commonware-storage 2026.4.0

//! Stateless Binary Merkle Tree (BMT).
//!
//! The Binary Merkle Tree is constructed level-by-level. The first level consists of position-hashed leaf digests.
//! On each additional level, pairs of nodes are hashed from the previous level (if a level contains an odd
//! number of nodes, the last node is duplicated). The finalized root of the tree incorporates the leaf count
//! to prevent proof malleability: `root = hash(leaf_count || tree_root)`.
//!
//! For example, given three leaves A, B, and C, the tree is constructed as follows:
//!
//! ```text
//!     Level 2 (tree_root):  [hash(hash(hash(0,A),hash(1,B)),hash(hash(2,C),hash(2,C)))]
//!     Level 1:              [hash(hash(0,A),hash(1,B)),hash(hash(2,C),hash(2,C))]
//!     Level 0 (leaves):     [hash(0,A),hash(1,B),hash(2,C)]
//!     Finalized root:       hash(3 || tree_root)
//! ```
//!
//! A proof for one or more leaves is generated by collecting the siblings needed to reconstruct the root.
//! An external process can then use this proof (with some trusted root) to verify that the leaves
//! are part of the tree.
//!
//! # Example
//!
//! ```rust
//! use commonware_storage::bmt::{Builder, Tree};
//! use commonware_cryptography::{Sha256, sha256::Digest, Hasher as _};
//!
//! // Create transactions and compute their digests
//! let txs = [b"tx1", b"tx2", b"tx3", b"tx4"];
//! let digests: Vec<Digest> = txs.iter().map(|tx| Sha256::hash(*tx)).collect();
//!
//! // Build a Merkle Tree from the digests
//! let mut builder = Builder::<Sha256>::new(digests.len());
//! for digest in &digests {
//!    builder.add(digest);
//! }
//! let tree = builder.build();
//! let root = tree.root();
//!
//! // Generate a proof for leaf at index 1
//! let mut hasher = Sha256::default();
//! let proof = tree.proof(1).unwrap();
//! assert!(proof.verify_element_inclusion(&mut hasher, &digests[1], 1, &root).is_ok());
//! ```

use alloc::collections::btree_set::BTreeSet;
use commonware_codec::{EncodeSize, Read, ReadExt, ReadRangeExt, Write};
use commonware_cryptography::{Digest, Hasher};
use commonware_runtime::{Buf, BufMut};
use commonware_utils::{non_empty_vec, vec::NonEmptyVec};
use thiserror::Error;

/// There should never be more than 255 levels in a proof (would mean the Binary Merkle Tree
/// has more than 2^255 leaves).
pub const MAX_LEVELS: usize = u8::MAX as usize;

/// Errors that can occur when working with a Binary Merkle Tree (BMT).
#[derive(Error, Debug)]
pub enum Error {
    #[error("invalid position: {0}")]
    InvalidPosition(u32),
    #[error("invalid proof: {0} != {1}")]
    InvalidProof(String, String),
    #[error("no leaves")]
    NoLeaves,
    #[error("unaligned proof")]
    UnalignedProof,
    #[error("duplicate position: {0}")]
    DuplicatePosition(u32),
}

/// Constructor for a Binary Merkle Tree (BMT).
pub struct Builder<H: Hasher> {
    hasher: H,
    leaves: Vec<H::Digest>,
}

impl<H: Hasher> Builder<H> {
    /// Creates a new Binary Merkle Tree builder.
    pub fn new(leaves: usize) -> Self {
        Self {
            hasher: H::new(),
            leaves: Vec::with_capacity(leaves),
        }
    }

    /// Adds a leaf to the Binary Merkle Tree.
    ///
    /// When added, the leaf is hashed with its position.
    pub fn add(&mut self, leaf: &H::Digest) -> u32 {
        let position: u32 = self.leaves.len().try_into().expect("too many leaves");
        self.hasher.update(&position.to_be_bytes());
        self.hasher.update(leaf);
        self.leaves.push(self.hasher.finalize());
        position
    }

    /// Builds the Binary Merkle Tree.
    ///
    /// It is valid to build a tree with no leaves, in which case
    /// just an "empty" node is included (no leaves will be provable).
    pub fn build(self) -> Tree<H::Digest> {
        Tree::new(self.hasher, self.leaves)
    }
}

