commonware_cryptography/ed25519/certificate/

mod.rs

//! Ed25519 signing scheme implementation.
//!
//! This module provides both the generic Ed25519 implementation and a macro to generate
//! protocol-specific wrappers.

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

use super::{PrivateKey, PublicKey, Signature as Ed25519Signature};
use crate::{
    BatchEntry, BatchVerifier as _, Signer as _, Verifier as _,
    certificate::{AssemblyError, Attestation, Namespace, Scheme, Signers, Subject, Verification},
};
#[cfg(not(feature = "std"))]
use alloc::{collections::BTreeSet, vec::Vec};
use bytes::{BufMut, Bytes};
use commonware_codec::{
    Buf, EncodeSize, Error, FixedSize, Read, ReadRangeExt, Write, types::lazy::Lazy,
};
use commonware_parallel::Strategy;
use commonware_utils::{
    Participant, Widen,
    iter::NonEmpty,
    ordered::{Quorum, Set},
};
use rand_core::CryptoRng;
#[cfg(feature = "std")]
use std::collections::BTreeSet;

/// Generic Ed25519 signing scheme implementation.
///
/// This struct contains the core cryptographic operations without protocol-specific
/// context types. It can be reused across different protocols (simplex, aggregation, etc.)
/// by wrapping it with protocol-specific trait implementations via the macro.
#[derive(Clone, Debug)]
pub struct Generic<N: Namespace> {
    /// Participants in the committee.
    pub participants: Set<PublicKey>,
    /// Key used for generating signatures.
    pub signer: Option<(Participant, PrivateKey)>,
    /// Pre-computed namespace(s) for this subject type.
    pub namespace: N,
}

impl<N: Namespace> Generic<N> {
    /// Creates a new generic Ed25519 scheme instance.
    pub fn signer(
        namespace: &[u8],
        participants: Set<PublicKey>,
        private_key: PrivateKey,
    ) -> Option<Self> {
        let signer = participants
            .index(&private_key.public_key())
            .map(|index| (index, private_key))?;

        Some(Self {
            participants,
            signer: Some(signer),
            namespace: N::derive(namespace),
        })
    }

    /// Builds a verifier that can authenticate signatures without generating them.
    pub fn verifier(namespace: &[u8], participants: Set<PublicKey>) -> Self {
        Self {
            participants,
            signer: None,
            namespace: N::derive(namespace),
        }
    }

    /// Returns the index this instance signs at, or `None` if it cannot sign.
    pub fn signer_index(&self) -> Option<Participant> {
        self.signer.as_ref().map(|(index, _)| *index)
    }

    /// Signs a subject and returns the signer index and signature.
    pub fn sign<S>(&self, subject: impl Subject<Namespace = N>) -> Option<Attestation<S>>
    where
        S: Scheme<Signature = Ed25519Signature>,
    {
        let (index, private_key) = self.signer.as_ref()?;

        let signature = private_key.sign(subject.namespace(&self.namespace), &subject.message());

        Some(Attestation {
            signer: *index,
            signature: signature.into(),
        })
    }

    /// Verifies a single attestation from a signer.
    pub fn verify_attestation<S>(
        &self,
        subject: impl Subject<Namespace = N>,
        attestation: &Attestation<S>,
    ) -> bool
    where
        S: Scheme<Signature = Ed25519Signature>,
    {
        let Some(public_key) = self.participants.key(attestation.signer) else {
            return false;
        };
        let Some(signature) = attestation.signature.get() else {
            return false;
        };

        public_key.verify(
            subject.namespace(&self.namespace),
            &subject.message(),
            signature,
        )
    }

    /// Batch-verifies attestations and returns verified attestations and invalid signers.
    pub fn verify_attestations<S, R, I>(
        &self,
        rng: &mut R,
        subject: impl Subject<Namespace = N>,
        attestations: I,
        strategy: &impl Strategy,
    ) -> Verification<S>
    where
        S: Scheme<Signature = Ed25519Signature>,
        R: CryptoRng,
        I: IntoIterator<Item = Attestation<S>>,
    {
        let namespace = subject.namespace(&self.namespace);
        let message = subject.message();

        let attestations = attestations.into_iter();
        let mut invalid = BTreeSet::new();
        let mut candidates = Vec::with_capacity(attestations.size_hint().0);

        for attestation in attestations {
            let Some(public_key) = self.participants.key(attestation.signer) else {
                invalid.insert(attestation.signer);
                continue;
            };
            if attestation.signature.get().is_none() {
                invalid.insert(attestation.signer);
                continue;
            }
            candidates.push((attestation, public_key));
        }

        if !candidates.is_empty()
            && !PublicKey::verify_batch(
                rng,
                &candidates,
                |_, (attestation, public_key)| BatchEntry {
                    namespace,
                    message: &message,
                    public_key,
                    signature: attestation.signature.get().expect("validated signature"),
                },
                strategy,
            )
        {
            // Batch failed: fall back to per-signer verification to isolate faulty attestations.
            for (attestation, public_key) in &candidates {
                let signature = attestation.signature.get().expect("validated signature");
                if !public_key.verify(namespace, &message, signature) {
                    invalid.insert(attestation.signer);
                }
            }
        }

        let verified = candidates
            .into_iter()
            .filter(|(attestation, _)| !invalid.contains(&attestation.signer))
            .map(|(attestation, _)| attestation)
            .collect();

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

    /// Assembles a certificate from a non-empty collection of attestations.
    pub fn assemble<S, I>(&self, attestations: NonEmpty<I>) -> Result<Certificate, AssemblyError>
    where
        S: Scheme<Signature = Ed25519Signature>,
        I: Iterator<Item = Attestation<S>>,
    {
        // Collect the signers and signatures.
        let mut entries = Vec::new();
        for Attestation { signer, signature } in attestations {
            self.participants
                .key(signer)
                .ok_or(AssemblyError::UnknownSigner(signer))?;
            let signature = signature
                .get()
                .cloned()
                .ok_or(AssemblyError::MalformedSignature(signer))?;
            entries.push((signer, signature));
        }

        // Sort the signatures by signer index.
        entries.sort_by_key(|(signer, _)| *signer);
        let (signer, signatures): (Vec<Participant>, Vec<_>) = entries.into_iter().unzip();
        let signers = Signers::try_from((&self.participants, signer))?
            .require(self.participants.quorum::<S::Faults>())?;
        let signatures = signatures.into_iter().map(Lazy::from).collect();

