single-value variant.
pub type FieldShares<F, M> =
    PairwiseAuthShare<SubfieldElements<F, M>, FieldElement<F>, FieldElements<F, M>>;

/// A share of a batch of `M` curve points, with its associated MACs and the keys for
/// all other parties' shares.
///
/// A vectorised counterpart of [`PointShare<C>`]: same MAC/key structure, but all slots
/// are stored as fixed-length [`HeapArray`]s of size `M`.
///
/// Alias for [`PairwiseAuthShare<CurvePoints<C,M>, ScalarAsExtension<C>, CurvePoints<C,M>>`].
/// See also [`PointShare<C>`] for the single-value variant.
pub type PointShares<C, M> =
    PairwiseAuthShare<CurvePoints<C, M>, ScalarAsExtension<C>, CurvePoints<C, M>>;

// ---- Scalar / BaseField / Bit convenience aliases ----

/// Authenticated share of a scalar field element. Alias for [`FieldShare<ScalarField<C>>`].
pub type ScalarShare<C> = FieldShare<ScalarField<C>>;
/// Authenticated share of a base field element. Alias for [`FieldShare<BaseField<C>>`].
pub type BaseFieldShare<C> = FieldShare<BaseField<C>>;
/// Authenticated share of a single GF(2^128) bit. Alias for [`FieldShare<Gf2_128>`].
pub type BitShare = FieldShare<Gf2_128>;

/// Authenticated batch share of scalar field elements. Alias for [`FieldShares<ScalarField<C>,
/// M>`].
pub type ScalarShares<C, M> = FieldShares<ScalarField<C>, M>;
/// Authenticated batch share of base field elements. Alias for [`FieldShares<BaseField<C>, M>`].
pub type BaseFieldShares<C, M> = FieldShares<BaseField<C>, M>;
/// Authenticated batch share of GF(2^128) bits. Alias for [`FieldShares<Gf2_128, M>`].
pub type BitShares<M> = FieldShares<Gf2_128, M>;

// --------------------
// |   Verification   |
// --------------------

impl<V, A, B> PairwiseAuthShare<V, A, B> {
    /// Compute the MAC of a value `x` for ( `α`-global,  `β`-local) keys as:
    /// `MAC(x) = α * x + β`
    pub fn compute_mac(value: V, key: &PairwiseAuthKey<A, B>) -> B
    where
        A: Clone,
        B: for<'b> Add<&'b B, Output = B>,
        for<'a> V: Mul<&'a A, Output = B>,
    {
        value * key.get_alpha() + key.get_beta()
    }

    /// Verify the MAC of a value `x` for ( `α`-global,  `β`-local) keys fulfills:
    /// `MAC(x) == α * x + β`
    pub fn verify_mac(key: &PairwiseAuthKey<A, B>, opening: PairwiseAuthOpenShare<V, B>) -> Choice
    where
        A: Clone,
        B: ConstantTimeEq + SubAssign + for<'b> Add<&'b B, Output = B>,
        for<'a> V: Mul<&'a A, Output = B>,
    {
        let PairwiseAuthOpenShare { value, mac } = opening;
        let expected_mac = Self::compute_mac(value, key);
        expected_mac.ct_eq(&mac)
    }

    pub(crate) fn compute_all_pairwise_macs(
        all_unauth_shares: &[V],
        all_keys: &[Box<[PairwiseAuthKey<A, B>]>],
    ) -> Vec<Box<[B]>>
    where
        A: Clone,
        V: Clone,
        B: for<'b> Add<&'b B, Output = B>,
        for<'a> V: Mul<&'a A, Output = B>,
    {
        let mut all_key_iters = all_keys.iter().map(|k| k.iter()).collect::<Vec<_>>();
        enumerate(all_unauth_shares.iter())
            .map(|(i, my_unauth_share)| {
                enumerate(all_key_iters.iter_mut())
                    .filter(|(j, _)| *j != i)
                    .map(|(_, keys_iter)| {
                        let next_key = keys_iter.next().unwrap();
                        Self::compute_mac(my_unauth_share.clone(), next_key)
                    })
                    .collect()
            })
            .collect()
    }
}

impl<V, A, B> PairwiseAuthenticated for PairwiseAuthShare<V, A, B>
where
    V: Random + Clone,
    A: Random + Clone + Any,
    B: Random + Clone + ConstantTimeEq + SubAssign + for<'b> Add<&'b B, Output = B>,
    for<'a> V: Mul<&'a A, Output = B>,
{
    type GlobalAuthKey = GlobalKey<A>;

    fn get_global_keys(&self) -> impl ExactSizeIterator<Item = Self::GlobalAuthKey> {
        self.get_alphas()
    }
}

impl<V, A, B> Verifiable for PairwiseAuthShare<V, A, B>
where
    V: Clone
        + PartialEq
        + Send
        + Sync
        + 'static
        + Serialize
        + DeserializeOwned
        + SchemaWrite<Src = V>
        + for<'de> SchemaRead<'de, Dst = V>,
    A: Clone,
    B: Clone
        + Send
        + Sync
        + 'static
        + Serialize
        + DeserializeOwned
        + SchemaWrite<Src = B>
        + for<'de> SchemaRead<'de, Dst = B>
        + ConstantTimeEq
        + SubAssign
        + for<'b> Add<&'b B, Output = B>,
    for<'a> V: Add<&'a V, Output = V>,
    for<'a> V: Mul<&'a A, Output = B>,
{
    /// Check the MACs of the share received from another peer.
    #[inline]
    fn verify_from(
        &self,
        open_share: PairwiseAuthOpenShare<V, B>,
        peer: PeerIndex,
    ) -> Result<(), PrimitiveError> {
        let key = self
            .get_key(peer)
            .ok_or(PrimitiveError::InvalidPeerIndex(peer, self.keys.len()))?;
        if bool::from(PairwiseAuthShare::<V, A, B>::verify_mac(key, open_share)) {
            Ok(())
        } else {
            Err(PrimitiveError::WrongMAC(format!("peer {peer}")).blame(peer))
        }
    }

    /// Check the MACs of each share received from all other peers.
    #[inline]
    fn verify(&self, open_shares: Vec<PairwiseAuthOpenShare<V, B>>) -> Result<(), PrimitiveError> {
        enumerate(izip_eq!(open_shares, &self.keys))
            .map(|(from_peer, (open_share, key))| {
                if bool::from(PairwiseAuthShare::<V, A, B>::verify_mac(key, open_share)) {
                    Ok(())
                } else {
                    Err(PrimitiveError::WrongMAC(format!("peer {from_peer}")).blame(from_peer))
                }
            })
            .collect_errors()?;
        Ok(())
    }
}

// --------------------------------
// |   Opening & Reconstruction   |
// --------------------------------

impl<V, A, B> Reconstructible for PairwiseAuthShare<V, A, B>
where
    V: Clone
        + PartialEq
        + Send
        + Sync
        + 'static
        + Serialize
        + DeserializeOwned
        + SchemaWrite<Src = V>
        + for<'de> SchemaRead<'de, Dst = V>,
    A: Clone,
    B: Clone
        + Send
        + Sync
        + 'static
        + Serialize
        + DeserializeOwned
        + SchemaWrite<Src = B>
        + for<'de> SchemaRead<'de, Dst = B>
        + ConstantTimeEq
        + SubAssign
        + for<'b> Add<&'b B, Output = B>,
    for<'a> V: Add<&'a V, Output = V>,
    for<'a> V: Mul<&'a A, Output = B>,
{
    type Opening = PairwiseAuthOpenShare<V, B>;
    type Value = V;

    /// Open the share towards another peer.
    fn open_to(&self, peer: PeerIndex) -> Result<PairwiseAuthOpenShare<V, B>, PrimitiveError> {
        let mac = self
            .get_mac(peer)
            .ok_or(PrimitiveError::InvalidPeerIndex(peer, self.macs.len()))?
            .to_owned();
        Ok(PairwiseAuthOpenShare::new(self.get_value().to_owned(), mac))
    }

    /// Open the share towards all other peers.
    fn open_to_all_others(&self) -> impl ExactSizeIterator<Item = PairwiseAuthOpenShare<V, B>> {
        self.get_macs()
            .iter()
            .map(|mac| PairwiseAuthOpenShare::new(self.get_value().to_owned(), mac.to_owned()))
    }

    /// Reconstruct a secret from openings coming from all other parties.
    fn reconstruct(&self, openings: Vec<PairwiseAuthOpenShare<V, B>>) -> Result<V, PrimitiveError> {
        if openings.len() != self.get_keys().len() {
            return Err(PrimitiveError::InvalidSize(
                self.get_keys().len(),
                openings.len(),
            ));
        }
        let reconstruct = enumerate(izip_eq!(openings, &self.keys)).try_fold_all(
            self.get_value().to_owned(),
            |mut reconstructed, (from_peer, (open_share, key))| {
                reconstructed = reconstructed + open_share.get_value();
                let mac_error = match bool::from(PairwiseAuthShare::<V, A, B>::verify_mac(
                    key,
                    open_share.clone(),
                )) {
                    true => None,
                    false => {
                        Some(PrimitiveError::WrongMAC(format!("peer {from_peer}")).blame(from_peer))
                    }
                };
                (reconstructed, mac_error)
            },
        )?;
        Ok(reconstruct)
    }
}

// -------------------------
// |   Random Generation   |
// -------------------------

/// Number of parties
type NParties = usize;

impl<V, A, B> Random for PairwiseAuthShare<V, A, B>
where
    V: Random + Clone,
    A: Random + Clone,
    B: Random + Clone + ConstantTimeEq + SubAssign + for<'b> Add<&'b B, Output = B>,
    for<'a> V: Mul<&'a A, Output = B>,
{
    fn random(_rng: impl CryptoRngCore) -> Self {
        unimplemented!(
            "Type {} does not support `random` since it needs to know `n_parties`. Use `random_with(..., n_parties)` instead.",
            std::any::type_name::<Self>()
        )
    }

    /// Generate one random authenticated share per peer, with consistent MACs and keys
    /// across all peers.
    fn random_n<Container: FromIterator<Self>>(
        mut rng: impl CryptoRngCore,
        n_parties: usize,
    ) -> Container {
        let all_unauth_shares: Vec<_> = V::random_n(&mut rng, n_parties);
        let all_keys = (0..n_parties)
            .map(|_| PairwiseAuthKey::<A, B>::random_n(&mut rng, n_parties - 1))
            .collect::<Vec<_>>();
        let all_macs = Self::compute_all_pairwise_macs(&all_unauth_shares, &all_keys);
        izip_eq!(all_unauth_shares, all_macs, all_keys)
            .map(|(value, macs, keys)| PairwiseAuthShare { value, macs, keys })
            .collect()
    }
}

impl<V, A, B> RandomWith<V> for PairwiseAuthShare<V, A, B>
where
    V: AdditiveShares,
    A: Random + Clone,
    B: Random + Clone + ConstantTimeEq + SubAssign + for<'b> Add<&'b B, Output = B>,
    for<'a> V: Mul<&'a A, Output = B>,
{
    fn random_with(_rng: impl CryptoRngCore, _data: V) -> Self {
        unimplemented!(
            "Type {} does not support `random_with` since it needs to know `n_parties`. Use `random_n_with` instead.",
            std::any::type_name::<Self>()
        )
    }

    /// Secret share a value among n parties, generating an authenticated share for each
    /// peer with consistent MACs and keys across all peers.
    fn random_n_with<Container: FromIterator<Self>>(
        mut rng: impl CryptoRngCore,
        n_parties: usize,
        value: V,
    ) -> Container {
        let all_unauth_shares = value.to_additive_shares(n_parties, &mut rng);
        let all_keys = (0..n_parties)
            .map(|_| PairwiseAuthKey::<A, B>::random_n(&mut rng, n_parties - 1))
            .collect::<Vec<_>>();
        let all_macs = Self::compute_all_pairwise_macs(&all_unauth_shares, &all_keys);
        izip_eq!(all_unauth_shares, all_macs, all_keys)
            .map(|(value, macs, keys)| PairwiseAuthShare { value, macs, keys })
            .collect()
    }