/// Constructed Binary Merkle Tree (BMT).
#[derive(Clone, Debug)]
pub struct Tree<D: Digest> {
    /// Records whether the tree is empty.
    empty: bool,

    /// The digests at each level of the tree (from leaves to root).
    levels: NonEmptyVec<NonEmptyVec<D>>,

    /// The finalized root digest, which incorporates the leaf count.
    ///
    /// This is computed as `H(leaf_count || tree_root)` to prevent
    /// proof malleability where proofs that declare different leaf
    /// counts could verify against the same root.
    root: D,
}

impl<D: Digest> Tree<D> {
    /// Builds a Merkle Tree from a slice of position-hashed leaf digests.
    fn new<H: Hasher<Digest = D>>(mut hasher: H, mut leaves: Vec<D>) -> Self {
        // If no leaves, add an empty node.
        //
        // Because this node only includes a position, there is no way a valid proof
        // can be generated that references it.
        let mut empty = false;
        let leaf_count = leaves.len() as u32;
        if leaves.is_empty() {
            leaves.push(hasher.finalize());
            empty = true;
        }

        // Create the first level
        let mut levels = non_empty_vec![non_empty_vec![@leaves]];

        // Construct the tree level-by-level
        let mut current_level = levels.last();
        while !current_level.is_singleton() {
            let mut next_level = Vec::with_capacity(current_level.len().get().div_ceil(2));
            for chunk in current_level.chunks(2) {
                // Hash the left child
                hasher.update(&chunk[0]);

                // Hash the right child
                if chunk.len() == 2 {
                    hasher.update(&chunk[1]);
                } else {
                    // If no right child exists, duplicate left child.
                    hasher.update(&chunk[0]);
                };

                // Compute the parent digest
                next_level.push(hasher.finalize());
            }

            // Add the computed level to the tree
            levels.push(non_empty_vec![@next_level]);
            current_level = levels.last();
        }

        // Compute the finalized root: H(leaf_count || tree_root)
        // This binds the root to the tree size, preventing malleability attacks.
        let tree_root = levels.last().first();
        hasher.update(&leaf_count.to_be_bytes());
        hasher.update(tree_root);
        let root = hasher.finalize();

        Self {
            empty,
            levels,
            root,
        }
    }

    /// Returns the finalized root of the tree.
    ///
    /// The root incorporates the leaf count via `H(leaf_count || tree_root)`,
    /// which prevents proof malleability attacks where different tree sizes
    /// could produce valid proofs for the same root.
    pub const fn root(&self) -> D {
        self.root
    }

    /// Generates a Merkle proof for the leaf at `position`.
    ///
    /// This is a single-element multi-proof, which includes the minimal siblings
    /// needed to reconstruct the root.
    pub fn proof(&self, position: u32) -> Result<Proof<D>, Error> {
        self.multi_proof(core::iter::once(position))
    }

    /// Generates a Merkle range proof for a contiguous set of leaves from `start`
    /// to `end` (inclusive).
    ///
    /// The proof contains the minimal set of sibling digests needed to reconstruct
    /// the root for all elements in the range. This is more efficient than individual
    /// proofs when proving multiple consecutive elements.
    pub fn range_proof(&self, start: u32, end: u32) -> Result<Proof<D>, Error> {
        // For empty trees, return an empty proof
        if self.empty {
            if start == 0 && end == 0 {
                return Ok(Proof::default());
            }
            return Err(Error::InvalidPosition(start));
        }

        // Validate range bounds
        if start > end {
            return Err(Error::InvalidPosition(start));
        }
        let leaf_count = self.levels.first().len().get() as u32;
        if start >= leaf_count {
            return Err(Error::InvalidPosition(start));
        }
        if end >= leaf_count {
            return Err(Error::InvalidPosition(end));
        }

        // Compute required siblings without enumerating every leaf in the range.
        let sibling_positions = siblings_required_for_range_proof(leaf_count, start, end)?;
        let siblings: Vec<D> = sibling_positions
            .iter()
            .map(|&(level, index)| self.levels[level][index])
            .collect();