        Ok(Certificate {
            signers,
            signatures,
        })
    }

    /// Stages a certificate and returns the subject's namespace and message.
    ///
    /// Returns `None` if the certificate structure or a signature encoding is invalid.
    /// Earlier signatures may already have been staged.
    fn stage_certificate<'a, S: Scheme>(
        &'a self,
        subject: impl Subject<Namespace = N>,
        certificate: &'a Certificate,
        mut stage: impl FnMut(&'a PublicKey, &'a Ed25519Signature),
    ) -> Option<(&'a [u8], Bytes)> {
        if certificate.signers.len() != self.participants.len()
            || certificate.signers.count() != certificate.signatures.len()
            || certificate.signers.count() < Widen::widen(self.participants.quorum::<S::Faults>())
        {
            return None;
        }

        for (signer, signature) in certificate.signers.iter().zip(&certificate.signatures) {
            stage(self.participants.key(signer)?, signature.get()?);
        }

        Some((subject.namespace(&self.namespace), subject.message()))
    }

    /// Verifies a certificate using batch verification.
    pub fn verify_certificate<S, R>(
        &self,
        rng: &mut R,
        subject: impl Subject<Namespace = N>,
        certificate: &Certificate,
        strategy: &impl Strategy,
    ) -> bool
    where
        S: Scheme,
        R: CryptoRng,
    {
        let mut entries = Vec::with_capacity(certificate.signatures.len());
        let Some((namespace, message)) =
            self.stage_certificate::<S>(subject, certificate, |public_key, signature| {
                entries.push((public_key, signature));
            })
        else {
            return false;
        };

        PublicKey::verify_batch(
            rng,
            &entries,
            |_, (public_key, signature)| BatchEntry {
                namespace,
                message: &message,
                public_key,
                signature,
            },
            strategy,
        )
    }

    /// Verifies multiple certificates in a batch.
    pub fn verify_certificates<'a, S, R, T, I>(
        &self,
        rng: &mut R,
        certificates: NonEmpty<I>,
        strategy: &impl Strategy,
    ) -> bool
    where
        S: Scheme,
        T: Subject<Namespace = N>,
        R: CryptoRng,
        I: Iterator<Item = (T, &'a Certificate)>,
    {
        // Each certificate stages at most one signature per participant.
        let per_certificate = self.participants.len();
        let certificates = certificates.into_iter();
        let mut messages = Vec::with_capacity(certificates.size_hint().0);
        let mut entries =
            Vec::with_capacity(certificates.size_hint().0.saturating_mul(per_certificate));
        for (subject, certificate) in certificates {
            let index = messages.len();
            let Some(message) =
                self.stage_certificate::<S>(subject, certificate, |public_key, signature| {
                    entries.push((index, public_key, signature));
                })
            else {
                return false;
            };
            messages.push(message);
        }

        PublicKey::verify_batch(
            rng,
            &entries,
            |_, (index, public_key, signature)| BatchEntry {
                namespace: messages[*index].0,
                message: &messages[*index].1,
                public_key,
                signature,
            },
            strategy,
        )
    }

    pub const fn is_attributable() -> bool {
        true
    }

    pub const fn is_batchable() -> bool {
        true
    }

    /// Returns an upper bound on the encoded certificate size for at most `participants`
    /// participants.
    pub fn max_certificate_size(participants: u32) -> usize {
        crate::certificate::max_individual_certificate_size(participants, Ed25519Signature::SIZE)
    }

    pub const fn certificate_codec_config(&self) -> <Certificate as commonware_codec::Read>::Cfg {
        self.participants.len()
    }

    pub const fn certificate_codec_config_unbounded() -> <Certificate as commonware_codec::Read>::Cfg
    {
        u32::MAX as usize
    }
}

#[derive(Clone, Debug, PartialEq, Eq, Hash)]
pub struct Certificate {
    /// Bitmap of participant indices that contributed signatures.
    pub signers: Signers,
    /// Ed25519 signatures emitted by the respective participants ordered by signer index.
    pub signatures: Vec<Lazy<Ed25519Signature>>,
}

#[cfg(feature = "arbitrary")]
impl arbitrary::Arbitrary<'_> for Certificate {
    fn arbitrary(u: &mut arbitrary::Unstructured<'_>) -> arbitrary::Result<Self> {
        let signers = Signers::arbitrary(u)?;
        let signatures = (0..signers.count())
            .map(|_| u.arbitrary::<Ed25519Signature>().map(Lazy::from))
            .collect::<arbitrary::Result<Vec<_>>>()?;
        Ok(Self {
            signers,
            signatures,
        })
    }
}

impl Write for Certificate {
    fn write(&self, writer: &mut impl BufMut) {
        self.signers.write(writer);
        self.signatures.write(writer);
    }
}

impl EncodeSize for Certificate {
    fn encode_size(&self) -> usize {
        self.signers.encode_size() + self.signatures.encode_size()
    }
}

impl Read for Certificate {
    type Cfg = usize;

    fn read_cfg(reader: &mut impl Buf, participants: &usize) -> Result<Self, Error> {
        let signers = Signers::read_cfg(reader, participants)?;
        if signers.count() == 0 {
            return Err(Error::Invalid(
                "cryptography::ed25519::certificate::Certificate",
                "Certificate contains no signers",
            ));
        }

        let signatures = Vec::<Lazy<Ed25519Signature>>::read_range(reader, ..=*participants)?;
        if signers.count() != signatures.len() {
            return Err(Error::Invalid(
                "cryptography::ed25519::certificate::Certificate",
                "Signers and signatures counts differ",
            ));
        }