    /// Generate an authenticated share for each peer given its additive share value,
    /// with consistent MACs and keys across all peers.
    fn random_n_with_each<Container: FromIterator<Self>>(
        mut rng: impl CryptoRngCore,
        unauth_shares: impl IntoExactSizeIterator<Item = V>,
    ) -> Container {
        let all_unauth_shares = unauth_shares.into_iter().collect::<Vec<_>>();
        let n_parties = all_unauth_shares.len();
        let all_keys = (0..n_parties)
            .map(|_| PairwiseAuthKey::<A, B>::random_n(&mut rng, n_parties - 1))
            .collect::<Vec<_>>();
        let all_macs = Self::compute_all_pairwise_macs(&all_unauth_shares, &all_keys);
        izip_eq!(all_unauth_shares, all_macs, all_keys)
            .map(|(value, macs, keys)| PairwiseAuthShare { value, macs, keys })
            .collect()
    }
}

impl<V, A, B> RandomWith<NParties> for PairwiseAuthShare<V, A, B>
where
    V: Random,
    A: Random + Clone,
    B: Random,
{
    /// Generate a random authenticated share with random MACs and keys for all other parties.
    fn random_with(mut rng: impl CryptoRngCore, n_parties: NParties) -> Self {
        PairwiseAuthShare {
            value: V::random(&mut rng),
            macs: B::random_n(&mut rng, n_parties - 1),
            keys: PairwiseAuthKey::<A, B>::random_n(&mut rng, n_parties - 1),
        }
    }
}

impl<V, A, B> RandomWith<(NParties, V)> for PairwiseAuthShare<V, A, B>
where
    V: Clone,
    A: Random + Clone,
    B: Random,
{
    /// Generate a random authenticated share with a given value and random MACs and keys.
    fn random_with(mut rng: impl CryptoRngCore, (n_parties, value): (NParties, V)) -> Self {
        PairwiseAuthShare {
            value,
            macs: B::random_n(&mut rng, n_parties - 1),
            keys: PairwiseAuthKey::<A, B>::random_n(&mut rng, n_parties - 1),
        }
    }
}

impl<V, A, B> RandomWith<Vec<GlobalKey<A>>> for PairwiseAuthShare<V, A, B>
where
    V: Random + Clone,
    A: Random + Clone,
    B: Random + Clone + ConstantTimeEq + SubAssign + for<'b> Add<&'b B, Output = B>,
    for<'a> V: Mul<&'a A, Output = B>,
{
    /// Generate a random authenticated share whose keys are derived from the given global keys.
    fn random_with(mut rng: impl CryptoRngCore, alphas: Vec<GlobalKey<A>>) -> Self {
        let value = V::random(&mut rng);
        let keys: Box<[_]> = PairwiseAuthKey::<A, B>::random_n_with_each(&mut rng, alphas);
        let macs: Box<[B]> = keys
            .iter()
            .map(|key| Self::compute_mac(value.clone(), key))
            .collect();
        PairwiseAuthShare { value, macs, keys }
    }

    /// Generate one authenticated share per peer, deriving each party's keys from their global
    /// keys.
    fn random_n_with_each<Container: FromIterator<Self>>(
        mut rng: impl CryptoRngCore,
        all_alphas: impl IntoExactSizeIterator<Item = Vec<GlobalKey<A>>>,
    ) -> Container {
        let all_alphas = all_alphas.into_iter();
        let all_unauth_shares: Vec<_> = V::random_n(&mut rng, all_alphas.len());
        let all_keys = all_alphas
            .into_iter()
            .map(|my_alphas| PairwiseAuthKey::<A, B>::random_n_with_each(&mut rng, my_alphas))
            .collect::<Vec<_>>();
        let all_macs = Self::compute_all_pairwise_macs(&all_unauth_shares, &all_keys);
        izip_eq!(all_unauth_shares, all_macs, all_keys)
            .map(|(value, macs, keys)| PairwiseAuthShare { value, macs, keys })
            .collect()
    }
}

impl<V, A, B> RandomWith<(V, Vec<GlobalKey<A>>)> for PairwiseAuthShare<V, A, B>
where
    V: Clone,
    A: Random + Clone,
    B: Random + Clone + ConstantTimeEq + SubAssign + for<'b> Add<&'b B, Output = B>,
    for<'a> V: Mul<&'a A, Output = B>,
{
    /// Generate a random authenticated share with a given value whose keys are derived from alphas.
    fn random_with(mut rng: impl CryptoRngCore, (value, alphas): (V, Vec<GlobalKey<A>>)) -> Self {
        let keys: Box<[_]> = PairwiseAuthKey::<A, B>::random_n_with_each(&mut rng, alphas);
        let macs: Box<[B]> = keys
            .iter()
            .map(|key| Self::compute_mac(value.clone(), key))
            .collect();
        PairwiseAuthShare { value, macs, keys }
    }

    /// Generate one authenticated share per peer from (value, alphas) pairs,
    /// computing MACs consistently across parties.
    fn random_n_with_each<Container: FromIterator<Self>>(
        mut rng: impl CryptoRngCore,
        unauth_shares_and_alphas: impl IntoExactSizeIterator<Item = (V, Vec<GlobalKey<A>>)>,
    ) -> Container {
        let (all_unauth_shares, all_keys): (Vec<_>, Vec<_>) = unauth_shares_and_alphas
            .into_iter()
            .map(|(value, my_alphas)| {
                (
                    value,
                    PairwiseAuthKey::<A, B>::random_n_with_each(&mut rng, my_alphas),
                )
            })
            .unzip();
        let all_macs = Self::compute_all_pairwise_macs(&all_unauth_shares, &all_keys);
        izip_eq!(all_unauth_shares, all_macs, all_keys)
            .map(|(value, macs, keys)| PairwiseAuthShare { value, macs, keys })
            .collect()
    }
}

impl<V, A, B> RandomWith<(V, Vec<Vec<GlobalKey<A>>>)> for PairwiseAuthShare<V, A, B>
where
    V: AdditiveShares,
    A: Random + Clone,
    B: Random + Clone + ConstantTimeEq + SubAssign + for<'b> Add<&'b B, Output = B>,
    for<'a> V: Mul<&'a A, Output = B>,
{
    fn random_with(_rng: impl CryptoRngCore, _: (V, Vec<Vec<GlobalKey<A>>>)) -> Self {
        unimplemented!(
            "Cannot discern what alpha/global key to use for this peer. Use `random_n_with` instead."
        )
    }

    /// Secret share a value among n parties, each supplied with their own list of global keys.
    fn random_n_with<Container: FromIterator<Self>>(
        mut rng: impl CryptoRngCore,
        n_parties: usize,
        (secret_value, all_alphas): (V, Vec<Vec<GlobalKey<A>>>),
    ) -> Container {
        assert_eq!(
            all_alphas.len(),
            n_parties,
            "Number of alphas must match the number of parties"
        );
        let all_unauth_shares = secret_value.to_additive_shares(all_alphas.len(), &mut rng);
        let all_keys = all_alphas
            .into_iter()
            .map(|my_alphas| PairwiseAuthKey::<A, B>::random_n_with_each(&mut rng, my_alphas))
            .collect::<Vec<_>>();
        let all_macs = Self::compute_all_pairwise_macs(&all_unauth_shares, &all_keys);
        izip_eq!(all_unauth_shares, all_macs, all_keys)
            .map(|(value, macs, keys)| PairwiseAuthShare { value, macs, keys })
            .collect()
    }
}

// --------------
// | Arithmetic |
// --------------

// === Addition === //

#[macros::op_variants(owned, borrowed, flipped_commutative)]
impl<'a, V, A, B> Add<&'a PairwiseAuthShare<V, A, B>> for PairwiseAuthShare<V, A, B>
where
    for<'v> V: Add<&'v V, Output = V>,
    for<'b> B: Add<&'b B, Output = B>,
    for<'k> PairwiseAuthKey<A, B>: Add<&'k PairwiseAuthKey<A, B>, Output = PairwiseAuthKey<A, B>>,
{
    type Output = PairwiseAuthShare<V, A, B>;

    #[inline]
    fn add(self, other: &'a PairwiseAuthShare<V, A, B>) -> Self::Output {
        PairwiseAuthShare {
            value: self.value + &other.value,
            macs: izip_eq!(self.macs, &other.macs)
                .map(|(mac_i, mac_j)| mac_i + mac_j)
                .collect(),
            keys: izip_eq!(self.keys, &other.keys)
                .map(|(key_i, key_j)| key_i + key_j)
                .collect(),
        }
    }
}

#[macros::op_variants(owned)]
impl<'a, V, A, B> AddAssign<&'a PairwiseAuthShare<V, A, B>> for PairwiseAuthShare<V, A, B>
where
    for<'v> V: AddAssign<&'v V>,
    for<'b> B: AddAssign<&'b B>,
    for<'k> PairwiseAuthKey<A, B>: AddAssign<&'k PairwiseAuthKey<A, B>>,
{
    #[inline]
    fn add_assign(&mut self, other: &'a PairwiseAuthShare<V, A, B>) {
        self.value += &other.value;
        izip_eq!(&mut self.macs, &other.macs).for_each(|(mac_i, mac_j)| *mac_i += mac_j);
        izip_eq!(&mut self.keys, &other.keys).for_each(|(key_i, key_j)| *key_i += key_j);
    }
}

impl<'a, V, A, B> Sum<&'a PairwiseAuthShare<V, A, B>> for PairwiseAuthShare<V, A, B>
where
    PairwiseAuthShare<V, A, B>: Clone + Default + AddAssign<&'a PairwiseAuthShare<V, A, B>>,
{
    #[inline]
    fn sum<I: Iterator<Item = &'a PairwiseAuthShare<V, A, B>>>(mut iter: I) -> Self {
        let first = iter.next().cloned().unwrap_or_default();
        iter.fold(first, |mut acc, item| {
            acc += item;
            acc
        })
    }
}

impl<V, A, B> Sum for PairwiseAuthShare<V, A, B>
where
    for<'v> V: AddAssign<&'v V>,
    for<'b> B: AddAssign<&'b B>,
    for<'k> PairwiseAuthKey<A, B>: AddAssign<&'k PairwiseAuthKey<A, B>>,
    PairwiseAuthShare<V, A, B>: Default,
{
    #[inline]
    fn sum<I: Iterator<Item = Self>>(mut iter: I) -> Self {
        let first = iter.next().unwrap_or_default();
        iter.fold(first, |mut acc, item| {
            acc += &item;
            acc
        })
    }
}

// === Subtraction === //

#[macros::op_variants(owned, borrowed, flipped)]
impl<'a, V, A, B> Sub<&'a PairwiseAuthShare<V, A, B>> for PairwiseAuthShare<V, A, B>
where
    for<'v> V: Sub<&'v V, Output = V>,
    for<'b> B: Sub<&'b B, Output = B>,
    for<'k> PairwiseAuthKey<A, B>: Sub<&'k PairwiseAuthKey<A, B>, Output = PairwiseAuthKey<A, B>>,
{
    type Output = PairwiseAuthShare<V, A, B>;

    #[inline]
    fn sub(self, other: &'a PairwiseAuthShare<V, A, B>) -> Self::Output {
        PairwiseAuthShare {
            value: self.value - &other.value,
            macs: izip_eq!(self.macs, &other.macs)
                .map(|(mac_i, mac_j)| mac_i - mac_j)
                .collect(),
            keys: izip_eq!(self.keys, &other.keys)
                .map(|(key_i, key_j)| key_i - key_j)
                .collect(),
        }
    }
}

#[macros::op_variants(owned)]
impl<'a, V, A, B> SubAssign<&'a PairwiseAuthShare<V, A, B>> for PairwiseAuthShare<V, A, B>
where
    for<'v> V: SubAssign<&'v V>,
    for<'b> B: SubAssign<&'b B>,
    for<'k> PairwiseAuthKey<A, B>: SubAssign<&'k PairwiseAuthKey<A, B>>,
{
    #[inline]
    fn sub_assign(&mut self, other: &'a PairwiseAuthShare<V, A, B>) {
        self.value -= &other.value;
        izip_eq!(&mut self.macs, &other.macs).for_each(|(mac_i, mac_j)| *mac_i -= mac_j);
        izip_eq!(&mut self.keys, &other.keys).for_each(|(key_i, key_j)| *key_i -= key_j);
    }
}

