commonware_cryptography/

certificate.rs

//! Cryptographic primitives for generating and verifying certificates.
//!
//! This module provides the [`Verifier`] and [`Scheme`] traits and implementations for
//! producing signatures, validating them (individually or in batches), assembling certificates, and
//! verifying recovered certificates.
//!
//! # Pluggable Cryptography
//!
//! Certificates are generic over the signing scheme, allowing users to choose
//! the scheme best suited for their requirements:
//!
//! - [`ed25519`]: Attributable signatures with individual verification. HSM-friendly, no trusted
//!   setup required, and widely supported. Certificates contain individual signatures from each
//!   signer.
//!
//! - [`secp256r1`]: Attributable signatures with individual verification. HSM-friendly, no trusted
//!   setup required, and widely supported by hardware security modules. Unlike ed25519, does not
//!   benefit from batch verification. Certificates contain individual signatures from each signer.
#![cfg_attr(
    feature = "bls12381",
    doc = "
- [`bls12381_multisig`]: Attributable signatures with aggregated verification. Signatures
  can be aggregated into a single multi-signature for compact certificates while preserving
  attribution (signer indices are stored alongside the aggregated signature). Callers must verify
  a proof of possession for every BLS signing key before constructing the scheme.

- [`bls12381_threshold`]: Non-attributable threshold signatures. Produces succinct
  certificates that are constant-size regardless of committee size. Requires a trusted
  setup (distributed key generation) and cannot attribute signatures to individual signers.
"
)]
//! # Attributable Schemes and Fault Evidence
//!
//! Signing schemes differ in whether per-participant activities can be used as evidence of
//! either liveness or of committing a fault:
//!
//! - **Attributable Schemes**: Individual signatures can be presented to some third party as
//!   evidence of either liveness or of committing a fault. Certificates contain signer indices
//!   alongside individual signatures, enabling secure per-participant activity tracking and
//!   conflict detection.
//!
//! - **Non-Attributable Schemes**: Individual signatures cannot be presented to some third party
//!   as evidence because they can be forged after collecting a quorum of partial signatures.
//!   Authenticated peer connections allow this evidence to be used locally, but not by an external
//!   observer.
//!
//! The [`Scheme::is_attributable()`] associated function signals whether evidence can be safely
//! exposed to third parties.
//!
//! # Identity Keys vs Signing Keys
//!
//! A participant may supply both an identity key and a signing key. The identity key
//! is used for assigning a unique order to the participant set and authenticating connections
//! whereas the signing key is used for producing and verifying signatures/certificates.
//!
#![cfg_attr(
    feature = "bls12381",
    doc = "Some cryptographic schemes are only performant when used in batch verification (like
[`bls12381_multisig`]) and/or are refreshed frequently (like [`bls12381_threshold`])."
)]
//! Refer to [ed25519] for an example of a scheme that uses the same key for both purposes.

#[cfg(feature = "bls12381")]
pub use crate::bls12381::certificate::{
    multisig as bls12381_multisig, threshold as bls12381_threshold,
};
pub use crate::ed25519::certificate as ed25519;
#[commonware_macros::stability(ALPHA)]
pub use crate::secp256r1::certificate as secp256r1;
use crate::{Digest, PublicKey};
#[cfg(not(feature = "std"))]
use alloc::{collections::BTreeSet, sync::Arc, vec, vec::Vec};
use bytes::{BufMut, Bytes};
use commonware_codec::{
    Buf, Codec, CodecFixed, EncodeSize, Error as CodecError, FixedSize, MaxEncodeSize, Read,
    ReadExt, Write, types::lazy::Lazy, util::max_items_size,
};
use commonware_parallel::Strategy;
use commonware_utils::{Faults, Participant, Widen, bitmap::BitMap, iter::NonEmpty, ordered::Set};
use core::{fmt::Debug, hash::Hash};
use rand_chacha::ChaCha20Rng;
use rand_core::{CryptoRng, SeedableRng};
#[cfg(feature = "std")]
use std::{collections::BTreeSet, sync::Arc, vec::Vec};
use thiserror::Error;

/// The scheme's own place in the participant set.
#[derive(Clone, Copy, Debug, PartialEq, Eq)]
pub enum Membership {
    /// A participant that holds signing material at this index.
    Signer(Participant),
    /// A participant without signing material at this index.
    Member(Participant),
}

impl Membership {
    /// Returns the participant's index.
    pub const fn index(&self) -> Participant {
        match self {
            Self::Signer(index) | Self::Member(index) => *index,
        }
    }

    /// Returns the participant's index if it holds signing material.
    pub const fn signer(&self) -> Option<Participant> {
        match self {
            Self::Signer(index) => Some(*index),
            Self::Member(_) => None,
        }
    }
}

/// A participant's attestation for a certificate.
#[derive(Clone, Debug)]
pub struct Attestation<S: Scheme> {
    /// Index of the signer inside the participant set.
    pub signer: Participant,
    /// Scheme-specific signature or share produced for a given subject.
    pub signature: Lazy<S::Signature>,
}

impl<S: Scheme> PartialEq for Attestation<S> {
    fn eq(&self, other: &Self) -> bool {
        self.signer == other.signer && self.signature == other.signature
    }
}

impl<S: Scheme> Eq for Attestation<S> {}

impl<S: Scheme> Hash for Attestation<S> {
    fn hash<H: core::hash::Hasher>(&self, state: &mut H) {
        self.signer.hash(state);
        self.signature.hash(state);
    }
}

impl<S: Scheme> Write for Attestation<S> {
    fn write(&self, writer: &mut impl BufMut) {
        self.signer.write(writer);
        self.signature.write(writer);
    }
}

impl<S: Scheme> EncodeSize for Attestation<S> {
    fn encode_size(&self) -> usize {
        self.signer.encode_size() + self.signature.encode_size()
    }
}

impl<S: Scheme> MaxEncodeSize for Attestation<S> {
    const MAX_ENCODE_SIZE: usize = Participant::MAX_ENCODE_SIZE + S::Signature::SIZE;
}

impl<S: Scheme> Read for Attestation<S> {
    type Cfg = ();

    fn read_cfg(reader: &mut impl Buf, _: &()) -> Result<Self, CodecError> {
        let signer = Participant::read(reader)?;
        let signature = ReadExt::read(reader)?;

        Ok(Self { signer, signature })
    }
}

#[cfg(feature = "arbitrary")]
impl<S: Scheme> arbitrary::Arbitrary<'_> for Attestation<S>
where
    S::Signature: for<'a> arbitrary::Arbitrary<'a>,
{
    fn arbitrary(u: &mut arbitrary::Unstructured<'_>) -> arbitrary::Result<Self> {
        let signer = Participant::arbitrary(u)?;
        let signature = S::Signature::arbitrary(u)?;
        Ok(Self {
            signer,
            signature: signature.into(),
        })
    }
}

/// Result of batch-verifying attestations.
pub struct Verification<S: Scheme> {
    /// Contains the attestations accepted by the scheme.
    pub verified: Vec<Attestation<S>>,
    /// Identifies the participant indices rejected during batch verification.
    pub invalid: Vec<Participant>,
}

impl<S: Scheme> Verification<S> {
    /// Creates a new `Verification` result.
    pub const fn new(verified: Vec<Attestation<S>>, invalid: Vec<Participant>) -> Self {
        Self { verified, invalid }
    }
}

/// Errors returned while assembling attestations into a certificate.
#[derive(Debug, Error, PartialEq, Eq)]
pub enum AssemblyError {
    /// Structurally valid attestations do not meet the scheme's quorum.
    #[error("insufficient attestations: expected={0}, found={1}")]
    InsufficientAttestations(u32, u32),
    /// An attestation references an index outside the participant set.
    #[error("unknown signer: {0}")]
    UnknownSigner(Participant),
    /// More than one attestation references the same signer.
    #[error("duplicate signer: {0}")]
    DuplicateSigner(Participant),
    /// An attestation contains a malformed encoded signature.
    #[error("malformed signature from signer: {0}")]
    MalformedSignature(Participant),
    /// The scheme could not recover a certificate from structurally valid attestations.
    #[error("certificate recovery failed")]
    RecoveryFailed,
}

/// Trait for namespace types that can derive themselves from a base namespace.
///
/// This trait is implemented by namespace types to define how they are computed
/// from a base namespace string.
pub trait Namespace: Clone + Send + Sync {
    /// Derive a namespace from the given base.
    fn derive(namespace: &[u8]) -> Self;
}

impl Namespace for Vec<u8> {
    fn derive(namespace: &[u8]) -> Self {
        namespace.to_vec()
    }
}

/// Identifies the subject of a signature or certificate.
pub trait Subject: Clone + Debug + Send + Sync {
    /// Pre-computed namespace(s) for this subject type.
    type Namespace: Namespace;

    /// Get the namespace bytes for this subject instance.
    fn namespace<'a>(&self, derived: &'a Self::Namespace) -> &'a [u8];

    /// Get the message bytes for this subject instance.
    fn message(&self) -> Bytes;
}

/// Cryptographic surface for recovered certificate verification.
///
/// A `Verifier` verifies recovered certificates, but does not expose participant
/// metadata or signing operations.
pub trait Verifier: Clone + Debug + Send + Sync + 'static {
    /// Subject type for certificate verification.
    type Subject<'a, D: Digest>: Subject;

    /// Fault model used to compute certificate quorums.
    type Faults: Faults;

    /// Public key type for participant identity used to order and index the participant set.
    type PublicKey: PublicKey;

    /// Certificate assembled from a set of attestations.
    type Certificate: Clone + Debug + Eq + Hash + Send + Sync + Codec;