        Ok(Self {
            signers,
            signatures,
        })
    }
}

/// Generates an Ed25519 signing scheme wrapper for a specific protocol.
///
/// This macro creates a complete wrapper struct with constructors, `Scheme` trait
/// implementation, and a `fixture` function for testing.
///
/// # Parameters
///
/// - `$subject`: The subject type used as `Scheme::Subject<'a, D>`. Use `'a` and `D`
///   in the subject type to bind to the GAT lifetime and digest type parameters.
///
/// - `$namespace`: The namespace type that implements [`Namespace`].
///   This type pre-computes and stores any protocol-specific namespace bytes derived from
///   a base namespace. The scheme calls `$namespace::derive(base)` at construction time
///   to create the namespace, then passes it to `Subject::namespace()` during signing
///   and verification. For simple protocols with only a base namespace, `Vec<u8>` can be used directly.
///   For protocols with multiple message types, a custom struct can pre-compute all variants.
///
/// - `$faults`: The [`Faults`](commonware_utils::Faults) implementation used to compute certificate
///   quorums.
///
/// # Example
/// ```ignore
/// // For non-generic subject types with a single namespace:
/// impl_certificate_ed25519!(MySubject, Vec<u8>, commonware_utils::N3f1);
///
/// // For protocols with generic subject types:
/// impl_certificate_ed25519!(Subject<'a, D>, Namespace, commonware_utils::N3f1);
/// ```
#[macro_export]
macro_rules! impl_certificate_ed25519 {
    ($subject:ty, $namespace:ty, $faults:ty) => {
        /// Generates a test fixture with Ed25519 identities and signing schemes.
        ///
        /// Returns a [`commonware_cryptography::certificate::mocks::Fixture`] whose keys and
        /// scheme instances share a consistent ordering.
        #[cfg(feature = "mocks")]
        #[allow(dead_code)]
        pub fn fixture<R>(
            rng: &mut R,
            namespace: &[u8],
            n: u32,
        ) -> $crate::certificate::mocks::Fixture<Scheme>
        where
            R: rand_core::CryptoRng,
        {
            $crate::ed25519::certificate::mocks::fixture(
                rng,
                namespace,
                n,
                Scheme::signer,
                Scheme::verifier,
            )
        }

        /// Ed25519 signing scheme wrapper.
        #[derive(Clone, Debug)]
        pub struct Scheme {
            /// Verification state, plus the signing material of a signer.
            generic: $crate::ed25519::certificate::Generic<$namespace>,
            /// Index of the local identity key for an instance built with [`Self::member`].
            member: Option<commonware_utils::Participant>,
        }

        impl Scheme {
            /// Creates a new scheme instance with the provided key material.
            ///
            /// Participants use the same key for both identity and signing.
            ///
            /// If the provided private key does not match any signing key in the participant set,
            /// the instance will act as a verifier (unable to generate signatures).
            ///
            /// Returns `None` if the provided private key does not match any participant
            /// in the participant set.
            pub fn signer(
                namespace: &[u8],
                participants: commonware_utils::ordered::Set<$crate::ed25519::PublicKey>,
                private_key: $crate::ed25519::PrivateKey,
            ) -> Option<Self> {
                Some(Self {
                    generic: $crate::ed25519::certificate::Generic::signer(
                        namespace,
                        participants,
                        private_key,
                    )?,
                    member: None,
                })
            }

            /// Builds a verifier that can authenticate signatures without generating them.
            ///
            /// Participants use the same key for both identity and signing.
            ///
            /// A participant without signing material should use [`Self::member`] instead, so the
            /// scheme reports its membership.
            pub fn verifier(
                namespace: &[u8],
                participants: commonware_utils::ordered::Set<$crate::ed25519::PublicKey>,
            ) -> Self {
                Self {
                    generic: $crate::ed25519::certificate::Generic::verifier(
                        namespace,
                        participants,
                    ),
                    member: None,
                }
            }

            /// Builds a committee member that verifies like [`Self::verifier`] but also knows
            /// its own place in the participant set.
            ///
            /// The instance cannot sign, and [`Scheme::me`] returns [`Membership::Member`] at
            /// the position of `public_key` in the participant set. Returns `None` if
            /// `public_key` is not a participant.
            ///
            /// [`Scheme::me`]: commonware_cryptography::certificate::Scheme::me
            /// [`Membership::Member`]: commonware_cryptography::certificate::Membership::Member
            pub fn member(
                namespace: &[u8],
                participants: commonware_utils::ordered::Set<$crate::ed25519::PublicKey>,
                public_key: &$crate::ed25519::PublicKey,
            ) -> Option<Self> {
                let member = commonware_utils::ordered::Quorum::index(&participants, public_key)?;
                Some(Self {
                    generic: $crate::ed25519::certificate::Generic::verifier(
                        namespace,
                        participants,
                    ),
                    member: Some(member),
                })
            }
        }

        impl $crate::certificate::Verifier for Scheme {
            type Subject<'a, D: $crate::Digest> = $subject;
            type Faults = $faults;
            type PublicKey = $crate::ed25519::PublicKey;
            type Certificate = $crate::ed25519::certificate::Certificate;

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

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

            fn is_batchable() -> bool {
                $crate::ed25519::certificate::Generic::<$namespace>::is_batchable()
            }

            fn max_certificate_size(participants: u32) -> usize {
                $crate::ed25519::certificate::Generic::<$namespace>::max_certificate_size(participants)
            }

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

            fn certificate_codec_config_unbounded(
            ) -> <Self::Certificate as commonware_codec::Read>::Cfg {
                $crate::ed25519::certificate::Generic::<$namespace>::certificate_codec_config_unbounded()
            }
        }

        impl $crate::certificate::Scheme for Scheme {
            type Signature = $crate::ed25519::Signature;

            fn me(&self) -> Option<$crate::certificate::Membership> {
                self.generic
                    .signer_index()
                    .map($crate::certificate::Membership::Signer)
                    .or(self.member.map($crate::certificate::Membership::Member))
            }

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

            fn sign<D: $crate::Digest>(
                &self,
                subject: Self::Subject<'_, D>,
            ) -> Option<$crate::certificate::Attestation<Self>> {
                self.generic.sign(subject)
            }

            fn verify_attestation<R, D>(
                &self,
                _rng: &mut R,
                subject: Self::Subject<'_, D>,
                attestation: &$crate::certificate::Attestation<Self>,
                _strategy: &impl commonware_parallel::Strategy,
            ) -> bool
            where
                R: rand_core::CryptoRng,
                D: $crate::Digest,
            {
                self.generic
                    .verify_attestation(subject, attestation)
            }

            fn verify_attestations<R, D, I>(
                &self,
                rng: &mut R,
                subject: Self::Subject<'_, D>,
                attestations: I,
                strategy: &impl commonware_parallel::Strategy,
            ) -> $crate::certificate::Verification<Self>
            where
                R: rand_core::CryptoRng,
                D: $crate::Digest,
                I: IntoIterator<Item = $crate::certificate::Attestation<Self>>,
            {
                self.generic
                    .verify_attestations(rng, subject, attestations, strategy)
            }