        Ok(Proof {
            leaf_count,
            siblings,
        })
    }

    /// Generates a Merkle proof for multiple non-contiguous leaves at the given `positions`.
    ///
    /// The proof contains the minimal set of sibling digests needed to reconstruct
    /// the root for all elements at the specified positions. This is more efficient
    /// than individual proofs when proving multiple elements because shared siblings
    /// are deduplicated.
    ///
    /// Positions are sorted internally; duplicate positions will return an error.
    pub fn multi_proof<I, P>(&self, positions: I) -> Result<Proof<D>, Error>
    where
        I: IntoIterator<Item = P>,
        P: core::borrow::Borrow<u32>,
    {
        let mut positions = positions.into_iter().peekable();

        // Handle empty positions first - can't prove zero elements
        let first = *positions.peek().ok_or(Error::NoLeaves)?.borrow();

        // Handle empty tree case
        if self.empty {
            return Err(Error::InvalidPosition(first));
        }

        let leaf_count = self.levels.first().len().get() as u32;

        // Get required sibling positions (this validates positions and checks for duplicates)
        let sibling_positions =
            siblings_required_for_multi_proof(leaf_count, positions.map(|p| *p.borrow()))?;

        // Collect sibling digests in order
        let siblings: Vec<D> = sibling_positions
            .iter()
            .map(|&(level, index)| self.levels[level][index])
            .collect();

        Ok(Proof {
            leaf_count,
            siblings,
        })
    }
}

/// A Merkle proof for multiple non-contiguous leaves in a Binary Merkle Tree.
///
/// This proof type is more space-efficient than generating individual proofs
/// for each leaf because sibling nodes that are shared between multiple paths
/// are deduplicated.
///
/// The proof contains the leaf count and sibling digests required for verification.
/// The leaf count is incorporated into the root hash during finalization, so
/// modifying it will cause verification to fail (preventing malleability attacks).
#[derive(Clone, Debug, Eq, PartialEq)]
pub struct Proof<D: Digest> {
    /// The number of leaves in the tree.
    ///
    /// This value is incorporated into the root hash during finalization,
    /// so modifying it will cause verification to fail (prevents malleability).
    pub leaf_count: u32,

    /// The deduplicated sibling digests required to verify all elements,
    /// ordered by their position in the tree (level-major, then index within level).
    pub siblings: Vec<D>,
}

impl<D: Digest> Default for Proof<D> {
    fn default() -> Self {
        Self {
            leaf_count: 0,
            siblings: Vec::new(),
        }
    }
}

impl<D: Digest> Write for Proof<D> {
    fn write(&self, writer: &mut impl BufMut) {
        self.leaf_count.write(writer);
        self.siblings.write(writer);
    }
}

impl<D: Digest> Read for Proof<D> {
    /// The maximum number of items being proven.
    ///
    /// The upper bound on sibling hashes is derived as `max_items * MAX_LEVELS`.
    type Cfg = usize;

    fn read_cfg(
        reader: &mut impl Buf,
        max_items: &Self::Cfg,
    ) -> Result<Self, commonware_codec::Error> {
        let leaf_count = u32::read(reader)?;
        let max_siblings = max_items.saturating_mul(MAX_LEVELS);
        let siblings = Vec::<D>::read_range(reader, ..=max_siblings)?;
        Ok(Self {
            leaf_count,
            siblings,
        })
    }
}

impl<D: Digest> EncodeSize for Proof<D> {
    fn encode_size(&self) -> usize {
        self.leaf_count.encode_size() + self.siblings.encode_size()
    }
}

#[cfg(feature = "arbitrary")]
impl<D: Digest> arbitrary::Arbitrary<'_> for Proof<D>
where
    D: for<'a> arbitrary::Arbitrary<'a>,
{
    fn arbitrary(u: &mut arbitrary::Unstructured<'_>) -> arbitrary::Result<Self> {
        Ok(Self {
            leaf_count: u.arbitrary()?,
            siblings: u.arbitrary()?,
        })
    }
}

/// Returns the number of levels in a tree with `leaf_count` leaves.
/// A tree with 1 leaf has 1 level, a tree with 2 leaves has 2 levels, etc.
const fn levels_in_tree(leaf_count: u32) -> usize {
    (u32::BITS - (leaf_count.saturating_sub(1)).leading_zeros() + 1) as usize
}