// === Constant multiplication === //

#[macros::op_variants(borrowed)]
impl<'a, V, V2, A, B, B2, Const> Mul<&'a Const> for PairwiseAuthShare<V, A, B>
where
    for<'v> V: Mul<&'v Const, Output = V2>,
    for<'b> B: Mul<&'b Const, Output = B2>,
{
    type Output = PairwiseAuthShare<V2, A, B2>;
    #[inline]
    fn mul(self, other: &'a Const) -> Self::Output {
        PairwiseAuthShare {
            value: self.value * other,
            macs: self
                .macs
                .into_vec()
                .into_iter()
                .map(|mac| mac * other)
                .collect(),
            keys: self
                .keys
                .into_vec()
                .into_iter()
                .map(|key| key * other)
                .collect(),
        }
    }
}

// === MulAssign === //

impl<'a, V, A, B, Const> MulAssign<&'a Const> for PairwiseAuthShare<V, A, B>
where
    for<'v> V: MulAssign<&'v Const>,
    for<'b> B: MulAssign<&'b Const>,
{
    #[inline]
    fn mul_assign(&mut self, other: &'a Const) {
        self.value *= other;
        izip_eq!(&mut self.keys).for_each(|key| *key *= other);
        izip_eq!(&mut self.macs).for_each(|mac| *mac *= other);
    }
}

// === Negation === //

#[macros::op_variants(borrowed)]
impl<V, A, B> Neg for PairwiseAuthShare<V, A, B>
where
    V: Neg<Output = V>,
    B: Neg<Output = B>,
    PairwiseAuthKey<A, B>: Neg<Output = PairwiseAuthKey<A, B>>,
{
    type Output = PairwiseAuthShare<V, A, B>;

    #[inline]
    fn neg(self) -> Self::Output {
        let PairwiseAuthShare { value, macs, keys } = self;
        PairwiseAuthShare {
            value: -value,
            keys: keys.into_vec().into_iter().map(|key| -key).collect(),
            macs: macs.into_vec().into_iter().map(|mac| -mac).collect(),
        }
    }
}

// === Constant addition / subtraction === //

impl<V, A, B> PlaintextOps<V> for PairwiseAuthShare<V, A, B>
where
    PairwiseAuthShare<V, A, B>: Reconstructible<Value = V>,
    V: Clone + for<'a> AddAssign<&'a V> + for<'a> SubAssign<&'a V>,
    A: Clone,
    B: Clone + for<'b> AddAssign<&'b B> + for<'b> SubAssign<&'b B> + ConstantTimeEq,
    for<'a> V: Mul<&'a A, Output = B>,
{
    /// If this is the first peer, adds the plaintext to the value;
    /// otherwise adjusts the first key's beta: `β₀ -= α₀ · ptx`.
    #[inline]
    fn add_plaintext(mut self, ptx: &V, is_first_peer: bool) -> Self {
        if is_first_peer {
            self.value += ptx;
        } else {
            let key0 = self.keys.get_mut(0).expect("Missing key 0");
            key0.beta -= &(ptx.to_owned() * &key0.alpha);
        }
        self
    }

    /// If this is the first peer, subtracts the plaintext from the value;
    /// otherwise adjusts the first key's beta: `β₀ += α₀ · ptx`.
    #[inline]
    fn sub_plaintext(mut self, ptx: &V, is_first_peer: bool) -> Self {
        if is_first_peer {
            self.value -= ptx;
        } else {
            let key0 = self.keys.get_mut(0).expect("Missing key 0");
            key0.beta += &(ptx.to_owned() * &key0.alpha);
        }
        self
    }
}

// ---------------------------------------
// |  Constant time Selection / Equality |
// ---------------------------------------

impl<V, A, B> ConstantTimeEq for PairwiseAuthShare<V, A, B>
where
    V: ConstantTimeEq,
    B: ConstantTimeEq,
    PairwiseAuthKey<A, B>: ConstantTimeEq,
{
    #[inline]
    fn ct_eq(&self, other: &Self) -> Choice {
        self.value.ct_eq(&other.value) & self.macs.ct_eq(&other.macs) & self.keys.ct_eq(&other.keys)
    }
}

impl<V, A, B> ConditionallySelectable for PairwiseAuthShare<V, A, B>
where
    V: ConditionallySelectable,
    B: ConditionallySelectable,
    PairwiseAuthKey<A, B>: ConditionallySelectable,
{
    #[inline]
    fn conditional_select(a: &Self, b: &Self, choice: Choice) -> Self {
        PairwiseAuthShare {
            value: V::conditional_select(&a.value, &b.value, choice),
            macs: izip_eq!(&a.macs, &b.macs)
                .map(|(a_mac, b_mac)| B::conditional_select(a_mac, b_mac, choice))
                .collect(),
            keys: izip_eq!(&a.keys, &b.keys)
                .map(|(a_key, b_key)| {
                    PairwiseAuthKey::<A, B>::conditional_select(a_key, b_key, choice)
                })
                .collect(),
        }
    }
}

/// Owning iterator over the element-wise single-element shares of a batched
/// [`PairwiseAuthShare`] such as `FieldShares<F, M>` or `PointShares<C, M>`.
///
/// Replaces the per-type `FieldSharesIterator` and `PointSharesIterator`.
#[derive(Clone, Debug)]
pub struct BatchedSharesIterator<VIter: Iterator, MacIter: Iterator, A, BIter: Iterator> {
    remaining: usize,
    value: VIter,
    macs: Vec<MacIter>,
    betas: Vec<BIter>,
    alphas: Vec<GlobalKey<A>>,
}

impl<VIter: Iterator, MacIter: Iterator, A: Clone, BIter: Iterator<Item = MacIter::Item>> Iterator
    for BatchedSharesIterator<VIter, MacIter, A, BIter>
{
    type Item = PairwiseAuthShare<VIter::Item, A, MacIter::Item>;

    fn next(&mut self) -> Option<Self::Item> {
        if self.remaining == 0 {
            return None;
        }
        let value = self.value.next()?;
        let macs: Box<[_]> = self
            .macs
            .iter_mut()
            .map(|it| it.next())
            .collect::<Option<_>>()?;
        let keys: Box<[_]> = izip!(&mut self.betas, &self.alphas)
            .map(|(beta_iter, alpha)| {
                beta_iter
                    .next()
                    .map(|beta| PairwiseAuthKey::new(alpha.clone(), beta))
            })
            .collect::<Option<_>>()?;
        self.remaining -= 1;
        Some(PairwiseAuthShare { value, macs, keys })
    }

    fn size_hint(&self) -> (usize, Option<usize>) {
        (self.remaining, Some(self.remaining))
    }
}

impl<VIter: Iterator, MacIter: Iterator, A: Clone, BIter: Iterator<Item = MacIter::Item>>
    ExactSizeIterator for BatchedSharesIterator<VIter, MacIter, A, BIter>
{
    fn len(&self) -> usize {
        self.remaining
    }
}

// ---------------------------------------------------------------
// |  IntoIterator for PairwiseAuthShare                        |
// ---------------------------------------------------------------

impl<V, A, B> IntoIterator for PairwiseAuthShare<V, A, B>
where
    V: IntoIterator,
    V::IntoIter: ExactSizeIterator,
    B: IntoIterator,
    A: Clone,
{
    type Item = PairwiseAuthShare<V::Item, A, B::Item>;
    type IntoIter = BatchedSharesIterator<V::IntoIter, B::IntoIter, A, B::IntoIter>;

    fn into_iter(self) -> Self::IntoIter {
        let PairwiseAuthShare { value, macs, keys } = self;
        let value_iter = value.into_iter();
        let remaining = value_iter.len();
        let macs = macs.into_vec().into_iter().map(|m| m.into_iter()).collect();
        let (betas, alphas): (Vec<_>, Vec<_>) = keys
            .into_vec()
            .into_iter()
            .map(|k| (k.beta.into_iter(), k.alpha))
            .unzip();
        BatchedSharesIterator {
            remaining,
            value: value_iter,
            macs,
            betas,
            alphas,
        }
    }
}

impl<V, A, B> IntoIterator for &PairwiseAuthShare<V, A, B>
where
    V: Clone + IntoIterator,
    V::IntoIter: ExactSizeIterator,
    B: Clone + IntoIterator,
    A: Clone,
{
    type Item = PairwiseAuthShare<V::Item, A, B::Item>;
    type IntoIter = BatchedSharesIterator<V::IntoIter, B::IntoIter, A, B::IntoIter>;

    fn into_iter(self) -> Self::IntoIter {
        let value_iter = self.value.clone().into_iter();
        let remaining = value_iter.len();
        let macs = self.macs.iter().map(|m| m.clone().into_iter()).collect();
        let (betas, alphas): (Vec<_>, Vec<_>) = self
            .keys
            .iter()
            .map(|k| (k.beta.clone().into_iter(), k.alpha.clone()))
            .unzip();
        BatchedSharesIterator {
            remaining,
            value: value_iter,
            macs,
            betas,
            alphas,
        }
    }
}

// -----------------------------------------------------------------
// |  FromIterator: collect single-element shares into a batch     |
// -----------------------------------------------------------------

impl<ItemV, A: Clone, ItemB, V, B> FromIterator<PairwiseAuthShare<ItemV, A, ItemB>>
    for PairwiseAuthShare<V, A, B>
where
    V: FromIterator<ItemV>,
    B: FromIterator<ItemB>,
{
    fn from_iter<T: IntoIterator<Item = PairwiseAuthShare<ItemV, A, ItemB>>>(iter: T) -> Self {
        let (values, macs, keys): (Vec<_>, Vec<Vec<_>>, Vec<Vec<_>>) = iter
            .into_iter()
            .map(|s| (s.value, s.macs.into_vec(), s.keys.into_vec()))
            .multiunzip();
        let macs: Box<[B]> = transpose(macs)
            .into_iter()
            .map(|pm| pm.into_iter().collect::<B>())
            .collect::<Vec<_>>()
            .into();
        let keys: Box<[PairwiseAuthKey<A, B>]> = transpose(keys)
            .into_iter()
            .map(|peer_keys: Vec<PairwiseAuthKey<A, ItemB>>| {
                let alpha = peer_keys[0].get_alpha().to_owned();
                let betas: B = peer_keys.into_iter().map(|k| k.beta).collect();
                PairwiseAuthKey::new(alpha.into(), betas)
            })
            .collect::<Vec<_>>()
            .into();
        PairwiseAuthShare {
            value: values.into_iter().collect::<V>(),
            macs,
            keys,
        }
    }
}

// -------------------------------------------------------
// |  From<single-element share> for U1-sized batch      |
// -------------------------------------------------------

impl<ItemV, A, ItemB> From<PairwiseAuthShare<ItemV, A, ItemB>>
    for BatchedShare<ItemV, A, ItemB, U1>
{
    fn from(share: PairwiseAuthShare<ItemV, A, ItemB>) -> Self {
        PairwiseAuthShare {
            value: HeapArray::from(share.value),
            macs: share
                .macs
                .into_vec()
                .into_iter()
                .map(HeapArray::from)
                .collect(),
            keys: share
                .keys
                .into_vec()
                .into_iter()
                .map(PairwiseAuthKey::from)
                .collect(),
        }
    }
}

// -------------------------------------------------------
// |  From<HeapArray<single, N>> for batched             |
// -------------------------------------------------------

impl<ItemV, A: Clone, ItemB, V, B, N: Positive>
    From<HeapArray<PairwiseAuthShare<ItemV, A, ItemB>, N>> for PairwiseAuthShare<V, A, B>
where
    V: FromIterator<ItemV>,
    B: FromIterator<ItemB>,
{
    fn from(shares: HeapArray<PairwiseAuthShare<ItemV, A, ItemB>, N>) -> Self {
        shares.into_iter().collect()
    }
}