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

            fn assemble<I>(
                &self,
                attestations: commonware_utils::iter::NonEmpty<I>,
                _strategy: &impl commonware_parallel::Strategy,
            ) -> Result<Self::Certificate, $crate::certificate::AssemblyError>
            where
                I: Iterator<Item = $crate::certificate::Attestation<Self>> + Send,
            {
                self.generic.assemble::<Self, _>(attestations)
            }

            fn is_attributable() -> bool {
                $crate::ed25519::certificate::Generic::<$namespace>::is_attributable()
            }
        }
    };
}

#[cfg(test)]
mod tests {
    use super::*;
    use crate::{
        certificate::{Membership, Scheme as _, Verifier as _},
        sha256::Digest as Sha256Digest,
    };
    use bytes::Bytes;
    use commonware_codec::{Decode, Encode, varint::MAX_U32_VARINT_SIZE};
    use commonware_math::algebra::Random;
    use commonware_parallel::{Rayon, Sequential};
    use commonware_utils::{
        Faults, N3f1, NZUsize, Participant, TestRng, TryCollect, non_empty, ordered::Set, test_rng,
    };
    use rand_core::Rng;

    const NAMESPACE: &[u8] = b"test-ed25519";
    const MESSAGE: &[u8] = b"test message";

    /// Test context type for generic scheme tests.
    #[derive(Clone, Debug)]
    pub struct TestSubject {
        pub message: Bytes,
    }

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

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

        fn message(&self) -> Bytes {
            self.message.clone()
        }
    }

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

    fn setup_signers(rng: &mut impl CryptoRng, n: u32) -> (Vec<Scheme>, Scheme) {
        let private_keys: Vec<_> = (0..n).map(|_| PrivateKey::random(&mut *rng)).collect();
        let participants: Set<PublicKey> = private_keys
            .iter()
            .map(|sk| sk.public_key())
            .try_collect()
            .unwrap();

        let signers = private_keys
            .into_iter()
            .map(|sk| Scheme::signer(NAMESPACE, participants.clone(), sk).unwrap())
            .collect();

        let verifier = Scheme::verifier(NAMESPACE, participants);

        (signers, verifier)
    }

    #[test]
    fn test_is_attributable() {
        assert!(Generic::<Vec<u8>>::is_attributable());
        assert!(Scheme::is_attributable());
    }

    #[test]
    fn test_is_batchable() {
        assert!(Generic::<Vec<u8>>::is_batchable());
        assert!(Scheme::is_batchable());
    }

    #[test]
    fn test_optimistic_assemble_reuses_verified_attestations() {
        let mut rng = test_rng();
        let (schemes, verifier) = setup_signers(&mut rng, 5);
        let quorum = N3f1::quorum(schemes.len()) as usize;
        let subject = TestSubject {
            message: Bytes::from_static(MESSAGE),
        };
        let attestations: Vec<_> = schemes
            .iter()
            .take(quorum)
            .map(|scheme| scheme.sign::<Sha256Digest>(subject.clone()).unwrap())
            .collect();

        // One seed per signature makes RNG consumption expose the size of the
        // verification batch, even when the single worker executes it serially.
        let strategy = Rayon::new(NZUsize!(1))
            .unwrap()
            .with_parallelism(NZUsize!(quorum));
        for pending_len in [quorum, 1, 0] {
            let (prior, pending) = attestations.split_at(quorum - pending_len);
            let verified = verifier.verify_attestations::<_, Sha256Digest, _>(
                &mut rng,
                subject.clone(),
                prior.iter().cloned(),
                &Sequential,
            );
            assert!(verified.invalid.is_empty());

            // Construction must do only the verification needed for fresh votes,
            // including when every vote was already authenticated.
            let mut expected_rng = TestRng::new(0);
            let expected = verifier.verify_attestations::<_, Sha256Digest, _>(
                &mut expected_rng,
                subject.clone(),
                pending.iter().cloned(),
                &strategy,
            );
            assert!(expected.invalid.is_empty());
            let mut actual_rng = TestRng::new(0);
            let certificate = verifier
                .optimistic_assemble::<_, Sha256Digest, _, _>(
                    &mut actual_rng,
                    subject.clone(),
                    pending.iter().cloned(),
                    &verified.verified,
                    &strategy,
                )
                .ok()
                .expect("verified quorum must certify");
            assert_eq!(
                actual_rng.next_u64(),
                expected_rng.next_u64(),
                "retained votes must not enter the verification batch"
            );
            assert!(verifier.verify_certificate::<_, Sha256Digest>(
                &mut rng,
                subject.clone(),
                &certificate,
                &Sequential,
            ));
        }
    }

    #[test]
    fn test_sign_vote_roundtrip() {
        let mut rng = test_rng();
        let (schemes, _) = setup_signers(&mut rng, 4);
        let scheme = &schemes[0];

        let attestation = scheme
            .sign::<Sha256Digest>(TestSubject {
                message: Bytes::from_static(MESSAGE),
            })
            .unwrap();
        assert!(scheme.verify_attestation::<_, Sha256Digest>(
            &mut rng,
            TestSubject {
                message: Bytes::from_static(MESSAGE),
            },
            &attestation,
            &Sequential,
        ));
    }

    #[test]
    fn test_verifier_cannot_sign() {
        let mut rng = test_rng();
        let (_, verifier) = setup_signers(&mut rng, 4);
        assert!(
            verifier
                .sign::<Sha256Digest>(TestSubject {
                    message: Bytes::from_static(MESSAGE)
                })
                .is_none()
        );
    }

    /// A member reports its membership, cannot sign, and verifies a quorum certificate, while a
    /// key outside the committee yields no member.
    #[test]
    fn test_member_reports_membership_without_signing() {
        let mut rng = test_rng();
        let (schemes, verifier) = setup_signers(&mut rng, 4);
        let participants = verifier.participants().clone();
        let subject = TestSubject {
            message: Bytes::from_static(MESSAGE),
        };

        // A key outside the committee yields no member.
        let outsider = PrivateKey::random(&mut rng).public_key();
        assert!(Scheme::member(NAMESPACE, participants.clone(), &outsider).is_none());

        // A member reports its membership but cannot sign. Verifiers report no membership, and
        // each signer reports the index it signs at.
        let index = Participant::new(2);
        let key = participants.key(index).unwrap().clone();
        let member = Scheme::member(NAMESPACE, participants, &key).unwrap();
        assert_eq!(member.me(), Some(Membership::Member(index)));
        assert_eq!(member.me().unwrap().signer(), None);
        assert!(member.sign::<Sha256Digest>(subject.clone()).is_none());
        assert_eq!(verifier.me(), None);
        for scheme in &schemes {
            let Some(Membership::Signer(signer)) = scheme.me() else {
                panic!("signer must report signing membership");
            };
            let attestation = scheme.sign::<Sha256Digest>(subject.clone()).unwrap();
            assert_eq!(attestation.signer, signer);
        }