    /// Verifies a certificate that was recovered or received from the network.
    ///
    /// Acceptance authenticates a quorum for `subject` under the scheme's key setup, fault model,
    /// and cryptographic assumptions. It need not authenticate the individual attestations used
    /// to assemble the certificate.
    fn verify_certificate<R, D>(
        &self,
        rng: &mut R,
        subject: Self::Subject<'_, D>,
        certificate: &Self::Certificate,
        strategy: &impl Strategy,
    ) -> bool
    where
        R: CryptoRng,
        D: Digest;

    /// Verifies a non-empty stream of certificates, returning `false` at the first verification
    /// failure.
    fn verify_certificates<'a, R, D, I>(
        &self,
        rng: &mut R,
        certificates: NonEmpty<I>,
        strategy: &impl Strategy,
    ) -> bool
    where
        R: CryptoRng,
        D: Digest,
        I: Iterator<Item = (Self::Subject<'a, D>, &'a Self::Certificate)>,
    {
        for (subject, certificate) in certificates {
            if !self.verify_certificate(rng, subject, certificate, strategy) {
                return false;
            }
        }

        true
    }

    /// Batch-verifies certificates and returns a per-item result.
    ///
    /// For batchable schemes, attempts batch verification first and bisects
    /// on failure to efficiently identify invalid certificates. For
    /// non-batchable schemes, verifies each certificate individually.
    /// Empty input returns an empty result.
    fn verify_certificates_bisect<'a, R, D>(
        &self,
        rng: &mut R,
        certificates: &[(Self::Subject<'a, D>, &'a Self::Certificate)],
        strategy: &impl Strategy,
    ) -> Vec<bool>
    where
        R: CryptoRng,
        D: Digest,
        Self::Subject<'a, D>: Copy,
    {
        let len = certificates.len();
        let mut verified = vec![false; len];
        if len == 0 {
            return verified;
        }

        // Non-batchable schemes (e.g. secp256r1) gain nothing from bisection
        // since verify_certificates already checks one-by-one.
        if !Self::is_batchable() {
            for (i, (subject, certificate)) in certificates.iter().enumerate() {
                verified[i] = self.verify_certificate(rng, *subject, certificate, strategy);
            }
            return verified;
        }

        // Iterative bisection: try the full range first. If batch verification
        // passes, mark the entire range valid. If it fails, split in half and
        // retry each half. Singletons that fail remain false.
        //
        //       [0..8) fail
        //      /            \
        //   [0..4) pass   [4..8) fail
        //                /          \
        //            [4..6) pass  [6..8) fail
        //                        /        \
        //                    [6..7) pass  [7..8) fail
        let mut stack = vec![(0, len)];
        while let Some((start, end)) = stack.pop() {
            let (first, rest) = certificates[start..end]
                .split_first()
                .expect("bisection ranges are non-empty");
            let certificates = NonEmpty::new(*first, rest.iter().copied());
            if self.verify_certificates(rng, certificates, strategy) {
                verified[start..end].fill(true);
            } else if end - start > 1 {
                let mid = start + (end - start) / 2;
                stack.push((mid, end));
                stack.push((start, mid));
            }
        }

        verified
    }

    /// Returns whether this scheme benefits from batch verification.
    ///
    /// Schemes that benefit from batch verification should return `true`, allowing callers to
    /// optimize by deferring verification until multiple signatures are available.
    ///
    /// Schemes that don't benefit from batch verification (like [`secp256r1`]) should
    /// return `false`, indicating that eager per-signature verification is preferred.
    fn is_batchable() -> bool;

    /// Returns an upper bound on the encoded size of a certificate that decodes under
    /// [`Self::certificate_codec_config`] for a verifier over at most `participants` participants.
    fn max_certificate_size(participants: u32) -> usize;

    /// Encoding configuration for bounded-size certificate decoding used in network payloads.
    fn certificate_codec_config(&self) -> <Self::Certificate as Read>::Cfg;

    /// Encoding configuration that allows unbounded certificate decoding.
    ///
    /// Only use this when decoding data from trusted local storage, it must not be exposed to
    /// adversarial inputs or network payloads.
    fn certificate_codec_config_unbounded() -> <Self::Certificate as Read>::Cfg;
}

/// Cryptographic surface for multi-party certificate schemes.
///
/// A `Scheme` extends [`Verifier`] with the signing surface: it produces attestations, validates
/// them (individually or in batches), and assembles certificates. Implementations may override the
/// provided defaults to take advantage of scheme-specific batching strategies.
pub trait Scheme: Verifier {
    /// Signature emitted by individual participants.
    type Signature: Clone + Debug + Eq + Hash + Send + Sync + CodecFixed<Cfg = ()>;

    /// Returns the scheme's own [`Membership`] in [`Self::participants`], or `None` if it
    /// holds no participant identity.
    fn me(&self) -> Option<Membership>;

    /// Returns the ordered set of participant public identity keys managed by the scheme.
    fn participants(&self) -> &Set<Self::PublicKey>;

    /// Signs a subject, or returns `None` if the scheme cannot sign (a verifier or member
    /// instance).
    fn sign<D: Digest>(&self, subject: Self::Subject<'_, D>) -> Option<Attestation<Self>>;

    /// Verifies a single attestation against the participant material managed by the scheme.
    fn verify_attestation<R, D>(
        &self,
        rng: &mut R,
        subject: Self::Subject<'_, D>,
        attestation: &Attestation<Self>,
        strategy: &impl Strategy,
    ) -> bool
    where
        R: CryptoRng,
        D: Digest;

    /// Batch-verifies attestations and separates valid attestations from signer indices that failed
    /// verification. Empty input produces an empty result in both sets.
    ///
    /// Callers must not include duplicate attestations from the same signer: duplicates may
    /// produce incorrect results.
    fn verify_attestations<R, D, I>(
        &self,
        rng: &mut R,
        subject: Self::Subject<'_, D>,
        attestations: I,
        strategy: &impl Strategy,
    ) -> Verification<Self>
    where
        R: CryptoRng,
        D: Digest,
        I: IntoIterator<Item = Attestation<Self>>,
        I::IntoIter: Send,
    {
        let mut invalid = BTreeSet::new();

        let verified = attestations.into_iter().filter_map(|attestation| {
            if self.verify_attestation(&mut *rng, subject.clone(), &attestation, strategy) {
                Some(attestation)
            } else {
                invalid.insert(attestation.signer);
                None
            }
        });

        Verification::new(verified.collect(), invalid.into_iter().collect())
    }

    /// Attempts to construct an authenticated certificate from pending and verified attestations.
    ///
    /// `verified` must already be valid for this exact scheme configuration and `subject`.
    /// Signers must be unique across both inputs. Only pending attestations undergo fallback
    /// verification.
    ///
    /// `Ok` authenticates the certificate for `subject`, but does not guarantee that each pending
    /// attestation was individually verified. Callers requiring individual correctness should use
    /// [`Self::verify_attestations`] followed by [`Self::assemble`].
    ///
    /// On failure, `Err` contains the verification results for `pending`. Accepted attestations
    /// can be retained alongside `verified` for subsequent assembly, and may already form a quorum.
    fn optimistic_assemble<'a, R, D, I, J>(
        &self,
        rng: &mut R,
        subject: Self::Subject<'_, D>,
        pending: I,
        verified: J,
        strategy: &impl Strategy,
    ) -> Result<Self::Certificate, Verification<Self>>
    where
        R: CryptoRng,
        D: Digest,
        I: IntoIterator<Item = Attestation<Self>>,
        I::IntoIter: ExactSizeIterator + Send,
        J: IntoIterator<Item = &'a Attestation<Self>>,
        J::IntoIter: Send;

    /// Assembles a non-empty stream of attestations into a candidate certificate.
    ///
    /// Inputs may be unverified. `Ok` does not authenticate them or the resulting certificate.
    /// Callers using such inputs must call [`Verifier::verify_certificate`] for the intended subject.
    ///
    /// Insufficient input returns [`AssemblyError::InsufficientAttestations`].
    /// A signer-unique quorum already verified for one subject must assemble successfully into a
    /// certificate that verifies for that subject.
    fn assemble<I>(
        &self,
        attestations: NonEmpty<I>,
        strategy: &impl Strategy,
    ) -> Result<Self::Certificate, AssemblyError>
    where
        I: Iterator<Item = Attestation<Self>> + Send;

    /// Returns whether per-participant fault evidence can be safely exposed.
    ///
    /// Schemes where individual signatures can be safely reported as fault evidence should
    /// return `true`.
    fn is_attributable() -> bool;
}

/// Verifies pending attestations before assembling them with verified attestations.
///
/// Inputs must satisfy [`Scheme::optimistic_assemble`]'s requirements.
/// Rejected attestations return `Err` even if the remaining attestations could certify,
/// preserving fault evidence for the caller. Assembly failure also returns the pending results.
pub fn verify_then_assemble<'a, S, R, D, I, J>(
    scheme: &S,
    rng: &mut R,
    subject: S::Subject<'_, D>,
    pending: I,
    verified: J,
    strategy: &impl Strategy,
) -> Result<S::Certificate, Verification<S>>
where
    S: Scheme,
    R: CryptoRng,
    D: Digest,
    I: IntoIterator<Item = Attestation<S>>,
    I::IntoIter: Send,
    J: IntoIterator<Item = &'a Attestation<S>>,
    J::IntoIter: Send,
{
    // Empty input already has a known verification result. Preserve rejected signer
    // evidence for non-empty input even when the accepted attestations could certify.
    let result = NonEmpty::try_new(pending.into_iter()).map_or_else(
        || Verification::new(Vec::new(), Vec::new()),
        |pending| scheme.verify_attestations::<_, D, _>(rng, subject, pending, strategy),
    );
    if !result.invalid.is_empty() {
        return Err(result);
    }