// --------------------------------
// |  IntoParallelIterator        |
// --------------------------------

impl<ItemV: Send, A: Clone + Send, ItemB: Send, M: Positive> IntoParallelIterator
    for BatchedShare<ItemV, A, ItemB, M>
where
    PairwiseAuthShare<ItemV, A, ItemB>: Send,
{
    type Item = PairwiseAuthShare<ItemV, A, ItemB>;
    type Iter = rayon::vec::IntoIter<Self::Item>;

    fn into_par_iter(self) -> Self::Iter {
        // Convert HeapArray → Vec (using the existing From impl) to get an
        // ExactSizeIterator without needing to add a bounds chain for the
        // derive_more-generated HeapArray: IntoIterator impl.
        let PairwiseAuthShare { value, macs, keys } = self;
        let value_iter = Vec::from(value).into_iter();
        let remaining = value_iter.len();
        let mac_iters: Vec<_> = macs
            .into_vec()
            .into_iter()
            .map(|m| Vec::from(m).into_iter())
            .collect();
        let (betas, alphas): (Vec<_>, Vec<_>) = keys
            .into_vec()
            .into_iter()
            .map(|k| (Vec::from(k.beta).into_iter(), k.alpha))
            .unzip();
        BatchedSharesIterator {
            remaining,
            value: value_iter,
            macs: mac_iters,
            betas,
            alphas,
        }
        .collect::<Vec<_>>()
        .into_par_iter()
    }
}

// --------------------------
// |  Batched Operations    |
// --------------------------

impl<V, A, B, M: Positive> Batched for BatchedShare<V, A, B, M>
where
    V: Send,
    B: Send,
    A: Clone + Send + Sync,
{
    type Size = M;
}

impl<V: Copy, A: Clone, B: Copy, M: Positive> BatchedShare<V, A, B, M> {
    #[allow(clippy::type_complexity)]
    /// Splits a batched share of size M into two smaller batched shares (M1, M2),
    /// where M = M1 + M2.
    pub fn split<M1, M2>(self) -> (BatchedShare<V, A, B, M1>, BatchedShare<V, A, B, M2>)
    where
        M1: Positive,
        M2: Positive + Add<M1, Output = M>,
    {
        let PairwiseAuthShare { value, macs, keys } = self;
        let (v1, v2) = value.split::<M1, M2>();
        let (macs1, macs2): (Vec<_>, Vec<_>) = macs
            .into_vec()
            .into_iter()
            .map(|m| m.split::<M1, M2>())
            .unzip();
        let (keys1, keys2): (Vec<_>, Vec<_>) = keys
            .into_vec()
            .into_iter()
            .map(|k| k.split::<M1, M2>())
            .unzip();
        (
            PairwiseAuthShare::try_new(v1, macs1.into(), keys1.into()).unwrap(),
            PairwiseAuthShare::try_new(v2, macs2.into(), keys2.into()).unwrap(),
        )
    }

    #[allow(clippy::type_complexity)]
    pub fn split_last_pos<M1>(self) -> (BatchedShare<V, A, B, M1>, PairwiseAuthShare<V, A, B>)
    where
        M1: Positive + Add<typenum::B1, Output = M>,
    {
        let PairwiseAuthShare { value, macs, keys } = self;
        let (v1, v2) = value.split_last_pos();
        let (macs1, macs2): (Vec<_>, Vec<_>) = macs
            .into_vec()
            .into_iter()
            .map(|m| m.split_last_pos())
            .unzip();
        let (keys1, keys2): (Vec<_>, Vec<_>) = keys
            .into_vec()
            .into_iter()
            .map(|k| k.split_last_pos())
            .unzip();
        (
            PairwiseAuthShare::try_new(v1, macs1.into(), keys1.into()).unwrap(),
            PairwiseAuthShare::try_new(v2, macs2.into(), keys2.into()).unwrap(),
        )
    }

    #[allow(clippy::type_complexity)]
    /// Splits a batched share of size M into two smaller batched shares (M1, M2),
    /// where M = M1 + M2.
    pub fn split_halves<MDiv2>(self) -> (BatchedShare<V, A, B, MDiv2>, BatchedShare<V, A, B, MDiv2>)
    where
        MDiv2: Positive + Mul<U2, Output = M>,
    {
        let PairwiseAuthShare { value, macs, keys } = self;
        let (v1, v2) = value.split_halves::<MDiv2>();
        let (macs1, macs2): (Vec<_>, Vec<_>) = macs
            .into_vec()
            .into_iter()
            .map(|m| m.split_halves::<MDiv2>())
            .unzip();
        let (keys1, keys2): (Vec<_>, Vec<_>) = keys
            .into_vec()
            .into_iter()
            .map(|k| k.split_halves::<MDiv2>())
            .unzip();
        (
            PairwiseAuthShare::try_new(v1, macs1.into(), keys1.into()).unwrap(),
            PairwiseAuthShare::try_new(v2, macs2.into(), keys2.into()).unwrap(),
        )
    }

    #[allow(clippy::type_complexity)]
    /// Merges two batched shares of sizes M/2 into a larger batched share of size M.
    pub fn merge_halves(this: Self, other: Self) -> BatchedShare<V, A, B, Prod<M, U2>>
    where
        M: Mul<U2, Output: Positive>,
        A: PartialEq,
    {
        let PairwiseAuthShare {
            value: v1,
            macs: m1,
            keys: k1,
        } = this;
        let PairwiseAuthShare {
            value: v2,
            macs: m2,
            keys: k2,
        } = other;
        let value = HeapArray::merge_halves(v1, v2);
        let macs: Box<[_]> = izip_eq!(m1, m2)
            .map(|(a, b)| HeapArray::merge_halves(a, b))
            .collect();
        let keys: Box<[_]> = izip_eq!(k1, k2)
            .map(|(a, b)| PairwiseAuthKey::merge_halves(a, b))
            .collect();
        PairwiseAuthShare::try_new(value, macs, keys).unwrap()
    }

    #[allow(clippy::type_complexity)]
    /// Splits a batched share of size M into three smaller batched shares (M1, M2, M3),
    /// where M = M1 + M2 + M3.
    pub fn split_thirds<MDiv3>(
        self,
    ) -> (
        BatchedShare<V, A, B, MDiv3>,
        BatchedShare<V, A, B, MDiv3>,
        BatchedShare<V, A, B, MDiv3>,
    )
    where
        MDiv3: Positive + Mul<U3, Output = M>,
    {
        let PairwiseAuthShare { value, macs, keys } = self;
        let (v1, v2, v3) = value.split_thirds::<MDiv3>();
        let (macs1, macs2, macs3): (Vec<_>, Vec<_>, Vec<_>) = macs
            .into_vec()
            .into_iter()
            .map(|m| m.split_thirds::<MDiv3>())
            .multiunzip();
        let (keys1, keys2, keys3): (Vec<_>, Vec<_>, Vec<_>) = keys
            .into_vec()
            .into_iter()
            .map(|k| k.split_thirds::<MDiv3>())
            .multiunzip();
        (
            PairwiseAuthShare::try_new(v1, macs1.into(), keys1.into()).unwrap(),
            PairwiseAuthShare::try_new(v2, macs2.into(), keys2.into()).unwrap(),
            PairwiseAuthShare::try_new(v3, macs3.into(), keys3.into()).unwrap(),
        )
    }

    #[allow(clippy::type_complexity)]
    /// Splits a batched share of size M into five smaller batched shares of size M/5.
    pub fn split_fifths<MDiv5>(
        self,
    ) -> (
        BatchedShare<V, A, B, MDiv5>,
        BatchedShare<V, A, B, MDiv5>,
        BatchedShare<V, A, B, MDiv5>,
        BatchedShare<V, A, B, MDiv5>,
        BatchedShare<V, A, B, MDiv5>,
    )
    where
        MDiv5: Positive + Mul<U5, Output = M>,
    {
        fn split_array<T: Copy, M: Positive, MDiv5: Positive + Mul<U5, Output = M>>(
            arr: HeapArray<T, M>,
        ) -> (
            HeapArray<T, MDiv5>,
            HeapArray<T, MDiv5>,
            HeapArray<T, MDiv5>,
            HeapArray<T, MDiv5>,
            HeapArray<T, MDiv5>,
        ) {
            let n = MDiv5::USIZE;
            let (a, rest) = arr.split_at(n);
            let (b, rest) = rest.split_at(n);
            let (c, rest) = rest.split_at(n);
            let (d, e) = rest.split_at(n);
            (
                HeapArray::<T, MDiv5>::try_from(a.to_vec()).unwrap(),
                HeapArray::<T, MDiv5>::try_from(b.to_vec()).unwrap(),
                HeapArray::<T, MDiv5>::try_from(c.to_vec()).unwrap(),
                HeapArray::<T, MDiv5>::try_from(d.to_vec()).unwrap(),
                HeapArray::<T, MDiv5>::try_from(e.to_vec()).unwrap(),
            )
        }

        let PairwiseAuthShare { value, macs, keys } = self;
        let (v1, v2, v3, v4, v5) = split_array::<V, M, MDiv5>(value);
        let (macs1, macs2, macs3, macs4, macs5): (Vec<_>, Vec<_>, Vec<_>, Vec<_>, Vec<_>) = macs
            .into_vec()
            .into_iter()
            .map(split_array::<B, M, MDiv5>)
            .multiunzip();
        let (keys1, keys2, keys3, keys4, keys5): (Vec<_>, Vec<_>, Vec<_>, Vec<_>, Vec<_>) = keys
            .into_vec()
            .into_iter()
            .map(|k| {
                let PairwiseAuthKey { alpha, beta } = k;
                let (b1, b2, b3, b4, b5) = split_array::<B, M, MDiv5>(beta);
                (
                    PairwiseAuthKey::new(alpha.clone(), b1),
                    PairwiseAuthKey::new(alpha.clone(), b2),
                    PairwiseAuthKey::new(alpha.clone(), b3),
                    PairwiseAuthKey::new(alpha.clone(), b4),
                    PairwiseAuthKey::new(alpha, b5),
                )
            })
            .multiunzip();
        (
            PairwiseAuthShare::try_new(v1, macs1.into(), keys1.into()).unwrap(),
            PairwiseAuthShare::try_new(v2, macs2.into(), keys2.into()).unwrap(),
            PairwiseAuthShare::try_new(v3, macs3.into(), keys3.into()).unwrap(),
            PairwiseAuthShare::try_new(v4, macs4.into(), keys4.into()).unwrap(),
            PairwiseAuthShare::try_new(v5, macs5.into(), keys5.into()).unwrap(),
        )
    }

    #[allow(clippy::type_complexity)]
    /// Merges three batched shares of sizes M/3 into a larger batched share of size M.
    pub fn merge_thirds(
        first: Self,
        second: Self,
        third: Self,
    ) -> BatchedShare<V, A, B, Prod<M, U3>>
    where
        M: Mul<U3, Output: Positive>,
        A: PartialEq,
    {
        let PairwiseAuthShare {
            value: v1,
            macs: m1,
            keys: k1,
        } = first;
        let PairwiseAuthShare {
            value: v2,
            macs: m2,
            keys: k2,
        } = second;
        let PairwiseAuthShare {
            value: v3,
            macs: m3,
            keys: k3,
        } = third;
        let value = HeapArray::merge_thirds(v1, v2, v3);
        let macs: Box<[_]> = izip_eq!(m1, m2, m3)
            .map(|(a, b, c)| HeapArray::merge_thirds(a, b, c))
            .collect();
        let keys: Box<[_]> = izip_eq!(k1, k2, k3)
            .map(|(a, b, c)| PairwiseAuthKey::merge_thirds(a, b, c))
            .collect();
        PairwiseAuthShare::try_new(value, macs, keys).unwrap()
    }

    #[allow(clippy::type_complexity)]
    /// Creates an iterator that yields fixed-size batched chunks of size `CS`.
    pub fn chunks<CS: Positive>(
        &self,
    ) -> BatchedSharesChunks<
        <HeapArray<V, M> as IntoIterator>::IntoIter,
        <HeapArray<B, M> as IntoIterator>::IntoIter,
        A,
        <HeapArray<B, M> as IntoIterator>::IntoIter,
        CS,
    >
    where
        M: PartialDiv<CS>,
    {
        BatchedSharesChunks {
            inner: self.into_iter(),
            remaining_chunks: M::USIZE / CS::USIZE,
            _ds: PhantomData,
        }
    }

    /// Swaps elements at positions `i` and `j` in-place across
    /// value, macs, and key betas arrays.
    pub fn swap(&mut self, i: usize, j: usize) {
        self.value.swap(i, j);
        for mac in self.macs.iter_mut() {
            mac.swap(i, j);
        }
        for key in self.keys.iter_mut() {
            key.beta.swap(i, j);
        }
    }
}