        // A member verifies a certificate assembled by a quorum of signers.
        let attestations: Vec<_> = schemes
            .iter()
            .take(Widen::widen(N3f1::quorum(schemes.len())))
            .map(|s| s.sign::<Sha256Digest>(subject.clone()).unwrap())
            .collect();
        let certificate = schemes[0]
            .assemble(non_empty![@attestations], &Sequential)
            .unwrap();
        assert!(member.verify_certificate::<_, Sha256Digest>(
            &mut rng,
            subject,
            &certificate,
            &Sequential,
        ));
    }

    #[test]
    fn test_verify_attestations_filters_invalid() {
        let mut rng = test_rng();
        let (schemes, _) = setup_signers(&mut rng, 5);
        let quorum = N3f1::quorum(schemes.len()) as usize;

        let attestations: Vec<_> = schemes
            .iter()
            .take(quorum)
            .map(|s| {
                s.sign::<Sha256Digest>(TestSubject {
                    message: Bytes::from_static(MESSAGE),
                })
                .unwrap()
            })
            .collect();

        let result = schemes[0].verify_attestations::<_, Sha256Digest, _>(
            &mut rng,
            TestSubject {
                message: Bytes::from_static(MESSAGE),
            },
            attestations.clone(),
            &Sequential,
        );
        assert!(result.invalid.is_empty());
        assert_eq!(result.verified.len(), quorum);

        // An unknown signer index must invalidate only that attestation.
        let mut attestations_corrupted = attestations.clone();
        attestations_corrupted[0].signer = Participant::new(999);
        let result = schemes[0].verify_attestations::<_, Sha256Digest, _>(
            &mut rng,
            TestSubject {
                message: Bytes::from_static(MESSAGE),
            },
            attestations_corrupted,
            &Sequential,
        );
        assert_eq!(result.invalid, vec![Participant::new(999)]);
        assert_eq!(result.verified.len(), quorum - 1);

        // Copying another signer's signature must invalidate exactly one attestation.
        let mut attestations_corrupted = attestations;
        attestations_corrupted[0].signature = attestations_corrupted[1].signature.clone();
        let result = schemes[0].verify_attestations::<_, Sha256Digest, _>(
            &mut rng,
            TestSubject {
                message: Bytes::from_static(MESSAGE),
            },
            attestations_corrupted,
            &Sequential,
        );
        assert_eq!(result.invalid.len(), 1);
        assert_eq!(result.verified.len(), quorum - 1);

        // Malformed signature encodings and unknown signers cannot reach batch verification.
        let subject = TestSubject {
            message: Bytes::from_static(MESSAGE),
        };
        let mut malformed = schemes[0].sign::<Sha256Digest>(subject.clone()).unwrap();
        let mut truncated = Bytes::from_static(&[0u8; 3]);
        malformed.signature = Lazy::deferred(&mut truncated, ());
        let mut unknown = schemes[1].sign::<Sha256Digest>(subject.clone()).unwrap();
        unknown.signer = Participant::new(999);

        // If no attestations reach batch verification, the caller's RNG state must remain unchanged.
        for attestations in [Vec::new(), vec![malformed, unknown]] {
            let expected_invalid = attestations.len();
            let mut actual_rng = TestRng::new(0);
            let mut expected_rng = TestRng::new(0);
            let result = schemes[0].verify_attestations::<_, Sha256Digest, _>(
                &mut actual_rng,
                subject.clone(),
                attestations,
                &Sequential,
            );
            assert!(result.verified.is_empty());
            assert_eq!(result.invalid.len(), expected_invalid);
            assert_eq!(actual_rng.next_u64(), expected_rng.next_u64());
        }
    }

    #[test]
    fn test_assemble_certificate() {
        let mut rng = test_rng();
        let (schemes, _) = setup_signers(&mut rng, 4);
        let quorum = N3f1::quorum(schemes.len()) as usize;

        let attestations: Vec<_> = schemes
            .iter()
            .take(quorum)
            .map(|s| {
                s.sign::<Sha256Digest>(TestSubject {
                    message: Bytes::from_static(MESSAGE),
                })
                .unwrap()
            })
            .collect();

        let certificate = schemes[0]
            .assemble(non_empty![@attestations], &Sequential)
            .unwrap();

        // Verify certificate has correct number of signers
        assert_eq!(certificate.signers.count(), quorum);
        assert_eq!(certificate.signatures.len(), quorum);
    }

    #[test]
    fn test_assemble_certificate_sorts_signers() {
        let mut rng = test_rng();
        let (schemes, _) = setup_signers(&mut rng, 4);

        // Get indices and sort them to create attestations in guaranteed reverse order
        let mut indexed: Vec<_> = (0..3)
            .map(|i| (schemes[i].me().unwrap().index(), i))
            .collect();
        indexed.sort_by_key(|(idx, _)| *idx);

        // Create attestations in reverse sorted order (guaranteed non-sorted)
        let attestations = vec![
            schemes[indexed[2].1]
                .sign::<Sha256Digest>(TestSubject {
                    message: Bytes::from_static(MESSAGE),
                })
                .unwrap(),
            schemes[indexed[1].1]
                .sign::<Sha256Digest>(TestSubject {
                    message: Bytes::from_static(MESSAGE),
                })
                .unwrap(),
            schemes[indexed[0].1]
                .sign::<Sha256Digest>(TestSubject {
                    message: Bytes::from_static(MESSAGE),
                })
                .unwrap(),
        ];

        let certificate = schemes[0]
            .assemble(non_empty![@attestations], &Sequential)
            .unwrap();

        // Verify signers are sorted by signer index
        let expected: Vec<_> = indexed.iter().map(|(idx, _)| *idx).collect();
        assert_eq!(certificate.signers.iter().collect::<Vec<_>>(), expected);
    }

    #[test]
    fn test_verify_certificate() {
        let mut rng = test_rng();
        let (schemes, verifier) = setup_signers(&mut rng, 4);
        let quorum = N3f1::quorum(schemes.len()) as usize;

        let attestations: Vec<_> = schemes
            .iter()
            .take(quorum)
            .map(|s| {
                s.sign::<Sha256Digest>(TestSubject {
                    message: Bytes::from_static(MESSAGE),
                })
                .unwrap()
            })
            .collect();

        let certificate = schemes[0]
            .assemble(non_empty![@attestations], &Sequential)
            .unwrap();

        assert!(verifier.verify_certificate::<_, Sha256Digest>(
            &mut rng,
            TestSubject {
                message: Bytes::from_static(MESSAGE)
            },
            &certificate,
            &Sequential,
        ));
    }