    // A verified quorum needs no further authentication. Keep the pending results
    // available if assembly fails.
    let Some(attestations) = NonEmpty::try_new(
        result
            .verified
            .iter()
            .cloned()
            .chain(verified.into_iter().cloned()),
    ) else {
        return Err(result);
    };

    scheme.assemble(attestations, strategy).map_err(|_| result)
}

/// Authenticates a candidate certificate first, verifying pending attestations only on failure.
///
/// Implements [`Scheme::optimistic_assemble`]'s input and result contract. A quorum consisting
/// entirely of verified attestations is assembled without another certificate check.
pub fn optimistic_assemble<'a, S, R, D, I, J>(
    scheme: &S,
    rng: &mut R,
    subject: S::Subject<'_, D>,
    pending: I,
    verified: J,
    strategy: &impl Strategy,
) -> Result<S::Certificate, Verification<S>>
where
    S: Scheme,
    R: CryptoRng,
    D: Digest,
    I: IntoIterator<Item = Attestation<S>>,
    I::IntoIter: ExactSizeIterator + Send,
    J: IntoIterator<Item = &'a Attestation<S>>,
    J::IntoIter: Send,
{
    let pending = pending.into_iter();
    let verified = verified.into_iter();

    // A verified-only quorum needs no further authentication.
    if pending.len() == 0 {
        return verify_then_assemble::<_, _, D, _, _>(
            scheme, rng, subject, pending, verified, strategy,
        );
    }

    // Decode through the strategy before cloning so assembly and fallback reuse
    // the decoded values.
    let mut pending = strategy.map_collect_vec(pending, |attestation| {
        let _ = attestation.signature.get();
        attestation
    });
    let attestations = pending.iter().cloned().chain(verified.cloned());
    if let Some(attestations) = NonEmpty::try_new(attestations)
        && let Ok(certificate) = scheme.assemble(attestations, strategy)
        && scheme.verify_certificate::<_, D>(rng, subject.clone(), &certificate, strategy)
    {
        return Ok(certificate);
    }

    // A single pending attestation is the leaf of the fallback search.
    if pending.len() == 1 {
        return Err(scheme.verify_attestations::<_, D, _>(rng, subject, pending, strategy));
    }

    // Each half needs ordinary verification, including every signed component
    // of schemes with more than one signature per attestation. Independent RNGs
    // allow both halves to run concurrently without sharing the caller's RNG.
    let rest = pending.split_off(pending.len().div_ceil(2));
    let mut first_rng = ChaCha20Rng::from_rng(&mut *rng);
    let mut rest_rng = ChaCha20Rng::from_rng(rng);
    let first_subject = subject.clone();
    let (mut result, rest) = strategy.join(
        || scheme.verify_attestations::<_, D, _>(&mut first_rng, first_subject, pending, strategy),
        || scheme.verify_attestations::<_, D, _>(&mut rest_rng, subject, rest, strategy),
    );
    result.verified.extend(rest.verified);
    result.invalid.extend(rest.invalid);
    Err(result)
}

/// A scheme handle returned by a [`Provider`] for one scope.
///
/// Always usable as a [`Verifier`] for certificate verification. The full signing scheme is
/// recoverable with [`Scoped::into_scheme`] only when the scope was built with [`Scoped::scheme`].
/// A scope built with [`Scoped::verifier`] yields `None`.
#[derive(Clone, Debug)]
pub struct Scoped<S: Scheme> {
    scheme: Arc<S>,
    can_sign: bool,
}

impl<S: Scheme> Scoped<S> {
    /// Builds a verify-only scope.
    pub const fn verifier(scheme: Arc<S>) -> Self {
        Self {
            scheme,
            can_sign: false,
        }
    }

    /// Builds a full signing scope.
    pub const fn scheme(scheme: Arc<S>) -> Self {
        Self {
            scheme,
            can_sign: true,
        }
    }

    /// Returns the full signing scheme, or `None` for a verify-only scope.
    pub fn into_scheme(self) -> Option<Arc<S>> {
        self.can_sign.then_some(self.scheme)
    }
}

impl<S: Scheme> Verifier for Scoped<S> {
    type Subject<'a, D: Digest> = S::Subject<'a, D>;
    type Faults = S::Faults;
    type PublicKey = S::PublicKey;
    type Certificate = S::Certificate;

    fn verify_certificate<R, D>(
        &self,
        rng: &mut R,
        subject: Self::Subject<'_, D>,
        certificate: &Self::Certificate,
        strategy: &impl Strategy,
    ) -> bool
    where
        R: CryptoRng,
        D: Digest,
    {
        self.scheme
            .verify_certificate(rng, subject, certificate, strategy)
    }

    fn verify_certificates<'a, R, D, I>(
        &self,
        rng: &mut R,
        certificates: NonEmpty<I>,
        strategy: &impl Strategy,
    ) -> bool
    where
        R: CryptoRng,
        D: Digest,
        I: Iterator<Item = (Self::Subject<'a, D>, &'a Self::Certificate)>,
    {
        self.scheme.verify_certificates(rng, certificates, strategy)
    }

    fn is_batchable() -> bool {
        S::is_batchable()
    }

    fn max_certificate_size(participants: u32) -> usize {
        S::max_certificate_size(participants)
    }

    fn certificate_codec_config(&self) -> <Self::Certificate as Read>::Cfg {
        self.scheme.certificate_codec_config()
    }

    fn certificate_codec_config_unbounded() -> <Self::Certificate as Read>::Cfg {
        S::certificate_codec_config_unbounded()
    }
}

/// Supplies the signing scheme for a given scope.
///
/// This trait uses an associated `Scope` type, allowing implementations to work
/// with any scope representation (e.g., epoch numbers, block heights, etc.).
pub trait Provider: Clone + Send + Sync + 'static {
    /// The scope type used to look up schemes.
    type Scope: Clone + Send + Sync + 'static;
    /// The signing scheme to provide.
    type Scheme: Scheme;

    /// Return a [`Scoped`] for `scope` capable of verifying certificates produced under it.
    ///
    /// A scheme that can verify certificates from any scope without scope-specific state should
    /// return a verify-only [`Scoped`] (via [`Scoped::verifier`]) for every scope. A fixed group
    /// public key that survives committee rotation is one such case. A scheme that needs
    /// scope-specific verification state should return `None` once that state is unavailable.
    fn scoped(&self, scope: Self::Scope) -> Option<Scoped<Self::Scheme>>;

    /// Return the full signing scheme that corresponds to `scope`, if available.
    ///
    /// The default returns a scheme only when [`Provider::scoped`] yields a signing scope, so a
    /// verify-only scope produces `None`. Override this when the signing scheme is available even
    /// for scopes that [`Provider::scoped`] serves with a verify-only result.
    fn scheme(&self, scope: Self::Scope) -> Option<Arc<Self::Scheme>> {
        self.scoped(scope).and_then(Scoped::into_scheme)
    }
}

/// Bitmap wrapper that tracks which participants signed a certificate.
///
/// Internally, it stores bits in 1-byte chunks for compact encoding.
#[derive(Clone, Debug, PartialEq, Eq, Hash)]
pub struct Signers {
    bitmap: BitMap<1>,
}

impl Signers {
    /// Returns the largest encoded size of a signer bitmap over at most `participants`
    /// participants.
    pub(crate) fn max_encode_size(participants: u32) -> usize {
        BitMap::<1>::max_encode_size(u64::from(participants))
    }

    /// Builds [`Signers`] from an iterator of signer indices.
    ///
    /// Indices need not be sorted: some signing schemes aggregate commutatively, so ordering
    /// is left to the caller.
    pub fn new(
        participants: u32,
        signers: impl IntoIterator<Item = Participant>,
    ) -> Result<Self, AssemblyError> {
        let mut bitmap = BitMap::zeroes(u64::from(participants));
        for signer in signers.into_iter() {
            let index = u64::from(signer.get());
            if index >= bitmap.len() {
                return Err(AssemblyError::UnknownSigner(signer));
            }
            if bitmap.get(index) {
                return Err(AssemblyError::DuplicateSigner(signer));
            }
            bitmap.set(index, true);
        }

        Ok(Self { bitmap })
    }

    /// Requires at least `required` signers in an already validated set.
    pub(crate) fn require(self, required: u32) -> Result<Self, AssemblyError> {
        let found = u32::try_from(self.count()).expect("signer count exceeds u32::MAX");
        if found < required {
            return Err(AssemblyError::InsufficientAttestations(required, found));
        }

        Ok(self)
    }

    /// Returns the length of the bitmap (the size of the participant set).
    #[allow(clippy::len_without_is_empty)]
    pub const fn len(&self) -> usize {
        self.bitmap.len() as usize
    }

    /// Returns how many participants are marked as signers.
    pub fn count(&self) -> usize {
        self.bitmap.count_ones() as usize
    }

    /// Iterates over signer indices in ascending order.
    pub fn iter(&self) -> impl Iterator<Item = Participant> + '_ {
        self.bitmap
            .ones_iter()
            .map(|index| Participant::from_usize(index as usize))
    }
}

/// Returns an upper bound on the encoded size of a certificate with a signer bitmap over at most
/// `participants` participants and one `signature_size`-byte signature per signer.
pub(crate) fn max_individual_certificate_size(participants: u32, signature_size: usize) -> usize {
    Signers::max_encode_size(participants)
        + max_items_size(Widen::widen(participants), signature_size)
}