// ---------------------------------------------------------------
// |  BatchedSharesChunks — chunk-level iterator               |
// ---------------------------------------------------------------

/// An iterator over fixed-size chunks of a batched [`PairwiseAuthShare`].
pub struct BatchedSharesChunks<VIter: Iterator, MacIter: Iterator, A, BIter: Iterator, DS: Positive>
{
    inner: BatchedSharesIterator<VIter, MacIter, A, BIter>,
    remaining_chunks: usize,
    _ds: PhantomData<DS>,
}

impl<VIter: Iterator, MacIter: Iterator, A: Clone, BIter: Iterator, DS: Positive>
    BatchedSharesChunks<VIter, MacIter, A, BIter, DS>
{
    pub fn len(&self) -> usize {
        self.remaining_chunks
    }

    pub fn is_empty(&self) -> bool {
        self.remaining_chunks == 0
    }
}

impl<
        VIter: Iterator,
        MacIter: Iterator,
        A: Clone,
        BIter: Iterator<Item = MacIter::Item>,
        DS: Positive,
    > Iterator for BatchedSharesChunks<VIter, MacIter, A, BIter, DS>
where
    HeapArray<VIter::Item, DS>: FromIterator<VIter::Item>,
    HeapArray<MacIter::Item, DS>: FromIterator<MacIter::Item>,
{
    type Item = BatchedShare<VIter::Item, A, MacIter::Item, DS>;

    fn next(&mut self) -> Option<Self::Item> {
        if self.remaining_chunks == 0 {
            return None;
        }
        let chunk: Vec<_> = self.inner.by_ref().take(DS::to_usize()).collect();
        if chunk.is_empty() {
            return None;
        }
        self.remaining_chunks -= 1;
        Some(chunk.into_iter().collect())
    }

    fn size_hint(&self) -> (usize, Option<usize>) {
        (self.remaining_chunks, Some(self.remaining_chunks))
    }
}

impl<
        VIter: Iterator,
        MacIter: Iterator,
        A: Clone,
        BIter: Iterator<Item = MacIter::Item>,
        DS: Positive,
    > ExactSizeIterator for BatchedSharesChunks<VIter, MacIter, A, BIter, DS>
where
    HeapArray<VIter::Item, DS>: FromIterator<VIter::Item>,
    HeapArray<MacIter::Item, DS>: FromIterator<MacIter::Item>,
{
    fn len(&self) -> usize {
        self.remaining_chunks
    }
}

// ------------------------------------------------------------------
// |  Reconstructible for HeapArray<Share, N>                       |
// ------------------------------------------------------------------

/// Reconstruction protocol for a length-`N` array of [`PairwiseAuthShare`]s.
/// Each element is independently reconstructed and the secrets are collected.
impl<V, A, B, N: Positive> Reconstructible for HeapArray<PairwiseAuthShare<V, A, B>, N>
where
    PairwiseAuthShare<V, A, B>: Reconstructible,
    <PairwiseAuthShare<V, A, B> as Reconstructible>::Opening: Clone,
{
    type Opening = HeapArray<<PairwiseAuthShare<V, A, B> as Reconstructible>::Opening, N>;
    type Value = HeapArray<<PairwiseAuthShare<V, A, B> as Reconstructible>::Value, N>;

    fn open_to(&self, for_peer: PeerIndex) -> Result<Self::Opening, PrimitiveError> {
        self.into_iter()
            .map(|s| s.open_to(for_peer))
            .collect::<Result<_, _>>()
    }

    fn open_to_all_others(&self) -> impl ExactSizeIterator<Item = Self::Opening> {
        let per_share: Vec<Vec<<PairwiseAuthShare<V, A, B> as Reconstructible>::Opening>> = self
            .into_iter()
            .map(|s| s.open_to_all_others().collect())
            .collect();
        transpose(per_share)
            .into_iter()
            .map(|col| col.try_into().expect("size mismatch in open_to_all_others"))
    }

    fn reconstruct(&self, openings: Vec<Self::Opening>) -> Result<Self::Value, PrimitiveError> {
        self.iter()
            .enumerate()
            .map(|(i, share)| {
                let my_openings: Vec<_> = openings
                    .iter()
                    .map(|o| o.get(i).cloned())
                    .collect::<Option<_>>()
                    .ok_or_else(|| {
                        PrimitiveError::InvalidParameters(
                            "Opening is missing for some share.".to_string(),
                        )
                    })?;
                share.reconstruct(my_openings)
            })
            .collect::<Result<_, _>>()
    }
}

// --- Type conversions --- //

impl<C: Curve> From<ScalarShare<C>> for PointShare<C> {
    #[inline]
    fn from(scalar_share: ScalarShare<C>) -> Self {
        scalar_share * &Point::<C>::generator()
    }
}

impl<C: Curve, M: Positive> From<ScalarShares<C, M>> for PointShares<C, M> {
    #[inline]
    fn from(scalar_shares: ScalarShares<C, M>) -> Self {
        scalar_shares * &Point::<C>::generator()
    }
}

impl<F: FieldExtension> From<FieldShare<F>> for FieldExtShare<F> {
    fn from(value: FieldShare<F>) -> Self {
        let PairwiseAuthShare { value, macs, keys } = value;
        let value = FieldElement(F::from_subfield_element(value.0));
        Self { value, macs, keys }
    }
}

#[cfg(test)]
mod tests {
    use std::{fmt::Debug, ops::Div};

    use typenum::{U2, U3};

    use super::*;
    use crate::{random::test_rng, sharing::Verifiable};

    /// `indexed_sum` equals the materialize-then-reduce reference over the selected columns.
    #[test]
    fn test_indexed_sum_matches_reference() {
        use crate::algebra::field::mersenne::Mersenne107;
        const N_PARTIES: usize = 3;
        let mut rng = test_rng();
        let alphas: Vec<GlobalKey<FieldElement<Mersenne107>>> =
            Random::random_n(&mut rng, N_PARTIES - 1);
        let singles: Vec<FieldShare<Mersenne107>> =
            FieldShare::<Mersenne107>::random_n_with(&mut rng, 8, alphas);
        let fs: FieldShares<Mersenne107, typenum::U8> = singles.iter().cloned().collect();
        let mask = [true, false, true, true, false, false, true, false];
        let indices = [0usize, 2, 3, 6];

        let expected = izip_eq!(&singles, &mask)
            .filter_map(|(s, &m)| m.then_some(s.clone()))
            .reduce(|a, b| a + &b);
        assert_eq!(fs.indexed_sum(&indices), expected);

        // No index selected → None (matches `reduce` over an empty iterator).
        assert!(fs.indexed_sum(&[]).is_none());
    }

    /// The scalar `add_plaintext`/`sub_plaintext` equal the full-width versions with the scalar
    /// broadcast to every column.
    #[test]
    fn test_add_plaintext_scalar_matches_reference() {
        use crate::{algebra::field::mersenne::Mersenne107, sharing::PlaintextOps};
        let mut rng = test_rng();
        let fs = FieldShares::<Mersenne107, typenum::U8>::random_with(&mut rng, 3);
        let scalar = SubfieldElement::<Mersenne107>::from(7u32);
        let broadcast: SubfieldElements<Mersenne107, typenum::U8> =
            std::iter::repeat_n(scalar, 8).collect();

        for is_first_peer in [true, false] {
            assert_eq!(
                PlaintextOps::<SubfieldElement<Mersenne107>>::add_plaintext(
                    fs.clone(),
                    &scalar,
                    is_first_peer,
                ),
                fs.clone().add_plaintext(&broadcast, is_first_peer),
            );
            assert_eq!(
                PlaintextOps::<SubfieldElement<Mersenne107>>::sub_plaintext(
                    fs.clone(),
                    &scalar,
                    is_first_peer,
                ),
                fs.clone().sub_plaintext(&broadcast, is_first_peer),
            );
        }
    }

    // ─── Marker Trait: ShareValue ────────────────────────────────────────────
    /// Bundle of all bounds required on the **value type `V`** by the test suite.
    ///
    /// Blanket-implemented for every type satisfying the constituent bounds, so
    /// callers only need to write `V: ShareValue<A, B, Const>`.
    pub(super) trait ShareValue<A, B, Const>:
        Clone
        + PartialEq
        + Debug
        + Random
        + AdditiveShares
        + ConstantTimeEq
        + ConditionallySelectable
        + Neg<Output = Self>
        + for<'a> Sub<&'a Self, Output = Self>
        + for<'a> AddAssign<&'a Self>
        + for<'a> Mul<&'a A, Output = B>
        + for<'a> Mul<&'a Const, Output = Self>
        + for<'a> MulAssign<&'a Const>
        + Send
        + Sync
        + 'static
        + Serialize
        + DeserializeOwned
        + SchemaWrite<Src = Self>
        + for<'de> SchemaRead<'de, Dst = Self>
    {
    }

    impl<V, A, B, Const> ShareValue<A, B, Const> for V where
        V: Clone
            + PartialEq
            + Debug
            + Random
            + AdditiveShares
            + ConstantTimeEq
            + ConditionallySelectable
            + Neg<Output = V>
            + for<'a> Sub<&'a V, Output = V>
            + for<'a> AddAssign<&'a V>
            + for<'a> Mul<&'a A, Output = B>
            + for<'a> Mul<&'a Const, Output = V>
            + for<'a> MulAssign<&'a Const>
            + Send
            + Sync
            + 'static
            + Serialize
            + DeserializeOwned
            + SchemaWrite<Src = V>
            + for<'de> SchemaRead<'de, Dst = V>
    {
    }

    // ─── Marker Trait: ShareKey ──────────────────────────────────────────────
    /// Bundle of all bounds required on the **global-key inner type `A`** by the
    /// test suite.
    pub(super) trait ShareKey:
        Clone + PartialEq + Debug + Random + ConstantTimeEq + ConditionallySelectable
    {
    }

    impl<A> ShareKey for A where
        A: Clone + PartialEq + Debug + Random + ConstantTimeEq + ConditionallySelectable
    {
    }

    // ─── Marker Trait: ShareMac ──────────────────────────────────────────────
    /// Bundle of all bounds required on the **MAC / local-key type `B`** by the
    /// test suite.
    pub(super) trait ShareMac<V, A, Const>:
        Clone
        + PartialEq
        + Debug
        + Random
        + ConstantTimeEq
        + ConditionallySelectable
        + SubAssign
        + Neg<Output = Self>
        + for<'b> Add<&'b Self, Output = Self>
        + for<'b> AddAssign<&'b Self>
        + for<'b> Sub<&'b Self, Output = Self>
        + for<'b> SubAssign<&'b Self>
        + for<'c> Mul<&'c Const, Output = Self>
        + for<'c> MulAssign<&'c Const>
        + Send
        + Sync
        + 'static
        + Serialize
        + DeserializeOwned
        + SchemaWrite<Src = Self>
        + for<'de> SchemaRead<'de, Dst = Self>
    {
    }

    impl<B, V, A, Const> ShareMac<V, A, Const> for B where
        B: Clone
            + PartialEq
            + Debug
            + Random
            + ConstantTimeEq
            + ConditionallySelectable
            + SubAssign
            + Neg<Output = B>
            + for<'b> Add<&'b B, Output = B>
            + for<'b> AddAssign<&'b B>
            + for<'b> Sub<&'b B, Output = B>
            + for<'b> SubAssign<&'b B>
            + for<'c> Mul<&'c Const, Output = B>
            + for<'c> MulAssign<&'c Const>
            + Send
            + Sync
            + 'static
            + Serialize
            + DeserializeOwned
            + SchemaWrite<Src = B>
            + for<'de> SchemaRead<'de, Dst = B>
    {
    }

    // ─── Batched Marker Trait: BatchedShareItem ──────────────────────────────
    /// Bounds on the **element type `IV`** inside a batched value
    /// `HeapArray<IV, M>`. Extends the general per-element requirements.
    ///
    /// Used exclusively by the batched-share test helpers.
    pub(super) trait BatchedShareItem<A, IB>:
        Copy
        + Clone
        + PartialEq
        + Debug
        + Random
        + ConstantTimeEq
        + ConditionallySelectable
        + for<'a> Mul<&'a A, Output = IB>
    {
    }

    impl<IV, A, IB> BatchedShareItem<A, IB> for IV where
        IV: Copy
            + Clone
            + PartialEq
            + Debug
            + Random
            + ConstantTimeEq
            + ConditionallySelectable
            + for<'a> Mul<&'a A, Output = IB>
    {
    }