    #[test]
    fn test_verify_certificate_detects_corruption() {
        let mut rng = test_rng();
        let (schemes, verifier) = setup_signers(&mut rng, 4);
        let quorum = N3f1::quorum(schemes.len()) as usize;

        let attestations: Vec<_> = schemes
            .iter()
            .take(quorum)
            .map(|s| {
                s.sign::<Sha256Digest>(TestSubject {
                    message: Bytes::from_static(MESSAGE),
                })
                .unwrap()
            })
            .collect();

        let certificate = schemes[0]
            .assemble(non_empty![@attestations], &Sequential)
            .unwrap();

        // Valid certificate passes
        assert!(verifier.verify_certificate::<_, Sha256Digest>(
            &mut rng,
            TestSubject {
                message: Bytes::from_static(MESSAGE),
            },
            &certificate,
            &Sequential,
        ));

        // Corrupted certificate fails
        let mut corrupted = certificate;
        corrupted.signatures[0] = corrupted.signatures[1].clone();
        assert!(!verifier.verify_certificate::<_, Sha256Digest>(
            &mut rng,
            TestSubject {
                message: Bytes::from_static(MESSAGE),
            },
            &corrupted,
            &Sequential,
        ));
    }

    #[test]
    fn test_certificate_codec_roundtrip() {
        let mut rng = test_rng();
        let (schemes, _) = setup_signers(&mut rng, 4);
        let quorum = N3f1::quorum(schemes.len()) as usize;

        let attestations: Vec<_> = schemes
            .iter()
            .take(quorum)
            .map(|s| {
                s.sign::<Sha256Digest>(TestSubject {
                    message: Bytes::from_static(MESSAGE),
                })
                .unwrap()
            })
            .collect();

        let certificate = schemes[0]
            .assemble(non_empty![@attestations], &Sequential)
            .unwrap();
        let encoded = certificate.encode();
        assert!(
            encoded.len() <= Scheme::max_certificate_size(u32::try_from(schemes.len()).unwrap())
        );
        let decoded = Certificate::decode_cfg(encoded, &schemes.len()).expect("decode certificate");
        assert_eq!(decoded, certificate);
    }

    #[test]
    fn test_max_certificate_size() {
        // The bound reserves the signature-list prefix at its type's maximum width.
        let mut rng = test_rng();
        let (schemes, _) = setup_signers(&mut rng, 128);
        let attestations = schemes.iter().map(|s| {
            s.sign::<Sha256Digest>(TestSubject {
                message: Bytes::from_static(MESSAGE),
            })
            .unwrap()
        });
        let certificate = schemes[0]
            .assemble(non_empty![@attestations], &Sequential)
            .unwrap();
        let prefix_slack = MAX_U32_VARINT_SIZE - schemes.len().encode_size();
        assert_eq!(
            certificate.encode().len() + prefix_slack,
            Scheme::max_certificate_size(u32::try_from(schemes.len()).unwrap())
        );
    }

    #[test]
    fn test_certificate_rejects_sub_quorum() {
        let mut rng = test_rng();
        let (schemes, _) = setup_signers(&mut rng, 4);
        let expected = N3f1::quorum(schemes.len());
        let found = expected - 1;
        let found_count = usize::try_from(found).expect("quorum exceeds usize::MAX");

        let attestations: Vec<_> = schemes
            .iter()
            .take(found_count)
            .map(|s| {
                s.sign::<Sha256Digest>(TestSubject {
                    message: Bytes::from_static(MESSAGE),
                })
                .unwrap()
            })
            .collect();

        assert_eq!(
            schemes[0].assemble(non_empty![@attestations], &Sequential),
            Err(AssemblyError::InsufficientAttestations(expected, found))
        );
    }

    #[test]
    fn test_certificate_rejects_invalid_signer() {
        let mut rng = test_rng();
        let (schemes, _) = setup_signers(&mut rng, 4);
        let quorum =
            usize::try_from(N3f1::quorum(schemes.len())).expect("quorum exceeds usize::MAX");

        let mut attestations: Vec<_> = schemes
            .iter()
            .take(quorum)
            .map(|s| {
                s.sign::<Sha256Digest>(TestSubject {
                    message: Bytes::from_static(MESSAGE),
                })
                .unwrap()
            })
            .collect();

        // Corrupt signer index to be out of range
        let unknown = Participant::new(999);
        attestations[0].signer = unknown;

        assert_eq!(
            schemes[0].assemble(non_empty![@attestations], &Sequential),
            Err(AssemblyError::UnknownSigner(unknown))
        );
    }

    #[test]
    fn test_certificate_rejects_malformed_signature() {
        // Build a valid quorum certificate to isolate malformed-signature rejection.
        let mut rng = test_rng();
        let (schemes, verifier) = setup_signers(&mut rng, 4);
        let quorum =
            usize::try_from(N3f1::quorum(schemes.len())).expect("quorum exceeds usize::MAX");

        let mut attestations: Vec<_> = schemes
            .iter()
            .take(quorum)
            .map(|s| {
                s.sign::<Sha256Digest>(TestSubject {
                    message: Bytes::from_static(MESSAGE),
                })
                .unwrap()
            })
            .collect();

        let valid = schemes[0]
            .assemble(non_empty![@attestations.clone()], &Sequential)
            .unwrap();

        // Assembly must identify the signer whose attestation cannot be decoded.
        let signer = attestations[0].signer;
        let mut truncated = Bytes::from_static(&[0u8; 3]);
        attestations[0].signature = Lazy::deferred(&mut truncated, ());

        assert_eq!(
            schemes[0].assemble(non_empty![@attestations], &Sequential),
            Err(AssemblyError::MalformedSignature(signer))
        );

        // Reject a malformed certificate before drawing any verification randomness.
        let subject = TestSubject {
            message: Bytes::from_static(MESSAGE),
        };
        let mut invalid = valid.clone();
        let mut truncated = Bytes::from_static(&[0u8; 3]);
        *invalid.signatures.last_mut().unwrap() = Lazy::deferred(&mut truncated, ());
        let mut actual_rng = TestRng::new(0);
        let mut expected_rng = TestRng::new(0);
        assert!(!verifier.verify_certificate::<_, Sha256Digest>(
            &mut actual_rng,
            subject.clone(),
            &invalid,
            &Sequential,
        ));
        assert_eq!(actual_rng.next_u64(), expected_rng.next_u64());