/// Builds [`Signers`] using the participant set as the valid signer-index range.
///
/// # Panics
///
/// Panics if the participant count exceeds `u32::MAX`.
impl<'a, P, I> TryFrom<(&'a Set<P>, I)> for Signers
where
    I: IntoIterator<Item = Participant>,
{
    type Error = AssemblyError;

    fn try_from((participants, signers): (&'a Set<P>, I)) -> Result<Self, Self::Error> {
        let total = u32::try_from(participants.len()).expect("participant count exceeds u32::MAX");
        Self::new(total, signers)
    }
}

impl Write for Signers {
    fn write(&self, writer: &mut impl BufMut) {
        self.bitmap.write(writer);
    }
}

impl EncodeSize for Signers {
    fn encode_size(&self) -> usize {
        self.bitmap.encode_size()
    }
}

impl Read for Signers {
    type Cfg = usize;

    fn read_cfg(reader: &mut impl Buf, max_participants: &usize) -> Result<Self, CodecError> {
        let bitmap = BitMap::read_cfg(reader, &(..=*max_participants as u64).into())?;
        // The participant count is treated as an upper bound for decoding flexibility, e.g. one
        // might use `Scheme::certificate_codec_config_unbounded` for decoding certificates from
        // local storage.
        //
        // Exact length validation **must** be enforced at verification time by the signing schemes
        // against the actual participant set size.
        Ok(Self { bitmap })
    }
}

#[cfg(feature = "arbitrary")]
impl arbitrary::Arbitrary<'_> for Signers {
    fn arbitrary(u: &mut arbitrary::Unstructured<'_>) -> arbitrary::Result<Self> {
        let participants = u.arbitrary_len::<u8>()? % 10;
        let signer_count = u.arbitrary_len::<u8>()?.min(participants);
        let signers = (0..u32::try_from(signer_count).expect("signer count exceeds u32::MAX"))
            .map(Participant::new)
            .collect::<Vec<_>>();
        Ok(Self::new(participants.try_into().unwrap(), signers)
            .expect("indices are unique and in range"))
    }
}

/// A scheme provider that always returns the same scheme regardless of scope.
#[derive(Clone, Debug)]
pub struct ConstantProvider<S: Scheme, Sc = ()> {
    scheme: Arc<S>,
    _scope: core::marker::PhantomData<Sc>,
}

impl<S: Scheme, Sc> ConstantProvider<S, Sc> {
    /// Creates a new provider that always returns the given scheme.
    pub fn new(scheme: S) -> Self {
        Self {
            scheme: Arc::new(scheme),
            _scope: core::marker::PhantomData,
        }
    }
}

impl<S: Scheme, Sc: Clone + Send + Sync + 'static> crate::certificate::Provider
    for ConstantProvider<S, Sc>
{
    type Scope = Sc;
    type Scheme = S;

    fn scoped(&self, _: Sc) -> Option<Scoped<S>> {
        Some(Scoped::scheme(self.scheme.clone()))
    }
}

#[cfg(feature = "mocks")]
pub mod mocks;

#[cfg(test)]
mod tests {
    use super::*;
    #[cfg(feature = "bls12381")]
    use crate::bls12381::{
        dkg::feldman_desmedt as dkg,
        primitives::{
            group::Private as BlsPrivate,
            ops::{compute_public, sign_proof_of_possession, verify_proof_of_possession},
            sharing::Mode,
            variant::{MinPk, MinSig, Variant},
        },
    };
    use crate::{
        Signer as _,
        ed25519::{PrivateKey, Signature},
        sha256::Digest as Sha256Digest,
    };
    use commonware_codec::{Decode, Encode, varint::MAX_U32_VARINT_SIZE};
    use commonware_math::algebra::Random;
    use commonware_parallel::Sequential;
    use commonware_utils::{
        N3f1, TryCollect, Widen, non_empty,
        ordered::{Quorum as _, Set},
        test_rng,
    };
    #[cfg(feature = "bls12381")]
    use commonware_utils::{NZU32, ordered::BiMap, sync::Mutex};
    #[cfg(feature = "bls12381")]
    use core::sync::atomic::{AtomicUsize, Ordering};
    use ed25519_fixture::{Scheme as Ed25519Scheme, TestSubject};

    #[test]
    fn test_max_individual_certificate_size() {
        // The bound covers every signature and never decreases as the committee grows.
        let mut previous = 0;
        for n in [0, 1, 7, 8, 9, 127, 128] {
            let signers = Signers::new(n, (0..n).map(Participant::new)).unwrap();
            let signatures = vec![[0u8; Signature::SIZE]; Widen::widen(n)];
            assert_eq!(Signers::max_encode_size(n), signers.encode().len());
            let size = max_individual_certificate_size(n, Signature::SIZE);
            assert_eq!(
                size,
                signers.encode().len() + MAX_U32_VARINT_SIZE + signatures.len() * Signature::SIZE
            );
            assert!(signers.encode().len() + signatures.encode().len() <= size);
            assert!(size >= previous);
            previous = size;
        }

        // Counts up to `u32::MAX` fit the signature length prefix.
        let n: usize = Widen::widen(u32::MAX);
        assert_eq!(
            max_individual_certificate_size(u32::MAX, Signature::SIZE),
            u64::SIZE + n.div_ceil(8) + MAX_U32_VARINT_SIZE + n * Signature::SIZE,
        );
    }

    #[test]
    fn test_new_signers() {
        let signers = Signers::new(6, [0, 3, 5].map(Participant::new)).unwrap();
        let collected: Vec<_> = signers.iter().collect();
        assert_eq!(
            collected,
            vec![0, 3, 5]
                .into_iter()
                .map(Participant::new)
                .collect::<Vec<_>>()
        );
        assert_eq!(signers.count(), 3);
    }

    #[test]
    fn test_new_out_of_bounds() {
        assert_eq!(
            Signers::new(4, [0, 4].map(Participant::new)),
            Err(AssemblyError::UnknownSigner(Participant::new(4)))
        );
    }

    #[test]
    fn test_new_duplicate() {
        assert_eq!(
            Signers::new(4, [0, 0, 1].map(Participant::new)),
            Err(AssemblyError::DuplicateSigner(Participant::new(0)))
        );
    }

    #[test]
    fn test_new_not_increasing() {
        assert!(Signers::new(4, [2, 1].map(Participant::new)).is_ok());
    }

    #[test]
    fn test_try_from_set_and_require() {
        let participants = Set::from_iter_dedup(0..4);
        let signers = Signers::try_from((&participants, [0, 2, 3].map(Participant::new)))
            .unwrap()
            .require(3)
            .unwrap();
        assert_eq!(signers.count(), 3);
        assert_eq!(
            Signers::try_from((&participants, [0, 2].map(Participant::new)))
                .unwrap()
                .require(3),
            Err(AssemblyError::InsufficientAttestations(3, 2))
        );
    }

    #[test]
    fn test_try_from_set_checks_signer_bounds() {
        let participants = Set::<u8>::default();
        let signer = Participant::new(0);
        assert_eq!(
            Signers::try_from((&participants, [signer])),
            Err(AssemblyError::UnknownSigner(signer))
        );
    }

    #[test]
    fn test_codec_round_trip() {
        let signers = Signers::new(9, [1, 6].map(Participant::new)).unwrap();
        let encoded = signers.encode();
        let decoded = Signers::decode_cfg(encoded, &9).unwrap();
        assert_eq!(decoded, signers);
    }

    #[test]
    fn test_decode_respects_participant_limit() {
        let signers = Signers::new(8, [0, 3, 7].map(Participant::new)).unwrap();
        let encoded = signers.encode();
        // More participants than expected should fail.
        assert!(Signers::decode_cfg(encoded.clone(), &2).is_err());
        // Exact participant bound succeeds.
        assert!(Signers::decode_cfg(encoded.clone(), &8).is_ok());
        // Less participants than expected succeeds (upper bound).
        assert!(Signers::decode_cfg(encoded, &10).is_ok());
    }

    mod ed25519_fixture {
        use crate::{certificate::Subject, impl_certificate_ed25519};
        use commonware_utils::N3f1;

        /// Test subject for certificate verification tests.
        #[derive(Copy, Clone, Debug)]
        pub struct TestSubject {
            pub message: &'static [u8],
        }

        impl Subject for TestSubject {
            type Namespace = Vec<u8>;

            fn namespace<'a>(&self, derived: &'a Self::Namespace) -> &'a [u8] {
                derived
            }

            fn message(&self) -> bytes::Bytes {
                bytes::Bytes::from_static(self.message)
            }
        }

        // Use the macro to generate the test scheme
        impl_certificate_ed25519!(TestSubject, Vec<u8>, N3f1);
    }

    const NAMESPACE: &[u8] = b"test-bisect";
    const MESSAGE: &[u8] = b"good message";
    const BAD_MESSAGE: &[u8] = b"bad message";

    fn make_certificate(
        schemes: &[Ed25519Scheme],
        message: &'static [u8],
    ) -> <Ed25519Scheme as Verifier>::Certificate {
        let attestations: Vec<_> = schemes
            .iter()
            .filter_map(|s| s.sign::<Sha256Digest>(TestSubject { message }))
            .collect();
        schemes[0]
            .assemble(non_empty![@attestations], &Sequential)
            .expect("assembly failed")
    }

    fn setup_ed25519(n: u32) -> (Vec<Ed25519Scheme>, Ed25519Scheme) {
        let mut rng = test_rng();
        let private_keys: Vec<_> = (0..n).map(|_| PrivateKey::random(&mut rng)).collect();
        let participants: Set<crate::ed25519::PublicKey> = private_keys
            .iter()
            .map(|sk| sk.public_key())
            .try_collect()
            .unwrap();
        let signers: Vec<_> = private_keys
            .into_iter()
            .map(|sk| Ed25519Scheme::signer(NAMESPACE, participants.clone(), sk).unwrap())
            .collect();
        let verifier = Ed25519Scheme::verifier(NAMESPACE, participants);
        (signers, verifier)
    }