    // ─── Batched Marker Trait: BatchedShareMacItem ───────────────────────────
    /// Bounds on the **element MAC type `IB`** inside a batched MAC
    /// `HeapArray<IB, M>`. Extends the general per-element requirements.
    pub(super) trait BatchedShareMacItem<IV, A>:
        Copy + Clone + PartialEq + Debug + Random + ConstantTimeEq + ConditionallySelectable
    {
    }

    impl<IB, IV, A> BatchedShareMacItem<IV, A> for IB where
        IB: Copy + Clone + PartialEq + Debug + Random + ConstantTimeEq + ConditionallySelectable
    {
    }

    // ─── Generic Pairwise Test Functions ─────────────────────────────────────

    pub(super) fn test_open_to<V, A, B, Const>(n_parties: usize)
    where
        V: ShareValue<A, B, Const>,
        A: ShareKey,
        B: ShareMac<V, A, Const>,
        Const: Random,
    {
        let mut rng = test_rng();
        let share = PairwiseAuthShare::<V, A, B>::random_with(&mut rng, n_parties);
        for i in 0..n_parties - 1 {
            let open = share.open_to(i).unwrap();
            assert_eq!(open.get_value(), &share.value);
            assert_eq!(open.get_mac(), &share.macs[i]);
        }
    }

    pub(super) fn test_random<V, A, B, Const>(n_parties: usize)
    where
        V: ShareValue<A, B, Const>,
        A: ShareKey,
        B: ShareMac<V, A, Const>,
        Const: Random,
    {
        let mut rng = test_rng();
        let share = PairwiseAuthShare::<V, A, B>::random_with(&mut rng, n_parties);
        assert_eq!(share.get_macs().len(), n_parties - 1);
        assert_eq!(share.get_keys().len(), n_parties - 1);
        let value = V::random(&mut rng);
        let share_with_value =
            PairwiseAuthShare::<V, A, B>::random_with(&mut rng, (n_parties, value.clone()));
        assert_eq!(share_with_value.get_value(), &value);
        assert_eq!(share_with_value.get_macs().len(), n_parties - 1);
        assert_eq!(share_with_value.get_keys().len(), n_parties - 1);
    }

    pub(super) fn test_random_vec_and_reconstruct<V, A, B, Const>(n_parties: usize)
    where
        V: ShareValue<A, B, Const>,
        A: ShareKey,
        B: ShareMac<V, A, Const>,
        Const: Random,
    {
        let mut rng = test_rng();
        let shares: Vec<_> = PairwiseAuthShare::<V, A, B>::random_n(&mut rng, n_parties);
        assert_eq!(shares.len(), n_parties);
        for share in &shares {
            assert_eq!(share.get_macs().len(), n_parties - 1);
            assert_eq!(share.get_keys().len(), n_parties - 1);
        }
        let unauth: Vec<_> = shares.iter().map(|s| s.get_value().clone()).collect();
        let expected = V::from_additive_shares(&unauth);
        let reconstructed = PairwiseAuthShare::<V, A, B>::reconstruct_all(shares).unwrap();
        assert_eq!(reconstructed, expected);

        let value = V::random(&mut rng);
        let shares: Vec<_> =
            PairwiseAuthShare::<V, A, B>::random_n_with(&mut rng, n_parties, value.clone());
        let reconstructed = PairwiseAuthShare::<V, A, B>::reconstruct_all(shares).unwrap();
        assert_eq!(reconstructed, value);
    }

    pub(super) fn test_random_vec_with_global_key_and_reconstruct<V, A, B, Const>(n_parties: usize)
    where
        V: ShareValue<A, B, Const>,
        A: ShareKey,
        B: ShareMac<V, A, Const>,
        Const: Random,
    {
        let mut rng = test_rng();
        // n shares, each built from n-1 per-peer global keys
        let alphas: Vec<Vec<GlobalKey<A>>> = (0..n_parties)
            .map(|_| GlobalKey::<A>::random_n::<Vec<_>>(&mut rng, n_parties - 1))
            .collect();
        let shares_from_alphas: Vec<_> =
            PairwiseAuthShare::<V, A, B>::random_n_with_each(&mut rng, alphas.clone());
        assert_eq!(shares_from_alphas.len(), n_parties);
        for (share, my_alphas) in izip_eq!(&shares_from_alphas, &alphas) {
            assert_eq!(share.get_macs().len(), n_parties - 1);
            assert_eq!(share.get_keys().len(), n_parties - 1);
            assert_eq!(share.get_alphas().collect::<Vec<_>>(), *my_alphas);
        }
        let _ = PairwiseAuthShare::<V, A, B>::reconstruct_all(shares_from_alphas).unwrap();

        // from a value + per-party alpha lists
        let value = V::random(&mut rng);
        let alphas: Vec<Vec<GlobalKey<A>>> = (0..n_parties)
            .map(|_| GlobalKey::<A>::random_n::<Vec<_>>(&mut rng, n_parties - 1))
            .collect();
        let shares_from_value_and_alphas: Vec<_> = PairwiseAuthShare::<V, A, B>::random_n_with(
            &mut rng,
            n_parties,
            (value.clone(), alphas.clone()),
        );
        assert_eq!(shares_from_value_and_alphas.len(), n_parties);
        for (share, my_alphas) in izip_eq!(&shares_from_value_and_alphas, &alphas) {
            assert_eq!(share.get_macs().len(), n_parties - 1);
            assert_eq!(share.get_keys().len(), n_parties - 1);
            assert_eq!(share.get_alphas().collect::<Vec<_>>(), *my_alphas);
        }
        let reconstructed =
            PairwiseAuthShare::<V, A, B>::reconstruct_all(shares_from_value_and_alphas).unwrap();
        assert_eq!(reconstructed, value);

        // from additive shares + per-party alpha lists
        let value = V::random(&mut rng);
        let unauth = value.to_additive_shares(n_parties, &mut rng);
        let alphas: Vec<Vec<GlobalKey<A>>> = (0..n_parties)
            .map(|_| GlobalKey::<A>::random_n::<Vec<_>>(&mut rng, n_parties - 1))
            .collect();
        let shares_from_unauth: Vec<_> = PairwiseAuthShare::<V, A, B>::random_n_with_each(
            &mut rng,
            izip_eq!(unauth, alphas.clone()),
        );
        assert_eq!(shares_from_unauth.len(), n_parties);
        for (share, my_alphas) in izip_eq!(&shares_from_unauth, &alphas) {
            assert_eq!(share.get_macs().len(), n_parties - 1);
            assert_eq!(share.get_keys().len(), n_parties - 1);
            assert_eq!(share.get_alphas().collect::<Vec<_>>(), *my_alphas);
        }
        let reconstructed =
            PairwiseAuthShare::<V, A, B>::reconstruct_all(shares_from_unauth).unwrap();
        assert_eq!(reconstructed, value);
    }

    pub(super) fn test_verify_mac<V, A, B, Const>(n_parties: usize)
    where
        V: ShareValue<A, B, Const>,
        A: ShareKey,
        B: ShareMac<V, A, Const>,
        Const: Random,
    {
        let mut rng = test_rng();
        let shares: Vec<_> = PairwiseAuthShare::<V, A, B>::random_n(&mut rng, n_parties);
        for i in 0..shares.len() {
            for j in 0..shares.len() {
                if i == j {
                    continue;
                }
                let open = shares[j].open_to(i - (i > j) as usize).unwrap();
                shares[i].verify_from(open, j - (j > i) as usize).unwrap();
            }
        }
        PairwiseAuthShare::<V, A, B>::verify_all(shares).unwrap();
    }

    pub(super) fn test_add<V, A, B, Const>(n_parties: usize)
    where
        V: ShareValue<A, B, Const>,
        A: ShareKey,
        B: ShareMac<V, A, Const>,
        Const: Random,
    {
        let mut rng = test_rng();
        let alphas: Vec<Vec<GlobalKey<A>>> = (0..n_parties)
            .map(|_| GlobalKey::<A>::random_n::<Vec<_>>(&mut rng, n_parties - 1))
            .collect();
        let a = V::random(&mut rng);
        let b = V::random(&mut rng);
        let shares_a: Vec<_> = PairwiseAuthShare::<V, A, B>::random_n_with(
            &mut rng,
            n_parties,
            (a.clone(), alphas.clone()),
        );
        let shares_b: Vec<_> =
            PairwiseAuthShare::<V, A, B>::random_n_with(&mut rng, n_parties, (b.clone(), alphas));
        let expected = a.clone() + &b;

        let sum: Vec<_> = izip_eq!(&shares_a, &shares_b)
            .map(|(sa, sb)| sa + sb)
            .collect();
        assert_eq!(
            PairwiseAuthShare::<V, A, B>::reconstruct_all(sum).unwrap(),
            expected
        );

        let sum: Vec<_> = izip_eq!(&shares_a, shares_b.clone())
            .map(|(sa, sb)| sa + sb)
            .collect();
        assert_eq!(
            PairwiseAuthShare::<V, A, B>::reconstruct_all(sum).unwrap(),
            expected
        );

        let sum: Vec<_> = izip_eq!(shares_a.clone(), &shares_b)
            .map(|(sa, sb)| sa + sb)
            .collect();
        assert_eq!(
            PairwiseAuthShare::<V, A, B>::reconstruct_all(sum).unwrap(),
            expected
        );

        let sum: Vec<_> = izip_eq!(shares_a.clone(), shares_b.clone())
            .map(|(sa, sb)| sa + sb)
            .collect();
        assert_eq!(
            PairwiseAuthShare::<V, A, B>::reconstruct_all(sum).unwrap(),
            expected
        );

        let mut shares_a_mut = shares_a.clone();
        izip_eq!(&mut shares_a_mut, &shares_b).for_each(|(sa, sb)| *sa += sb);
        assert_eq!(
            PairwiseAuthShare::<V, A, B>::reconstruct_all(shares_a_mut).unwrap(),
            expected
        );

        let mut shares_a_mut = shares_a;
        izip_eq!(&mut shares_a_mut, shares_b).for_each(|(sa, sb)| *sa += sb);
        assert_eq!(
            PairwiseAuthShare::<V, A, B>::reconstruct_all(shares_a_mut).unwrap(),
            expected
        );
    }

    pub(super) fn test_add_plaintext<V, A, B, Const>(n_parties: usize)
    where
        V: ShareValue<A, B, Const>,
        A: ShareKey,
        B: ShareMac<V, A, Const>,
        Const: Random,
    {
        let mut rng = test_rng();
        let a = V::random(&mut rng);
        let k = V::random(&mut rng);
        let shares_a: Vec<_> =
            PairwiseAuthShare::<V, A, B>::random_n_with(&mut rng, n_parties, a.clone());

        let shares_plus_k_ref: Vec<_> = shares_a
            .iter()
            .enumerate()
            .map(|(i, share_a)| share_a.to_owned().add_plaintext(&k, i == 0))
            .collect();
        assert_eq!(
            PairwiseAuthShare::<V, A, B>::reconstruct_all(shares_plus_k_ref).unwrap(),
            a.clone() + &k,
        );

        let shares_plus_k: Vec<_> = shares_a
            .into_iter()
            .enumerate()
            .map(|(i, share_a)| share_a.to_owned().add_plaintext(&k, i == 0))
            .collect();
        assert_eq!(
            PairwiseAuthShare::<V, A, B>::reconstruct_all(shares_plus_k).unwrap(),
            a + &k,
        );
    }

    pub(super) fn test_mul_constant<V, A, B, Const>(n_parties: usize)
    where
        V: ShareValue<A, B, Const>,
        A: ShareKey,
        B: ShareMac<V, A, Const>,
        Const: Random + PartialEq + Debug,
    {
        let mut rng = test_rng();
        let a = V::random(&mut rng);
        let k = Const::random(&mut rng);
        let shares_a: Vec<_> =
            PairwiseAuthShare::<V, A, B>::random_n_with(&mut rng, n_parties, a.clone());