        // A later malformed certificate must reject the combined batch before drawing randomness.
        let mut actual_rng = TestRng::new(0);
        let mut expected_rng = TestRng::new(0);
        assert!(!verifier.verify_certificates::<_, Sha256Digest, _>(
            &mut actual_rng,
            non_empty![(subject.clone(), &valid), (subject, &invalid)],
            &Sequential,
        ));
        assert_eq!(actual_rng.next_u64(), expected_rng.next_u64());
    }

    #[test]
    fn test_verify_certificate_rejects_sub_quorum() {
        let mut rng = test_rng();
        let (schemes, verifier) = setup_signers(&mut rng, 4);
        let participants_len = schemes.len();

        let attestations: Vec<_> = schemes
            .iter()
            .take(3)
            .map(|s| {
                s.sign::<Sha256Digest>(TestSubject {
                    message: Bytes::from_static(MESSAGE),
                })
                .unwrap()
            })
            .collect();

        let mut certificate = schemes[0]
            .assemble(non_empty![@attestations], &Sequential)
            .unwrap();

        // Artificially truncate to below quorum
        let mut signers: Vec<Participant> = certificate.signers.iter().collect();
        signers.pop();
        certificate.signers = Signers::new(participants_len.try_into().unwrap(), signers).unwrap();
        certificate.signatures.pop();

        assert!(!verifier.verify_certificate::<_, Sha256Digest>(
            &mut rng,
            TestSubject {
                message: Bytes::from_static(MESSAGE),
            },
            &certificate,
            &Sequential,
        ));
    }

    #[test]
    fn test_verify_certificate_rejects_mismatched_signature_count() {
        let mut rng = test_rng();
        let (schemes, verifier) = setup_signers(&mut rng, 4);

        let attestations: Vec<_> = schemes
            .iter()
            .take(3)
            .map(|s| {
                s.sign::<Sha256Digest>(TestSubject {
                    message: Bytes::from_static(MESSAGE),
                })
                .unwrap()
            })
            .collect();

        let mut certificate = schemes[0]
            .assemble(non_empty![@attestations], &Sequential)
            .unwrap();

        // Remove one signature but keep signers bitmap unchanged
        certificate.signatures.pop();

        assert!(!verifier.verify_certificate::<_, Sha256Digest>(
            &mut rng,
            TestSubject {
                message: Bytes::from_static(MESSAGE),
            },
            &certificate,
            &Sequential,
        ));
    }

    #[test]
    fn test_verify_certificates_batch() {
        let mut rng = test_rng();
        let (schemes, verifier) = setup_signers(&mut rng, 4);
        let quorum = N3f1::quorum(schemes.len()) as usize;

        let messages: Vec<Bytes> = [b"msg1".as_slice(), b"msg2".as_slice(), b"msg3".as_slice()]
            .into_iter()
            .map(Bytes::from_static)
            .collect();
        let mut certificates = Vec::new();

        for msg in &messages {
            let attestations: Vec<_> = schemes
                .iter()
                .take(quorum)
                .map(|s| {
                    s.sign::<Sha256Digest>(TestSubject {
                        message: msg.clone(),
                    })
                    .unwrap()
                })
                .collect();
            certificates.push(
                schemes[0]
                    .assemble(non_empty![@attestations], &Sequential)
                    .unwrap(),
            );
        }

        // Sequential verification of multiple certificates consumes the same
        // randomness as verification of one certificate.
        let certs_iter = messages.iter().zip(&certificates).map(|(msg, cert)| {
            (
                TestSubject {
                    message: msg.clone(),
                },
                cert,
            )
        });

        let mut actual_rng = TestRng::new(0);
        let mut expected_rng = TestRng::new(0);
        assert!(verifier.verify_certificate::<_, Sha256Digest>(
            &mut expected_rng,
            TestSubject {
                message: messages[0].clone(),
            },
            &certificates[0],
            &Sequential,
        ));
        assert!(verifier.verify_certificates::<_, Sha256Digest, _>(
            &mut actual_rng,
            non_empty![@certs_iter],
            &Sequential
        ));
        assert_eq!(actual_rng.next_u64(), expected_rng.next_u64());
    }

    #[test]
    fn test_verify_certificates_batch_detects_failure() {
        let mut rng = test_rng();
        let (schemes, verifier) = setup_signers(&mut rng, 4);
        let quorum = N3f1::quorum(schemes.len()) as usize;

        let messages: Vec<Bytes> = [b"msg1".as_slice(), b"msg2".as_slice()]
            .into_iter()
            .map(Bytes::from_static)
            .collect();
        let mut certificates = Vec::new();

        for msg in &messages {
            let attestations: Vec<_> = schemes
                .iter()
                .take(quorum)
                .map(|s| {
                    s.sign::<Sha256Digest>(TestSubject {
                        message: msg.clone(),
                    })
                    .unwrap()
                })
                .collect();
            certificates.push(
                schemes[0]
                    .assemble(non_empty![@attestations], &Sequential)
                    .unwrap(),
            );
        }

        // Corrupt second certificate
        certificates[1].signatures[0] = certificates[1].signatures[1].clone();

        let certs_iter = messages.iter().zip(&certificates).map(|(msg, cert)| {
            (
                TestSubject {
                    message: msg.clone(),
                },
                cert,
            )
        });

        assert!(!verifier.verify_certificates::<_, Sha256Digest, _>(
            &mut rng,
            non_empty![@certs_iter],
            &Sequential
        ));
    }

    #[test]
    fn test_assemble_certificate_rejects_duplicate_signers() {
        let mut rng = test_rng();
        let (schemes, _) = setup_signers(&mut rng, 4);

        let mut attestations: Vec<_> = schemes
            .iter()
            .take(3)
            .map(|s| {
                s.sign::<Sha256Digest>(TestSubject {
                    message: Bytes::from_static(MESSAGE),
                })
                .unwrap()
            })
            .collect();

        // Add a duplicate of the last vote
        let duplicate = attestations.last().unwrap().clone();
        let signer = duplicate.signer;
        attestations.push(duplicate);

        assert_eq!(
            schemes[0].assemble(non_empty![@attestations], &Sequential),
            Err(AssemblyError::DuplicateSigner(signer))
        );
    }