    /// Signers report a signing membership, members report a non-signing one at their
    /// identity key's position, and an identity-less verifier reports none.
    #[test]
    fn membership_reports_index_and_signing() {
        let (signers, verifier) = setup_ed25519(4);
        let participants = verifier.participants().clone();
        let signer = signers[0].me().unwrap();
        let index = signer.index();
        let key = participants.key(index).unwrap().clone();

        let member = Ed25519Scheme::member(NAMESPACE, participants, &key).unwrap();
        assert_eq!(member.me(), Some(Membership::Member(index)));
        assert_eq!(member.me().unwrap().index(), index);
        assert_eq!(member.me().unwrap().signer(), None);

        assert_eq!(signer, Membership::Signer(index));
        assert_eq!(signer.signer(), Some(index));

        assert_eq!(verifier.me(), None);
    }

    #[test]
    fn test_bisect_empty() {
        let mut rng = test_rng();
        let (_, verifier) = setup_ed25519(4);
        let result =
            verifier.verify_certificates_bisect::<_, Sha256Digest>(&mut rng, &[], &Sequential);
        assert!(result.is_empty());
    }

    #[test]
    fn test_bisect_all_valid() {
        let mut rng = test_rng();
        let (schemes, verifier) = setup_ed25519(4);
        let cert = make_certificate(&schemes, MESSAGE);
        let good = TestSubject { message: MESSAGE };
        let pairs: Vec<_> = (0..5).map(|_| (good, &cert)).collect();
        let result =
            verifier.verify_certificates_bisect::<_, Sha256Digest>(&mut rng, &pairs, &Sequential);
        assert_eq!(result, vec![true; 5]);
    }

    #[test]
    fn test_bisect_mixed() {
        let mut rng = test_rng();
        let (schemes, verifier) = setup_ed25519(4);
        let cert = make_certificate(&schemes, MESSAGE);
        let good = TestSubject { message: MESSAGE };
        let bad = TestSubject {
            message: BAD_MESSAGE,
        };
        let pairs = vec![
            (good, &cert),
            (bad, &cert),
            (good, &cert),
            (bad, &cert),
            (good, &cert),
            (good, &cert),
            (bad, &cert),
            (bad, &cert),
        ];
        let expected = vec![true, false, true, false, true, true, false, false];
        let result =
            verifier.verify_certificates_bisect::<_, Sha256Digest>(&mut rng, &pairs, &Sequential);
        assert_eq!(result, expected);
    }

    #[test]
    fn test_bisect_all_invalid() {
        let mut rng = test_rng();
        let (schemes, verifier) = setup_ed25519(4);
        let cert = make_certificate(&schemes, MESSAGE);
        let bad = TestSubject {
            message: BAD_MESSAGE,
        };
        let pairs: Vec<_> = (0..4).map(|_| (bad, &cert)).collect();
        let result =
            verifier.verify_certificates_bisect::<_, Sha256Digest>(&mut rng, &pairs, &Sequential);
        assert_eq!(result, vec![false; 4]);
    }

    #[test]
    fn test_bisect_single_valid() {
        let mut rng = test_rng();
        let (schemes, verifier) = setup_ed25519(4);
        let cert = make_certificate(&schemes, MESSAGE);
        let pairs = vec![(TestSubject { message: MESSAGE }, &cert)];
        let result =
            verifier.verify_certificates_bisect::<_, Sha256Digest>(&mut rng, &pairs, &Sequential);
        assert_eq!(result, vec![true]);
    }

    #[test]
    fn test_bisect_single_invalid() {
        let mut rng = test_rng();
        let (schemes, verifier) = setup_ed25519(4);
        let cert = make_certificate(&schemes, MESSAGE);
        let pairs = vec![(
            TestSubject {
                message: BAD_MESSAGE,
            },
            &cert,
        )];
        let result =
            verifier.verify_certificates_bisect::<_, Sha256Digest>(&mut rng, &pairs, &Sequential);
        assert_eq!(result, vec![false]);
    }

    #[test]
    fn test_scoped_verifies_and_into_scheme() {
        let mut rng = test_rng();
        let (schemes, verifier) = setup_ed25519(4);
        let cert = make_certificate(&schemes, MESSAGE);
        let subject = TestSubject { message: MESSAGE };

        let as_verifier = Scoped::verifier(Arc::new(verifier));
        let as_scheme = Scoped::scheme(Arc::new(schemes[0].clone()));

        // Both scopes verify a valid certificate through the `Verifier` impl.
        assert!(as_verifier.verify_certificate::<_, Sha256Digest>(
            &mut rng,
            subject,
            &cert,
            &Sequential,
        ));
        assert!(as_scheme.verify_certificate::<_, Sha256Digest>(
            &mut rng,
            subject,
            &cert,
            &Sequential,
        ));
        let pairs = [(subject, &cert)];
        assert!(as_verifier.verify_certificates::<_, Sha256Digest, _>(
            &mut rng,
            non_empty![@pairs.iter().copied()],
            &Sequential,
        ));
        assert_eq!(
            <Scoped<Ed25519Scheme> as Verifier>::is_batchable(),
            <Ed25519Scheme as Verifier>::is_batchable(),
        );
        assert_eq!(
            as_verifier.certificate_codec_config(),
            schemes[0].certificate_codec_config(),
        );
        for participants in [0, 4, 128] {
            assert_eq!(
                <Scoped<Ed25519Scheme> as Verifier>::max_certificate_size(participants),
                <Ed25519Scheme as Verifier>::max_certificate_size(participants),
            );
        }
        let _ = <Scoped<Ed25519Scheme> as Verifier>::certificate_codec_config_unbounded();

        // A verify-only scope never yields its scheme; a full scope always does.
        assert!(as_verifier.into_scheme().is_none());
        assert!(as_scheme.into_scheme().is_some());

        let provider = ConstantProvider::<_, ()>::new(schemes[0].clone());
        assert!(provider.scoped(()).is_some());
        assert!(provider.scheme(()).is_some());
    }

    #[cfg(feature = "bls12381")]
    #[allow(dead_code)]
    mod threshold {
        use super::TestSubject;
        use crate::impl_certificate_bls12381_threshold;
        use commonware_utils::N3f1;

        impl_certificate_bls12381_threshold!(TestSubject, Vec<u8>, N3f1);
    }

    #[cfg(feature = "bls12381")]
    #[allow(dead_code)]
    mod multisig {
        use super::TestSubject;
        use crate::impl_certificate_bls12381_multisig;
        use commonware_utils::N3f1;

        impl_certificate_bls12381_multisig!(TestSubject, Vec<u8>, N3f1);
    }

    const SUBJECT: TestSubject = TestSubject {
        message: b"subject",
    };
    const OTHER_SUBJECT: TestSubject = TestSubject {
        message: b"other-subject",
    };

    #[cfg(feature = "bls12381")]
    const THRESHOLD_NAMESPACE: &[u8] =
        b"_COMMONWARE_CRYPTOGRAPHY_CERTIFICATE_THRESHOLD_OPTIMISTIC_ASSEMBLE";
    #[cfg(feature = "bls12381")]
    const MULTISIG_NAMESPACE: &[u8] =
        b"_COMMONWARE_CRYPTOGRAPHY_CERTIFICATE_MULTISIG_OPTIMISTIC_ASSEMBLE";
    #[cfg(feature = "bls12381")]
    const MULTISIG_POP_NAMESPACE: &[u8] =
        b"_COMMONWARE_CRYPTOGRAPHY_CERTIFICATE_MULTISIG_OPTIMISTIC_ASSEMBLE_POP";

    #[cfg(feature = "bls12381")]
    fn threshold_signers<V: Variant>(
        rng: &mut impl CryptoRng,
        n: u32,
    ) -> Vec<threshold::Scheme<crate::ed25519::PublicKey, V>> {
        let participants: Set<crate::ed25519::PublicKey> = (0..n)
            .map(|_| PrivateKey::random(&mut *rng).public_key())
            .try_collect()
            .unwrap();
        let (polynomial, shares) =
            dkg::deal_anonymous::<V, N3f1>(&mut *rng, Mode::NonZeroCounter, NZU32!(n));
        shares
            .into_iter()
            .map(|share| {
                threshold::Scheme::signer(
                    THRESHOLD_NAMESPACE,
                    participants.clone(),
                    polynomial.clone(),
                    share,
                )
                .unwrap()
            })
            .collect()
    }