        let shares_a_times_k: Vec<_> = izip_eq!(shares_a.clone()).map(|sa| sa * &k).collect();
        assert_eq!(
            PairwiseAuthShare::<V, A, B>::reconstruct_all(shares_a_times_k).unwrap(),
            a.clone() * &k,
        );

        let mut shares_a_mut = shares_a;
        izip_eq!(&mut shares_a_mut).for_each(|sa| *sa *= &k);
        assert_eq!(
            PairwiseAuthShare::<V, A, B>::reconstruct_all(shares_a_mut).unwrap(),
            a * &k,
        );
    }

    pub(super) fn test_sub<V, A, B, Const>(n_parties: usize)
    where
        V: ShareValue<A, B, Const>,
        A: ShareKey,
        B: ShareMac<V, A, Const>,
        Const: Random,
    {
        let mut rng = test_rng();
        let alphas: Vec<Vec<GlobalKey<A>>> = (0..n_parties)
            .map(|_| GlobalKey::<A>::random_n::<Vec<_>>(&mut rng, n_parties - 1))
            .collect();
        let a = V::random(&mut rng);
        let b = V::random(&mut rng);
        let shares_a: Vec<_> = PairwiseAuthShare::<V, A, B>::random_n_with(
            &mut rng,
            n_parties,
            (a.clone(), alphas.clone()),
        );
        let shares_b: Vec<_> =
            PairwiseAuthShare::<V, A, B>::random_n_with(&mut rng, n_parties, (b.clone(), alphas));
        let expected = a.clone() - &b;

        let diff: Vec<_> = izip_eq!(&shares_a, &shares_b)
            .map(|(sa, sb)| sa - sb)
            .collect();
        assert_eq!(
            PairwiseAuthShare::<V, A, B>::reconstruct_all(diff).unwrap(),
            expected
        );

        let diff: Vec<_> = izip_eq!(&shares_a, shares_b.clone())
            .map(|(sa, sb)| sa - sb)
            .collect();
        assert_eq!(
            PairwiseAuthShare::<V, A, B>::reconstruct_all(diff).unwrap(),
            expected
        );

        let diff: Vec<_> = izip_eq!(shares_a.clone(), &shares_b)
            .map(|(sa, sb)| sa - sb)
            .collect();
        assert_eq!(
            PairwiseAuthShare::<V, A, B>::reconstruct_all(diff).unwrap(),
            expected
        );

        let diff: Vec<_> = izip_eq!(shares_a.clone(), shares_b.clone())
            .map(|(sa, sb)| sa - sb)
            .collect();
        assert_eq!(
            PairwiseAuthShare::<V, A, B>::reconstruct_all(diff).unwrap(),
            expected
        );

        let mut shares_a_mut = shares_a.clone();
        izip_eq!(&mut shares_a_mut, &shares_b).for_each(|(sa, sb)| *sa -= sb);
        assert_eq!(
            PairwiseAuthShare::<V, A, B>::reconstruct_all(shares_a_mut).unwrap(),
            expected
        );

        let mut shares_a_mut = shares_a;
        izip_eq!(&mut shares_a_mut, shares_b).for_each(|(sa, sb)| *sa -= sb);
        assert_eq!(
            PairwiseAuthShare::<V, A, B>::reconstruct_all(shares_a_mut).unwrap(),
            expected
        );
    }

    pub(super) fn test_neg<V, A, B, Const>(n_parties: usize)
    where
        V: ShareValue<A, B, Const>,
        A: ShareKey,
        B: ShareMac<V, A, Const>,
        Const: Random,
    {
        let mut rng = test_rng();
        let a = V::random(&mut rng);
        let shares_a: Vec<_> =
            PairwiseAuthShare::<V, A, B>::random_n_with(&mut rng, n_parties, a.clone());

        let neg_ref: Vec<_> = shares_a.iter().map(|sa| -sa).collect();
        assert_eq!(
            PairwiseAuthShare::<V, A, B>::reconstruct_all(neg_ref).unwrap(),
            -a.clone(),
        );
        let neg: Vec<_> = shares_a.into_iter().map(|sa| -sa).collect();
        assert_eq!(
            PairwiseAuthShare::<V, A, B>::reconstruct_all(neg).unwrap(),
            -a,
        );
    }

    pub(super) fn test_conditional_select<V, A, B, Const>(n_parties: usize)
    where
        V: ShareValue<A, B, Const>,
        A: ShareKey,
        B: ShareMac<V, A, Const>,
        Const: Random,
    {
        let mut rng = test_rng();
        let shares_a = PairwiseAuthShare::<V, A, B>::random_with(&mut rng, n_parties);
        let shares_b = PairwiseAuthShare::<V, A, B>::random_with(&mut rng, n_parties);
        let selected = PairwiseAuthShare::<V, A, B>::conditional_select(
            &shares_a,
            &shares_b,
            Choice::from(0u8),
        );
        assert_eq!(selected, shares_a);
        let selected = PairwiseAuthShare::<V, A, B>::conditional_select(
            &shares_a,
            &shares_b,
            Choice::from(1u8),
        );
        assert_eq!(selected, shares_b);
    }

    pub(super) fn test_ct_eq<V, A, B, Const>(n_parties: usize)
    where
        V: ShareValue<A, B, Const>,
        A: ShareKey,
        B: ShareMac<V, A, Const>,
        Const: Random,
    {
        let mut rng = test_rng();
        let shares_a = PairwiseAuthShare::<V, A, B>::random_with(&mut rng, n_parties);
        let shares_b = PairwiseAuthShare::<V, A, B>::random_with(&mut rng, n_parties);
        assert!(Into::<bool>::into(shares_a.ct_eq(&shares_a.clone())));
        assert!(Into::<bool>::into(shares_b.ct_eq(&shares_b.clone())));
        assert!(!Into::<bool>::into(shares_a.ct_eq(&shares_b)));
        assert!(!Into::<bool>::into(shares_b.ct_eq(&shares_a)));
    }

    // ─── Generic Batched Test Functions ──────────────────────────────────────

    pub(super) fn test_split_halves<IV, A, IB, M, MDiv2>(n_parties: usize)
    where
        IV: BatchedShareItem<A, IB>,
        A: ShareKey,
        IB: BatchedShareMacItem<IV, A>,
        M: Positive + Div<U2, Output = MDiv2>,
        MDiv2: Positive + Mul<U2, Output = M>,
    {
        let mut rng = test_rng();
        let m_div2 = MDiv2::to_usize();
        let shares = BatchedShare::<IV, A, IB, M>::random_with(&mut rng, n_parties);
        let (shares1, shares2) = shares.clone().split_halves::<MDiv2>();

        assert_eq!(shares1.get_value().len(), m_div2);
        assert_eq!(shares2.get_value().len(), m_div2);
        assert_eq!(shares1.get_value().as_ref(), &shares.get_value()[..m_div2]);
        assert_eq!(shares2.get_value().as_ref(), &shares.get_value()[m_div2..]);

        izip_eq!(&shares1.macs, &shares2.macs, &shares.macs).for_each(|(mac1, mac2, mac)| {
            assert_eq!(mac1.as_ref(), &mac[..m_div2]);
            assert_eq!(mac2.as_ref(), &mac[m_div2..]);
        });
        izip_eq!(&shares1.keys, &shares2.keys, &shares.keys).for_each(|(key1, key2, key)| {
            assert_eq!(key1.alpha, key.alpha);
            assert_eq!(key2.alpha, key.alpha);
            assert_eq!(key1.beta.as_ref(), &key.beta[..m_div2]);
            assert_eq!(key2.beta.as_ref(), &key.beta[m_div2..]);
        });

        let merged = BatchedShare::<IV, A, IB, MDiv2>::merge_halves(shares1, shares2);
        assert_eq!(merged, shares);
    }

    pub(super) fn test_split_thirds<IV, A, IB, M, MDiv3>(n_parties: usize)
    where
        IV: BatchedShareItem<A, IB>,
        A: ShareKey,
        IB: BatchedShareMacItem<IV, A>,
        M: Positive,
        MDiv3: Positive + Mul<U3, Output = M>,
        M: Mul<U3, Output: Positive>,
    {
        let mut rng = test_rng();
        let m_div3 = MDiv3::to_usize();
        let shares = BatchedShare::<IV, A, IB, M>::random_with(&mut rng, n_parties);
        let (shares1, shares2, shares3) = shares.clone().split_thirds::<MDiv3>();

        assert_eq!(shares1.get_value().len(), m_div3);
        assert_eq!(shares2.get_value().len(), m_div3);
        assert_eq!(shares3.get_value().len(), m_div3);
        assert_eq!(shares1.get_value().as_ref(), &shares.get_value()[..m_div3]);
        assert_eq!(
            shares2.get_value().as_ref(),
            &shares.get_value()[m_div3..(2 * m_div3)]
        );
        assert_eq!(
            shares3.get_value().as_ref(),
            &shares.get_value()[(2 * m_div3)..]
        );

        izip_eq!(&shares1.macs, &shares2.macs, &shares3.macs, &shares.macs).for_each(
            |(mac1, mac2, mac3, mac)| {
                assert_eq!(mac1.as_ref(), &mac[..m_div3]);
                assert_eq!(mac2.as_ref(), &mac[m_div3..(2 * m_div3)]);
                assert_eq!(mac3.as_ref(), &mac[(2 * m_div3)..(3 * m_div3)]);
            },
        );
        izip_eq!(&shares1.keys, &shares2.keys, &shares3.keys, &shares.keys).for_each(
            |(key1, key2, key3, key)| {
                assert_eq!(key1.alpha, key.alpha);
                assert_eq!(key2.alpha, key.alpha);
                assert_eq!(key3.alpha, key.alpha);
                assert_eq!(key1.beta.as_ref(), &key.beta[..m_div3]);
                assert_eq!(key2.beta.as_ref(), &key.beta[m_div3..(2 * m_div3)]);
                assert_eq!(key3.beta.as_ref(), &key.beta[(2 * m_div3)..(3 * m_div3)]);
            },
        );

        let merged = BatchedShare::<IV, A, IB, MDiv3>::merge_thirds(shares1, shares2, shares3);
        assert_eq!(merged, shares);
    }

    pub(super) fn test_into_iter<IV, A, IB, M>(n_parties: usize)
    where
        IV: BatchedShareItem<A, IB>,
        A: ShareKey,
        IB: BatchedShareMacItem<IV, A>,
        M: Positive,
    {
        let mut rng = test_rng();
        let m = M::to_usize();
        let shares = BatchedShare::<IV, A, IB, M>::random_with(&mut rng, n_parties);
        let mut iter = shares.clone().into_iter();
        assert_eq!(iter.len(), m);
        for i in 0..m {
            assert_eq!(iter.len(), m - i);
            let share = iter.next().unwrap();
            assert_eq!(share.value, shares.get_value()[i]);
            for j in 0..n_parties - 1 {
                assert_eq!(share.macs[j], shares.macs[j][i]);
                assert_eq!(share.keys[j].alpha, shares.keys[j].alpha);
                assert_eq!(share.keys[j].beta, shares.keys[j].beta[i]);
            }
        }
    }

    pub(super) fn test_from_iterator<IV, A, IB, M>(n_parties: usize)
    where
        IV: BatchedShareItem<A, IB>,
        A: ShareKey,
        IB: BatchedShareMacItem<IV, A>,
        M: Positive,
    {
        let mut rng = test_rng();
        let shares = BatchedShare::<IV, A, IB, M>::random_with(&mut rng, n_parties);
        let collected: Vec<_> = shares.clone().into_iter().collect();
        let from_iterator: BatchedShare<IV, A, IB, M> = collected.into_iter().collect();
        assert_eq!(shares, from_iterator);
    }

    pub(super) fn test_from_iterator_unequal_sizes<IV, A, IB, M>(n_parties: usize)
    where
        IV: BatchedShareItem<A, IB>,
        A: ShareKey,
        IB: BatchedShareMacItem<IV, A>,
        M: Positive,
        BatchedShare<IV, A, IB, M>: RandomWith<usize>,
    {
        let mut rng = test_rng();
        let shares = BatchedShare::<IV, A, IB, M>::random_with(&mut rng, n_parties);
        let mut collected: Vec<_> = shares.into_iter().collect();
        collected.pop();
        let _: BatchedShare<IV, A, IB, M> = collected.into_iter().collect();
    }

    pub(super) fn test_chunks<IV, A, IB, M, CS>(n_parties: usize)
    where
        IV: BatchedShareItem<A, IB>,
        A: ShareKey,
        IB: BatchedShareMacItem<IV, A>,
        M: Positive + typenum::PartialDiv<CS>,
        CS: Positive,
        BatchedShare<IV, A, IB, M>: RandomWith<usize> + Clone + Debug,
    {
        let mut rng = test_rng();
        let m = M::to_usize();
        let chunk_size = CS::to_usize();
        let n_chunks = m / chunk_size;
        let shares = BatchedShare::<IV, A, IB, M>::random_with(&mut rng, n_parties);
        let mut chunks_iter = shares.chunks::<CS>();
        assert_eq!(chunks_iter.len(), n_chunks);
        for i in 0..n_chunks {
            assert_eq!(chunks_iter.len(), n_chunks - i);
            let chunk = chunks_iter.next().unwrap();
            assert_eq!(chunk.value.len(), chunk_size);
            for j in 0..chunk_size {
                assert_eq!(chunk.value[j], shares.get_value()[i * chunk_size + j]);
            }
            for (mac_chunk, macs) in izip_eq!(&chunk.macs, &shares.macs) {
                for j in 0..chunk_size {
                    assert_eq!(mac_chunk[j], macs[i * chunk_size + j]);
                }
            }
            for (key_chunk, keys) in izip_eq!(&chunk.keys, &shares.keys) {
                assert_eq!(key_chunk.alpha, keys.alpha);
                for j in 0..chunk_size {
                    assert_eq!(key_chunk.beta[j], keys.beta[i * chunk_size + j]);
                }
            }
        }
        assert!(chunks_iter.next().is_none());
    }