    #[test]
    fn test_scheme_clone_and_verifier() {
        let mut rng = test_rng();
        let (schemes, _) = setup_signers(&mut rng, 4);
        let participants = schemes[0].participants().clone();

        // Clone a signer
        let signer = schemes[0].clone();
        assert!(
            signer
                .sign::<Sha256Digest>(TestSubject {
                    message: Bytes::from_static(MESSAGE),
                })
                .is_some(),
            "signer should produce votes"
        );

        // A verifier cannot produce votes
        let verifier = Scheme::verifier(NAMESPACE, participants);
        assert!(
            verifier
                .sign::<Sha256Digest>(TestSubject {
                    message: Bytes::from_static(MESSAGE),
                })
                .is_none(),
            "verifier should not produce votes"
        );
    }

    #[test]
    fn test_certificate_decode_validation() {
        let mut rng = test_rng();
        let (schemes, _) = setup_signers(&mut rng, 4);
        let participants_len = schemes.len();
        let participant_count =
            u32::try_from(participants_len).expect("participant count exceeds u32::MAX");

        let attestations: Vec<_> = schemes
            .iter()
            .take(3)
            .map(|s| {
                s.sign::<Sha256Digest>(TestSubject {
                    message: Bytes::from_static(MESSAGE),
                })
                .unwrap()
            })
            .collect();

        let certificate = schemes[0]
            .assemble(non_empty![@attestations], &Sequential)
            .unwrap();

        // Well-formed certificate decodes successfully
        let encoded = certificate.encode();
        let decoded =
            Certificate::decode_cfg(encoded, &participants_len).expect("decode certificate");
        assert_eq!(decoded, certificate);

        // Certificate with no signers is rejected
        let empty = Certificate {
            signers: Signers::new(participant_count, std::iter::empty::<Participant>()).unwrap(),
            signatures: Vec::new(),
        };
        assert!(Certificate::decode_cfg(empty.encode(), &participants_len).is_err());

        // Certificate with mismatched signature count is rejected
        let mismatched = Certificate {
            signers: Signers::new(participant_count, [0u32, 1].map(Participant::new)).unwrap(),
            signatures: vec![certificate.signatures[0].clone()],
        };
        assert!(Certificate::decode_cfg(mismatched.encode(), &participants_len).is_err());

        // Certificate containing more signers than the participant set is rejected
        let mut signers = certificate.signers.iter().collect::<Vec<_>>();
        signers.push(Participant::from_usize(participants_len));
        let mut sigs = certificate.signatures.clone();
        sigs.push(certificate.signatures[0].clone());
        let extended = Certificate {
            signers: Signers::new(participant_count + 1, signers).unwrap(),
            signatures: sigs,
        };
        assert!(Certificate::decode_cfg(extended.encode(), &participants_len).is_err());
    }

    #[test]
    fn test_verify_certificate_rejects_unknown_signer() {
        let mut rng = test_rng();
        let (schemes, verifier) = setup_signers(&mut rng, 4);
        let participants_len = schemes.len();

        let attestations: Vec<_> = schemes
            .iter()
            .take(3)
            .map(|s| {
                s.sign::<Sha256Digest>(TestSubject {
                    message: Bytes::from_static(MESSAGE),
                })
                .unwrap()
            })
            .collect();

        let mut certificate = schemes[0]
            .assemble(non_empty![@attestations], &Sequential)
            .unwrap();

        // Add an unknown signer (out of range)
        let mut signers: Vec<Participant> = certificate.signers.iter().collect();
        signers.push(Participant::from_usize(participants_len));
        certificate.signers =
            Signers::new((participants_len + 1).try_into().unwrap(), signers).unwrap();
        certificate
            .signatures
            .push(certificate.signatures[0].clone());

        assert!(!verifier.verify_certificate::<_, Sha256Digest>(
            &mut rng,
            TestSubject {
                message: Bytes::from_static(MESSAGE),
            },
            &certificate,
            &Sequential,
        ));
    }

    #[test]
    fn test_verify_certificate_rejects_invalid_certificate_signers_size() {
        let mut rng = test_rng();
        let (schemes, verifier) = setup_signers(&mut rng, 4);
        let participants_len = schemes.len();

        let attestations: Vec<_> = schemes
            .iter()
            .take(3)
            .map(|s| {
                s.sign::<Sha256Digest>(TestSubject {
                    message: Bytes::from_static(MESSAGE),
                })
                .unwrap()
            })
            .collect();

        let mut certificate = schemes[0]
            .assemble(non_empty![@attestations], &Sequential)
            .unwrap();

        // Valid certificate passes
        assert!(verifier.verify_certificate::<_, Sha256Digest>(
            &mut rng,
            TestSubject {
                message: Bytes::from_static(MESSAGE),
            },
            &certificate,
            &Sequential,
        ));

        // Make the signers bitmap size larger (mismatched with participants)
        let signers: Vec<Participant> = certificate.signers.iter().collect();
        certificate.signers =
            Signers::new((participants_len + 1).try_into().unwrap(), signers).unwrap();

        // Certificate verification should fail due to size mismatch
        assert!(!verifier.verify_certificate::<_, Sha256Digest>(
            &mut rng,
            TestSubject {
                message: Bytes::from_static(MESSAGE),
            },
            &certificate,
            &Sequential,
        ));
    }

    #[test]
    fn test_verify_certificate_rejects_signers_size_mismatch() {
        let mut rng = test_rng();
        let (schemes, verifier) = setup_signers(&mut rng, 4);
        let participants_len = schemes.len();

        let attestations: Vec<_> = schemes
            .iter()
            .take(3)
            .map(|s| {
                s.sign::<Sha256Digest>(TestSubject {
                    message: Bytes::from_static(MESSAGE),
                })
                .unwrap()
            })
            .collect();

        let mut certificate = schemes[0]
            .assemble(non_empty![@attestations], &Sequential)
            .unwrap();

        // Make the signers bitmap size larger than participants
        let signers: Vec<Participant> = certificate.signers.iter().collect();
        certificate.signers =
            Signers::new((participants_len + 1).try_into().unwrap(), signers).unwrap();
        certificate
            .signatures
            .push(certificate.signatures[0].clone());

        assert!(!verifier.verify_certificate::<_, Sha256Digest>(
            &mut rng,
            TestSubject {
                message: Bytes::from_static(MESSAGE),
            },
            &certificate,
            &Sequential,
        ));
    }

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

        commonware_conformance::conformance_tests! {
            CodecConformance<Certificate>,
        }
    }
}