    #[cfg(feature = "bls12381")]
    fn multisig_signers<V: Variant>(
        rng: &mut impl CryptoRng,
        n: u32,
    ) -> Vec<multisig::Scheme<crate::ed25519::PublicKey, V>> {
        let identity_keys: Vec<_> = (0..n).map(|_| PrivateKey::random(&mut *rng)).collect();
        let signing_keys: Vec<_> = (0..n).map(|_| BlsPrivate::random(&mut *rng)).collect();
        let signing_publics: Vec<_> = signing_keys.iter().map(compute_public::<V>).collect();

        for (private, public) in signing_keys.iter().zip(&signing_publics) {
            let proof = sign_proof_of_possession::<V>(private, MULTISIG_POP_NAMESPACE);
            verify_proof_of_possession::<V>(public, MULTISIG_POP_NAMESPACE, &proof)
                .expect("proof of possession must verify");
        }

        let participants: BiMap<_, _> = identity_keys
            .iter()
            .map(|key| key.public_key())
            .zip(signing_publics)
            .try_collect()
            .unwrap();
        signing_keys
            .into_iter()
            .map(|private| {
                multisig::Scheme::signer(MULTISIG_NAMESPACE, participants.clone(), private)
                    .expect("signer must be a participant")
            })
            .collect()
    }

    #[cfg(feature = "bls12381")]
    fn threshold_success<V: Variant>() {
        let mut rng = test_rng();
        let schemes = threshold_signers::<V>(&mut rng, 5);
        let quorum = N3f1::quorum(schemes.len()) as usize;
        let attestations: Vec<_> = schemes
            .iter()
            .take(quorum)
            .map(|scheme| scheme.sign::<Sha256Digest>(SUBJECT).unwrap())
            .collect();
        let expected = schemes[0]
            .assemble(non_empty![@attestations.clone()], &Sequential)
            .unwrap();
        let prior: Vec<_> = attestations[..1]
            .iter()
            .cloned()
            .map(Recording::outer)
            .collect();
        let calls = Arc::new(RecordingCalls::default());
        let verifier = Recording {
            inner: schemes[0].clone(),
            calls: Arc::clone(&calls),
        };

        let result = verifier.optimistic_assemble::<_, Sha256Digest, _, _>(
            &mut rng,
            SUBJECT,
            attestations[1..].iter().cloned().map(Recording::outer),
            &prior,
            &Sequential,
        );
        let certificate = result.ok().expect("valid quorum must certify");
        assert_eq!(certificate, expected);
        assert!(calls.attestations.lock().is_empty());
        assert!(schemes[0].verify_certificate::<_, Sha256Digest>(
            &mut rng,
            SUBJECT,
            &certificate,
            &Sequential,
        ));
        assert!(!schemes[0].verify_certificate::<_, Sha256Digest>(
            &mut rng,
            OTHER_SUBJECT,
            &certificate,
            &Sequential,
        ));

        // Threshold recovery uses the lowest quorum of signer indices.
        let unused_bad = schemes[quorum].sign::<Sha256Digest>(OTHER_SUBJECT).unwrap();
        let pending: Vec<_> = attestations
            .into_iter()
            .chain([unused_bad])
            .map(Recording::outer)
            .collect();
        let result = verifier.optimistic_assemble::<_, Sha256Digest, _, _>(
            &mut rng,
            SUBJECT,
            pending,
            std::iter::empty(),
            &Sequential,
        );
        assert_eq!(result.ok(), Some(expected));
        assert!(calls.attestations.lock().is_empty());
    }

    #[cfg(feature = "bls12381")]
    #[test]
    fn test_threshold_recovers_exact_certificate_with_verified_attestations() {
        threshold_success::<MinPk>();
        threshold_success::<MinSig>();
    }

    #[cfg(feature = "bls12381")]
    fn multisig_optimistic_assemble_uses_one_certificate_check<V: Variant>() {
        let mut rng = test_rng();
        let schemes = multisig_signers::<V>(&mut rng, 5);
        let quorum = N3f1::quorum(schemes.len()) as usize;
        let attestations: Vec<_> = schemes
            .iter()
            .take(quorum)
            .map(|scheme| scheme.sign::<Sha256Digest>(SUBJECT).unwrap())
            .collect();
        let prior: Vec<_> = attestations[..1]
            .iter()
            .cloned()
            .map(Recording::outer)
            .collect();
        let calls = Arc::new(RecordingCalls::default());
        let verifier = Recording {
            inner: schemes[0].clone(),
            calls: Arc::clone(&calls),
        };

        let certificate = verifier
            .optimistic_assemble::<_, Sha256Digest, _, _>(
                &mut rng,
                SUBJECT,
                attestations[1..].iter().cloned().map(Recording::outer),
                &prior,
                &Sequential,
            )
            .ok()
            .expect("valid mixed quorum must certify");

        assert_eq!(calls.certificates.load(Ordering::Relaxed), 1);
        assert!(calls.attestations.lock().is_empty());
        assert!(schemes[0].verify_certificate::<_, Sha256Digest>(
            &mut rng,
            SUBJECT,
            &certificate,
            &Sequential,
        ));
        assert!(!schemes[0].verify_certificate::<_, Sha256Digest>(
            &mut rng,
            OTHER_SUBJECT,
            &certificate,
            &Sequential,
        ));
    }

    #[cfg(feature = "bls12381")]
    #[test]
    fn test_multisig_optimistic_assemble_uses_one_certificate_check() {
        multisig_optimistic_assemble_uses_one_certificate_check::<MinPk>();
        multisig_optimistic_assemble_uses_one_certificate_check::<MinSig>();
    }

    #[test]
    fn test_optimistic_assemble_individual_inputs() {
        let mut rng = test_rng();
        let (schemes, verifier) = setup_ed25519(5);
        let empty = verifier.optimistic_assemble::<_, Sha256Digest, _, _>(
            &mut rng,
            SUBJECT,
            Vec::new(),
            std::iter::empty(),
            &Sequential,
        );
        let verification = empty.unwrap_err();
        assert!(verification.verified.is_empty());
        assert!(verification.invalid.is_empty());

        let pending: Vec<_> = schemes
            .iter()
            .map(|scheme| scheme.sign::<Sha256Digest>(SUBJECT).unwrap())
            .collect();
        let certificate = verifier
            .optimistic_assemble::<_, Sha256Digest, _, _>(
                &mut rng,
                SUBJECT,
                pending,
                std::iter::empty(),
                &Sequential,
            )
            .ok()
            .expect("valid quorum must certify");
        assert!(verifier.verify_certificate::<_, Sha256Digest>(
            &mut rng,
            SUBJECT,
            &certificate,
            &Sequential,
        ));

        let pending: Vec<_> = schemes
            .iter()
            .enumerate()
            .map(|(i, scheme)| {
                scheme
                    .sign::<Sha256Digest>(if i == 0 { OTHER_SUBJECT } else { SUBJECT })
                    .unwrap()
            })
            .collect();
        let signers: Vec<_> = pending.iter().map(|a| a.signer).collect();
        let result = verifier.optimistic_assemble::<_, Sha256Digest, _, _>(
            &mut rng,
            SUBJECT,
            pending,
            std::iter::empty(),
            &Sequential,
        );
        let verification = result.unwrap_err();
        assert_eq!(verification.invalid, vec![signers[0]]);
        assert_eq!(
            verification
                .verified
                .iter()
                .map(|a| a.signer)
                .collect::<Vec<_>>(),
            signers[1..]
        );
        let certificate = verifier
            .assemble(non_empty![@verification.verified], &Sequential)
            .unwrap();
        assert!(verifier.verify_certificate::<_, Sha256Digest>(
            &mut rng,
            SUBJECT,
            &certificate,
            &Sequential,
        ));
    }

    #[test]
    fn test_optimistic_assemble_individual_quorum() {
        let mut rng = test_rng();
        let (schemes, verifier) = setup_ed25519(5);
        let quorum = N3f1::quorum(schemes.len()) as usize;
        let attestations: Vec<_> = schemes
            .iter()
            .take(quorum)
            .map(|s| s.sign::<Sha256Digest>(SUBJECT).unwrap())
            .collect();

        // Both pending-only and verified-only inputs require quorum. On failure,
        // the result contains only pending attestations, never retained inputs.
        for count in [0, quorum - 1, quorum] {
            for pending in [0, count] {
                let result = verifier.optimistic_assemble::<_, Sha256Digest, _, _>(
                    &mut rng,
                    SUBJECT,
                    attestations[..pending].iter().cloned(),
                    &attestations[pending..count],
                    &Sequential,
                );
                assert_eq!(result.is_ok(), count == quorum);
                match result {
                    Ok(certificate) => assert!(verifier.verify_certificate::<_, Sha256Digest>(
                        &mut rng,
                        SUBJECT,
                        &certificate,
                        &Sequential,
                    )),
                    Err(verification) => {
                        assert_eq!(verification.verified, attestations[..pending]);
                        assert!(verification.invalid.is_empty());
                    }
                }
            }
        }
    }

    #[test]
    fn test_optimistic_assemble_empty_committee() {
        let mut rng = test_rng();
        let (_, verifier) = setup_ed25519(0);
        let (schemes, _) = setup_ed25519(1);
        let unknown = schemes[0].sign::<Sha256Digest>(SUBJECT).unwrap();
        for pending in [Vec::new(), vec![unknown]] {
            let expected: Vec<_> = pending.iter().map(|a| a.signer).collect();
            let result = verifier.optimistic_assemble::<_, Sha256Digest, _, _>(
                &mut rng,
                SUBJECT,
                pending,
                std::iter::empty(),
                &Sequential,
            );
            let verification = result.unwrap_err();
            assert!(verification.verified.is_empty());
            assert_eq!(verification.invalid, expected);
        }
    }

    #[cfg(feature = "bls12381")]
    #[derive(Debug, Default)]
    struct RecordingCalls {
        attestations: Mutex<Vec<Vec<Participant>>>,
        assemblies: AtomicUsize,
        certificates: AtomicUsize,
    }

    #[cfg(feature = "bls12381")]
    #[derive(Clone, Debug)]
    struct Recording<S> {
        inner: S,
        calls: Arc<RecordingCalls>,
    }