    // ─── Concrete Test Sub-modules ────────────────────────────────────────────

    mod field_share_tests {
        use crate::algebra::{
            elliptic_curve::{Curve25519Ristretto as C, ScalarAsExtension, ScalarField},
            field::SubfieldElement,
        };

        // ScalarShare<C> = PairwiseAuthShare<SubfieldElement<F>, FieldElement<F>, FieldElement<F>>
        // where F = ScalarField<C>.
        type V = SubfieldElement<ScalarField<C>>;
        type A = ScalarAsExtension<C>; // = FieldElement<ScalarField<C>>
        type B = ScalarAsExtension<C>;
        type Const = SubfieldElement<ScalarField<C>>;
        const N: usize = 3;

        #[test]
        fn test_open_to() {
            super::test_open_to::<V, A, B, Const>(N);
        }
        #[test]
        fn test_random() {
            super::test_random::<V, A, B, Const>(N);
        }
        #[test]
        fn test_random_vec_and_reconstruct() {
            super::test_random_vec_and_reconstruct::<V, A, B, Const>(N);
        }
        #[test]
        fn test_random_vec_with_global_key_and_reconstruct() {
            super::test_random_vec_with_global_key_and_reconstruct::<V, A, B, Const>(N);
        }
        #[test]
        fn test_verify_mac() {
            super::test_verify_mac::<V, A, B, Const>(N);
        }
        #[test]
        fn test_add() {
            super::test_add::<V, A, B, Const>(N);
        }
        #[test]
        fn test_add_plaintext() {
            super::test_add_plaintext::<V, A, B, Const>(N);
        }
        #[test]
        fn test_mul_constant() {
            super::test_mul_constant::<V, A, B, Const>(N);
        }
        #[test]
        fn test_sub() {
            super::test_sub::<V, A, B, Const>(N);
        }
        #[test]
        fn test_neg() {
            super::test_neg::<V, A, B, Const>(N);
        }
        #[test]
        fn test_conditional_select() {
            super::test_conditional_select::<V, A, B, Const>(N);
        }
        #[test]
        fn test_ct_eq() {
            super::test_ct_eq::<V, A, B, Const>(N);
        }
    }

    mod point_share_tests {
        use crate::algebra::{
            elliptic_curve::{Curve25519Ristretto as C, Point, ScalarAsExtension, ScalarField},
            field::SubfieldElement,
        };

        // PointShare<C> = PairwiseAuthShare<Point<C>, ScalarAsExtension<C>, Point<C>>
        type V = Point<C>;
        type A = ScalarAsExtension<C>;
        type B = Point<C>;
        type Const = SubfieldElement<ScalarField<C>>; // = Scalar<C>
        const N: usize = 3;

        #[test]
        fn test_open_to() {
            super::test_open_to::<V, A, B, Const>(N);
        }
        #[test]
        fn test_random() {
            super::test_random::<V, A, B, Const>(N);
        }
        #[test]
        fn test_random_vec_and_reconstruct() {
            super::test_random_vec_and_reconstruct::<V, A, B, Const>(N);
        }
        #[test]
        fn test_random_vec_with_global_key_and_reconstruct() {
            super::test_random_vec_with_global_key_and_reconstruct::<V, A, B, Const>(N);
        }
        #[test]
        fn test_verify_mac() {
            super::test_verify_mac::<V, A, B, Const>(N);
        }
        #[test]
        fn test_add() {
            super::test_add::<V, A, B, Const>(N);
        }
        #[test]
        fn test_add_plaintext() {
            super::test_add_plaintext::<V, A, B, Const>(N);
        }
        #[test]
        fn test_mul_constant() {
            super::test_mul_constant::<V, A, B, Const>(N);
        }
        #[test]
        fn test_sub() {
            super::test_sub::<V, A, B, Const>(N);
        }
        #[test]
        fn test_neg() {
            super::test_neg::<V, A, B, Const>(N);
        }
        #[test]
        fn test_conditional_select() {
            super::test_conditional_select::<V, A, B, Const>(N);
        }
        #[test]
        fn test_ct_eq() {
            super::test_ct_eq::<V, A, B, Const>(N);
        }
    }

    mod field_shares_tests {
        use std::ops::Div;

        use typenum::{U12, U2, U3, U4};

        use crate::{
            algebra::{
                elliptic_curve::{Curve25519Ristretto as C, ScalarAsExtension, ScalarField},
                field::SubfieldElement,
            },
            types::heap_array::{FieldElements, SubfieldElements},
        };

        // ScalarShares<C, M> = PairwiseAuthShare<SubfieldElements<F, M>, FieldElement<F>,
        // FieldElements<F, M>> where F = ScalarField<C>.
        type F = ScalarField<C>;
        type M = U12;
        type IV = SubfieldElement<F>;
        type A = ScalarAsExtension<C>; // = FieldElement<F>
        type IB = ScalarAsExtension<C>; // = FieldElement<F>
        type V = SubfieldElements<F, M>;
        type B = FieldElements<F, M>;
        type Const = V; // SubfieldElements — same as V
        const N: usize = 3;

        // ── General (pairwise) tests ─────────────────────────────────

        #[test]
        fn test_open_to() {
            super::test_open_to::<V, A, B, Const>(N);
        }
        #[test]
        fn test_random() {
            super::test_random::<V, A, B, Const>(N);
        }
        #[test]
        fn test_random_vec_and_reconstruct() {
            super::test_random_vec_and_reconstruct::<V, A, B, Const>(N);
        }
        #[test]
        fn test_random_vec_with_global_key_and_reconstruct() {
            super::test_random_vec_with_global_key_and_reconstruct::<V, A, B, Const>(N);
        }
        #[test]
        fn test_verify_mac() {
            super::test_verify_mac::<V, A, B, Const>(N);
        }
        #[test]
        fn test_add() {
            super::test_add::<V, A, B, Const>(N);
        }
        #[test]
        fn test_add_plaintext() {
            super::test_add_plaintext::<V, A, B, Const>(N);
        }
        #[test]
        fn test_mul_constant() {
            super::test_mul_constant::<V, A, B, Const>(N);
        }
        #[test]
        fn test_sub() {
            super::test_sub::<V, A, B, Const>(N);
        }
        #[test]
        fn test_neg() {
            super::test_neg::<V, A, B, Const>(N);
        }
        #[test]
        fn test_conditional_select() {
            super::test_conditional_select::<V, A, B, Const>(N);
        }
        #[test]
        fn test_ct_eq() {
            super::test_ct_eq::<V, A, B, Const>(N);
        }

        // ── Batched-specific tests ───────────────────────────────────

        type MDiv2 = <U12 as Div<U2>>::Output;
        type MDiv3 = <U12 as Div<U3>>::Output;

        #[test]
        fn test_split_halves() {
            super::test_split_halves::<IV, A, IB, M, MDiv2>(N);
        }
        #[test]
        fn test_split_thirds() {
            super::test_split_thirds::<IV, A, IB, M, MDiv3>(N);
        }
        #[test]
        fn test_into_iter() {
            super::test_into_iter::<IV, A, IB, M>(N);
        }
        #[test]
        fn test_from_iterator() {
            super::test_from_iterator::<IV, A, IB, M>(N);
        }
        #[test]
        #[should_panic]
        fn test_from_iterator_unequal_sizes() {
            super::test_from_iterator_unequal_sizes::<IV, A, IB, M>(N);
        }
        #[test]
        fn test_chunks() {
            super::test_chunks::<IV, A, IB, M, U4>(N);
        }
    }

    mod point_shares_tests {
        use std::ops::Div;

        use typenum::{U12, U2, U3, U4};

        use crate::{
            algebra::elliptic_curve::{Curve25519Ristretto as C, Point, ScalarAsExtension},
            types::heap_array::{CurvePoints, Scalars},
        };

        // PointShares<C, M> = PairwiseAuthShare<CurvePoints<C, M>, ScalarAsExtension<C>,
        // CurvePoints<C, M>>
        type M = U12;
        type IV = Point<C>;
        type A = ScalarAsExtension<C>;
        type IB = Point<C>;
        type V = CurvePoints<C, M>;
        type B = CurvePoints<C, M>;
        type Const = Scalars<C, M>;
        const N: usize = 3;

        // ── General (pairwise) tests ─────────────────────────────────

        #[test]
        fn test_open_to() {
            super::test_open_to::<V, A, B, Const>(N);
        }
        #[test]
        fn test_random() {
            super::test_random::<V, A, B, Const>(N);
        }
        #[test]
        fn test_random_vec_and_reconstruct() {
            super::test_random_vec_and_reconstruct::<V, A, B, Const>(N);
        }
        #[test]
        fn test_random_vec_with_global_key_and_reconstruct() {
            super::test_random_vec_with_global_key_and_reconstruct::<V, A, B, Const>(N);
        }
        #[test]
        fn test_verify_mac() {
            super::test_verify_mac::<V, A, B, Const>(N);
        }
        #[test]
        fn test_add() {
            super::test_add::<V, A, B, Const>(N);
        }
        #[test]
        fn test_add_plaintext() {
            super::test_add_plaintext::<V, A, B, Const>(N);
        }
        #[test]
        fn test_mul_constant() {
            super::test_mul_constant::<V, A, B, Const>(N);
        }
        #[test]
        fn test_sub() {
            super::test_sub::<V, A, B, Const>(N);
        }
        #[test]
        fn test_neg() {
            super::test_neg::<V, A, B, Const>(N);
        }
        #[test]
        fn test_conditional_select() {
            super::test_conditional_select::<V, A, B, Const>(N);
        }
        #[test]
        fn test_ct_eq() {
            super::test_ct_eq::<V, A, B, Const>(N);
        }

        // ── Batched-specific tests ───────────────────────────────────

        type MDiv2 = <U12 as Div<U2>>::Output;
        type MDiv3 = <U12 as Div<U3>>::Output;

        #[test]
        fn test_split_halves() {
            super::test_split_halves::<IV, A, IB, M, MDiv2>(N);
        }
        #[test]
        fn test_split_thirds() {
            super::test_split_thirds::<IV, A, IB, M, MDiv3>(N);
        }
        #[test]
        fn test_into_iter() {
            super::test_into_iter::<IV, A, IB, M>(N);
        }
        #[test]
        fn test_from_iterator() {
            super::test_from_iterator::<IV, A, IB, M>(N);
        }
        #[test]
        #[should_panic]
        fn test_from_iterator_unequal_sizes() {
            super::test_from_iterator_unequal_sizes::<IV, A, IB, M>(N);
        }
        #[test]
        fn test_chunks() {
            super::test_chunks::<IV, A, IB, M, U4>(N);
        }
    }
}