    #[cfg(feature = "bls12381")]
    impl<S: Scheme> Recording<S> {
        fn inner(attestation: Attestation<Self>) -> Attestation<S> {
            Attestation {
                signer: attestation.signer,
                signature: attestation.signature,
            }
        }

        fn outer(attestation: Attestation<S>) -> Attestation<Self> {
            Attestation {
                signer: attestation.signer,
                signature: attestation.signature,
            }
        }
    }

    #[cfg(feature = "bls12381")]
    impl<S: Scheme> Verifier for Recording<S> {
        type Subject<'a, D: Digest> = S::Subject<'a, D>;
        type Faults = S::Faults;
        type PublicKey = S::PublicKey;
        type Certificate = S::Certificate;

        fn verify_certificate<R, D>(
            &self,
            rng: &mut R,
            subject: Self::Subject<'_, D>,
            certificate: &Self::Certificate,
            strategy: &impl Strategy,
        ) -> bool
        where
            R: CryptoRng,
            D: Digest,
        {
            self.calls.certificates.fetch_add(1, Ordering::Relaxed);
            self.inner
                .verify_certificate(rng, subject, certificate, strategy)
        }

        fn is_batchable() -> bool {
            S::is_batchable()
        }

        fn max_certificate_size(participants: u32) -> usize {
            S::max_certificate_size(participants)
        }

        fn certificate_codec_config(&self) -> <Self::Certificate as Read>::Cfg {
            self.inner.certificate_codec_config()
        }

        fn certificate_codec_config_unbounded() -> <Self::Certificate as Read>::Cfg {
            S::certificate_codec_config_unbounded()
        }
    }

    #[cfg(feature = "bls12381")]
    impl<S: Scheme> Scheme for Recording<S> {
        type Signature = S::Signature;

        fn me(&self) -> Option<Membership> {
            self.inner.me()
        }

        fn participants(&self) -> &Set<Self::PublicKey> {
            self.inner.participants()
        }

        fn sign<D: Digest>(&self, subject: Self::Subject<'_, D>) -> Option<Attestation<Self>> {
            self.inner.sign(subject).map(Self::outer)
        }

        fn verify_attestation<R, D>(
            &self,
            rng: &mut R,
            subject: Self::Subject<'_, D>,
            attestation: &Attestation<Self>,
            strategy: &impl Strategy,
        ) -> bool
        where
            R: CryptoRng,
            D: Digest,
        {
            self.calls
                .attestations
                .lock()
                .push(vec![attestation.signer]);
            self.inner
                .verify_attestation(rng, subject, &Self::inner(attestation.clone()), strategy)
        }

        fn verify_attestations<R, D, I>(
            &self,
            rng: &mut R,
            subject: Self::Subject<'_, D>,
            attestations: I,
            strategy: &impl Strategy,
        ) -> Verification<Self>
        where
            R: CryptoRng,
            D: Digest,
            I: IntoIterator<Item = Attestation<Self>>,
            I::IntoIter: Send,
        {
            let attestations: Vec<_> = attestations.into_iter().collect();
            self.calls
                .attestations
                .lock()
                .push(attestations.iter().map(|a| a.signer).collect());
            let result = self.inner.verify_attestations(
                rng,
                subject,
                attestations.into_iter().map(Self::inner),
                strategy,
            );
            Verification::new(
                result.verified.into_iter().map(Self::outer).collect(),
                result.invalid,
            )
        }

        fn optimistic_assemble<'a, R, D, I, J>(
            &self,
            rng: &mut R,
            subject: Self::Subject<'_, D>,
            pending: I,
            verified: J,
            strategy: &impl Strategy,
        ) -> Result<Self::Certificate, Verification<Self>>
        where
            R: CryptoRng,
            D: Digest,
            I: IntoIterator<Item = Attestation<Self>>,
            I::IntoIter: ExactSizeIterator + Send,
            J: IntoIterator<Item = &'a Attestation<Self>>,
            J::IntoIter: Send,
        {
            crate::certificate::optimistic_assemble::<Self, _, D, _, _>(
                self, rng, subject, pending, verified, strategy,
            )
        }

        fn assemble<I>(
            &self,
            attestations: NonEmpty<I>,
            strategy: &impl Strategy,
        ) -> Result<Self::Certificate, AssemblyError>
        where
            I: Iterator<Item = Attestation<Self>> + Send,
        {
            self.calls.assemblies.fetch_add(1, Ordering::Relaxed);
            self.inner.assemble(
                non_empty![@attestations.into_iter().map(Self::inner)],
                strategy,
            )
        }

        fn is_attributable() -> bool {
            S::is_attributable()
        }
    }

    #[cfg(feature = "bls12381")]
    fn expected_halves(len: usize) -> Vec<Vec<Participant>> {
        let middle = len.div_ceil(2);
        let first = (0..middle).map(Participant::from_usize).collect();
        if middle == len {
            vec![first]
        } else {
            vec![first, (middle..len).map(Participant::from_usize).collect()]
        }
    }

    #[cfg(feature = "bls12381")]
    #[test]
    fn test_rejected_certificate_verifies_pending_halves_directly() {
        for n in [1, 5, 7] {
            let mut rng = test_rng();
            let schemes = threshold_signers::<MinPk>(&mut rng, n);
            let calls = Arc::new(RecordingCalls::default());
            let verifier = Recording {
                inner: schemes[0].clone(),
                calls: Arc::clone(&calls),
            };
            let quorum = N3f1::quorum(n) as usize;
            let pending: Vec<_> = schemes
                .iter()
                .take(quorum)
                .map(|s| Recording::outer(s.sign::<Sha256Digest>(OTHER_SUBJECT).unwrap()))
                .collect();
            let result = verifier.optimistic_assemble::<_, Sha256Digest, _, _>(
                &mut rng,
                SUBJECT,
                pending,
                std::iter::empty(),
                &Sequential,
            );
            let verification = result.unwrap_err();
            assert!(verification.verified.is_empty());
            assert_eq!(
                verification.invalid,
                (0..quorum).map(Participant::from_usize).collect::<Vec<_>>()
            );
            assert_eq!(*calls.attestations.lock(), expected_halves(quorum));
        }
    }

    #[cfg(feature = "bls12381")]
    #[test]
    fn test_malformed_assembly_falls_back_to_pending_halves() {
        let mut rng = test_rng();
        let schemes = threshold_signers::<MinPk>(&mut rng, 5);
        let quorum = N3f1::quorum(schemes.len()) as usize;
        for count in [quorum, schemes.len()] {
            let calls = Arc::new(RecordingCalls::default());
            let verifier = Recording {
                inner: schemes[0].clone(),
                calls: Arc::clone(&calls),
            };
            let mut pending: Vec<_> = schemes
                .iter()
                .take(count)
                .map(|s| Recording::outer(s.sign::<Sha256Digest>(SUBJECT).unwrap()))
                .collect();
            let mut malformed = Bytes::from_static(&[0]);
            pending[0].signature = Lazy::deferred(&mut malformed, ());
            let result = verifier.optimistic_assemble::<_, Sha256Digest, _, _>(
                &mut rng,
                SUBJECT,
                pending,
                std::iter::empty(),
                &Sequential,
            );
            let verification = result.unwrap_err();
            assert_eq!(verification.verified.len(), count - 1);
            assert_eq!(verification.invalid, vec![Participant::new(0)]);
            assert_eq!(*calls.attestations.lock(), expected_halves(count));
            if count > quorum {
                let certificate = verifier
                    .assemble(non_empty![@verification.verified], &Sequential)
                    .unwrap();
                assert!(verifier.verify_certificate::<_, Sha256Digest>(
                    &mut rng,
                    SUBJECT,
                    &certificate,
                    &Sequential,
                ));
            }
        }
    }

    #[cfg(feature = "bls12381")]
    #[test]
    fn test_optimistic_assemble_retains_verified_inputs() {
        let mut rng = test_rng();
        let schemes = threshold_signers::<MinPk>(&mut rng, 5);
        let mut prior: Vec<_> = schemes[..2]
            .iter()
            .map(|s| Recording::outer(s.sign::<Sha256Digest>(SUBJECT).unwrap()))
            .collect();
        let accepted = Recording::outer(schemes[2].sign::<Sha256Digest>(SUBJECT).unwrap());
        let rejected = Recording::outer(schemes[3].sign::<Sha256Digest>(OTHER_SUBJECT).unwrap());
        let invalid = rejected.signer;
        let calls = Arc::new(RecordingCalls::default());
        let verifier = Recording {
            inner: schemes[0].clone(),
            calls: Arc::clone(&calls),
        };
        let result = verifier.optimistic_assemble::<_, Sha256Digest, _, _>(
            &mut rng,
            SUBJECT,
            vec![accepted.clone(), rejected],
            &prior,
            &Sequential,
        );
        let verification = result.unwrap_err();
        assert_eq!(verification.verified, vec![accepted.clone()]);
        assert_eq!(verification.invalid, vec![invalid]);
        assert_eq!(
            *calls.attestations.lock(),
            vec![vec![accepted.signer], vec![invalid]]
        );

        prior.extend(verification.verified);
        calls.attestations.lock().clear();
        let replacement = Recording::outer(schemes[4].sign::<Sha256Digest>(SUBJECT).unwrap());
        let signer = replacement.signer;
        let verification = verifier.verify_attestations::<_, Sha256Digest, _>(
            &mut rng,
            SUBJECT,
            vec![replacement.clone()],
            &Sequential,
        );
        assert_eq!(verification.verified, vec![replacement]);
        assert!(verification.invalid.is_empty());
        assert_eq!(*calls.attestations.lock(), vec![vec![signer]]);
        prior.extend(verification.verified);
        let certificate = verifier.assemble(non_empty![@prior], &Sequential).unwrap();
        assert!(verifier.verify_certificate::<_, Sha256Digest>(
            &mut rng,
            SUBJECT,
            &certificate,
            &Sequential,
        ));
    }

    #[cfg(feature = "bls12381")]
    #[test]
    fn test_optimistic_assemble_with_verified_votes() {
        let mut rng = test_rng();
        let schemes = threshold_signers::<MinPk>(&mut rng, 5);
        let quorum = N3f1::quorum(schemes.len()) as usize;
        let attestations: Vec<_> = schemes[..quorum]
            .iter()
            .map(|scheme| scheme.sign::<Sha256Digest>(SUBJECT).unwrap())
            .collect();

        for pending_len in [0, 1, 2] {
            // Retained votes are authenticated for this configuration and subject.
            // The remaining votes cover empty, singleton, and evenly split inputs.
            let (prior, pending) = attestations.split_at(quorum - pending_len);
            let prior = schemes[0].verify_attestations::<_, Sha256Digest, _>(
                &mut rng,
                SUBJECT,
                prior.iter().cloned(),
                &Sequential,
            );
            assert!(prior.invalid.is_empty());
            let prior: Vec<_> = prior.verified.into_iter().map(Recording::outer).collect();
            let calls = Arc::new(RecordingCalls::default());
            let verifier = Recording {
                inner: schemes[0].clone(),
                calls: Arc::clone(&calls),
            };
            let certificate = verifier
                .optimistic_assemble::<_, Sha256Digest, _, _>(
                    &mut rng,
                    SUBJECT,
                    pending.iter().cloned().map(Recording::outer),
                    &prior,
                    &Sequential,
                )
                .ok()
                .expect("verified quorum must certify");

            // Pending votes require certificate authentication, even when most
            // inputs are already verified. A verified-only quorum needs assembly alone.
            assert_eq!(calls.assemblies.load(Ordering::Relaxed), 1);
            assert_eq!(
                calls.certificates.load(Ordering::Relaxed),
                usize::from(pending_len != 0)
            );
            assert!(calls.attestations.lock().is_empty());
            assert!(schemes[0].verify_certificate::<_, Sha256Digest>(
                &mut rng,
                SUBJECT,
                &certificate,
                &Sequential,
            ));
        }
    }

    #[cfg(feature = "bls12381")]
    #[test]
    fn test_optimistic_assemble_retries_with_replacements() {
        let mut rng = test_rng();
        let schemes = threshold_signers::<MinPk>(&mut rng, 10);
        let quorum = N3f1::quorum(schemes.len()) as usize;

        for failures in [1, 2] {
            let calls = Arc::new(RecordingCalls::default());
            let verifier = Recording {
                inner: schemes[0].clone(),
                calls: Arc::clone(&calls),
            };

            // Ten participants permit three faulty signers across these attempts.
            // A failed initial quorum retains the local vote and its valid peer votes.
            let own = schemes[0].verify_attestations::<_, Sha256Digest, _>(
                &mut rng,
                SUBJECT,
                [schemes[0].sign::<Sha256Digest>(SUBJECT).unwrap()],
                &Sequential,
            );
            assert!(own.invalid.is_empty());
            let mut prior: Vec<_> = own.verified.into_iter().map(Recording::outer).collect();
            let pending: Vec<_> = schemes[1..quorum]
                .iter()
                .enumerate()
                .map(|(index, scheme)| {
                    let subject = if index + 1 >= quorum - failures {
                        OTHER_SUBJECT
                    } else {
                        SUBJECT
                    };
                    Recording::outer(scheme.sign::<Sha256Digest>(subject).unwrap())
                })
                .collect();
            let result = verifier
                .optimistic_assemble::<_, Sha256Digest, _, _>(
                    &mut rng,
                    SUBJECT,
                    pending,
                    &prior,
                    &Sequential,
                )
                .unwrap_err();
            assert_eq!(result.invalid.len(), failures);
            prior.extend(result.verified);
            assert_eq!(prior.len(), quorum - failures);

            // A new faulty signer is mixed with any honest replacements. The
            // candidate fails authentication, so fallback identifies the bad vote.
            let pending: Vec<_> = schemes[quorum..quorum + failures]
                .iter()
                .enumerate()
                .map(|(index, scheme)| {
                    let subject = if index + 1 == failures {
                        OTHER_SUBJECT
                    } else {
                        SUBJECT
                    };
                    Recording::outer(scheme.sign::<Sha256Digest>(subject).unwrap())
                })
                .collect();
            let signers: Vec<_> = pending.iter().map(|vote| vote.signer).collect();
            let invalid = *signers.last().unwrap();
            calls.attestations.lock().clear();
            calls.assemblies.store(0, Ordering::Relaxed);
            calls.certificates.store(0, Ordering::Relaxed);
            let result = verifier
                .optimistic_assemble::<_, Sha256Digest, _, _>(
                    &mut rng,
                    SUBJECT,
                    pending,
                    &prior,
                    &Sequential,
                )
                .unwrap_err();
            assert_eq!(result.invalid, vec![invalid]);
            assert_eq!(result.verified.len(), failures - 1);
            assert_eq!(calls.assemblies.load(Ordering::Relaxed), 1);
            assert_eq!(calls.certificates.load(Ordering::Relaxed), 1);
            assert_eq!(
                *calls.attestations.lock(),
                signers
                    .into_iter()
                    .map(|signer| vec![signer])
                    .collect::<Vec<_>>()
            );
            prior.extend(result.verified);
            assert_eq!(prior.len(), quorum - 1);

            // The last honest replacement completes the same authenticated subject.
            let replacement = Recording::outer(
                schemes[quorum + failures]
                    .sign::<Sha256Digest>(SUBJECT)
                    .unwrap(),
            );
            calls.attestations.lock().clear();
            calls.assemblies.store(0, Ordering::Relaxed);
            calls.certificates.store(0, Ordering::Relaxed);
            let certificate = verifier
                .optimistic_assemble::<_, Sha256Digest, _, _>(
                    &mut rng,
                    SUBJECT,
                    [replacement],
                    &prior,
                    &Sequential,
                )
                .ok()
                .expect("valid replacement must certify");
            assert_eq!(calls.assemblies.load(Ordering::Relaxed), 1);
            assert_eq!(calls.certificates.load(Ordering::Relaxed), 1);
            assert!(calls.attestations.lock().is_empty());
            assert!(schemes[0].verify_certificate::<_, Sha256Digest>(
                &mut rng,
                SUBJECT,
                &certificate,
                &Sequential,
            ));
            assert!(!schemes[0].verify_certificate::<_, Sha256Digest>(
                &mut rng,
                OTHER_SUBJECT,
                &certificate,
                &Sequential,
            ));
        }
    }

    #[cfg(feature = "bls12381")]
    #[test]
    fn test_optimistic_assemble_below_quorum() {
        let mut rng = test_rng();
        let schemes = threshold_signers::<MinPk>(&mut rng, 5);
        let pending: Vec<_> = schemes[..2]
            .iter()
            .map(|s| Recording::outer(s.sign::<Sha256Digest>(SUBJECT).unwrap()))
            .collect();
        let expected = pending.clone();
        let calls = Arc::new(RecordingCalls::default());
        let verifier = Recording {
            inner: schemes[0].clone(),
            calls: Arc::clone(&calls),
        };
        let result = verifier.optimistic_assemble::<_, Sha256Digest, _, _>(
            &mut rng,
            SUBJECT,
            pending,
            std::iter::empty(),
            &Sequential,
        );
        let verification = result.unwrap_err();
        assert_eq!(verification.verified, expected);
        assert!(verification.invalid.is_empty());
        assert_eq!(*calls.attestations.lock(), expected_halves(expected.len()));
    }

    #[cfg(feature = "bls12381")]
    #[test]
    fn test_optimistic_assemble_unknown_pending_signer() {
        let mut rng = test_rng();
        let schemes = threshold_signers::<MinPk>(&mut rng, 5);
        let quorum = N3f1::quorum(schemes.len()) as usize;
        let mut pending: Vec<_> = schemes
            .iter()
            .take(quorum)
            .map(|s| Recording::outer(s.sign::<Sha256Digest>(SUBJECT).unwrap()))
            .collect();
        pending[0].signer = Participant::new(999);
        let calls = Arc::new(RecordingCalls::default());
        let verifier = Recording {
            inner: schemes[0].clone(),
            calls: Arc::clone(&calls),
        };
        let result = verifier.optimistic_assemble::<_, Sha256Digest, _, _>(
            &mut rng,
            SUBJECT,
            pending,
            std::iter::empty(),
            &Sequential,
        );
        let verification = result.unwrap_err();
        assert_eq!(verification.verified.len(), quorum - 1);
        assert_eq!(verification.invalid, vec![Participant::new(999)]);
        assert_eq!(
            *calls.attestations.lock(),
            vec![
                vec![Participant::new(999), Participant::new(1)],
                vec![Participant::new(2), Participant::new(3)],
            ]
        );
    }

    #[cfg(feature = "arbitrary")]
    mod conformance {
        use super::{ed25519_fixture::Scheme, *};
        use commonware_codec::conformance::CodecConformance;

        commonware_conformance::conformance_tests! {
            CodecConformance<Signers>,
            CodecConformance<Attestation<Scheme>>,
        }
    }
}