/// Returns the sorted, deduplicated positions of siblings required to prove
/// inclusion of leaves at the given positions.
///
/// Each position in the result is encoded as `(level, index)` where level 0 is the leaf level.
fn siblings_required_for_multi_proof(
    leaf_count: u32,
    positions: impl IntoIterator<Item = u32>,
) -> Result<BTreeSet<(usize, usize)>, Error> {
    // Validate positions and check for duplicates.
    let mut current = BTreeSet::new();
    for pos in positions {
        if pos >= leaf_count {
            return Err(Error::InvalidPosition(pos));
        }
        if !current.insert(pos as usize) {
            return Err(Error::DuplicatePosition(pos));
        }
    }

    if current.is_empty() {
        return Err(Error::NoLeaves);
    }

    // Track positions we can compute at each level and record missing siblings.
    // This keeps the work proportional to the number of positions, not the tree size.
    let mut sibling_positions = BTreeSet::new();
    let levels_count = levels_in_tree(leaf_count);
    let mut level_size = leaf_count as usize;
    for level in 0..levels_count - 1 {
        for &index in &current {
            let sibling_index = if index.is_multiple_of(2) {
                if index + 1 < level_size {
                    index + 1
                } else {
                    index
                }
            } else {
                index - 1
            };

            if sibling_index != index && !current.contains(&sibling_index) {
                sibling_positions.insert((level, sibling_index));
            }
        }

        current = current.iter().map(|idx| idx / 2).collect();
        level_size = level_size.div_ceil(2);
    }

    Ok(sibling_positions)
}

/// Returns the sorted, deduplicated positions of siblings required to prove
/// inclusion of a contiguous range of leaves from `start` to `end` (inclusive).
fn siblings_required_for_range_proof(
    leaf_count: u32,
    start: u32,
    end: u32,
) -> Result<BTreeSet<(usize, usize)>, Error> {
    if leaf_count == 0 {
        return Err(Error::NoLeaves);
    }
    if start > end {
        return Err(Error::InvalidPosition(start));
    }
    if start >= leaf_count {
        return Err(Error::InvalidPosition(start));
    }
    if end >= leaf_count {
        return Err(Error::InvalidPosition(end));
    }

    let mut sibling_positions = BTreeSet::new();
    let levels_count = levels_in_tree(leaf_count);
    let mut level_start = start as usize;
    let mut level_end = end as usize;
    let mut level_size = leaf_count as usize;

    for level in 0..levels_count - 1 {
        if !level_start.is_multiple_of(2) {
            sibling_positions.insert((level, level_start - 1));
        }
        if level_end.is_multiple_of(2) {
            let right = level_end + 1;
            if right < level_size {
                sibling_positions.insert((level, right));
            }
        }

        level_start /= 2;
        level_end /= 2;
        level_size = level_size.div_ceil(2);
    }

    Ok(sibling_positions)
}

impl<D: Digest> Proof<D> {
    /// Verifies that a given `leaf` at `position` is included in a Binary Merkle Tree
    /// with `root` using the provided `hasher`.
    ///
    /// The proof consists of sibling hashes stored from the leaf up to the root. At each
    /// level, if the current node is a left child (even index), the sibling is combined
    /// to the right; if it is a right child (odd index), the sibling is combined to the
    /// left.
    ///
    /// The `leaf_count` stored in the proof is incorporated into the finalized root
    /// computation, so any modification to it will cause verification to fail.
    pub fn verify_element_inclusion<H: Hasher<Digest = D>>(
        &self,
        hasher: &mut H,
        leaf: &D,
        mut position: u32,
        root: &D,
    ) -> Result<(), Error> {
        // Validate position
        if position >= self.leaf_count {
            return Err(Error::InvalidPosition(position));
        }

        // Compute the position-hashed leaf
        hasher.update(&position.to_be_bytes());
        hasher.update(leaf);
        let mut computed = hasher.finalize();

        // Track level size to handle odd-sized levels
        let mut level_size = self.leaf_count as usize;
        let mut sibling_iter = self.siblings.iter();

        // Traverse from leaf to root
        while level_size > 1 {
            // Check if this is the last node at an odd-sized level (no real sibling)
            let is_last_odd = position.is_multiple_of(2) && position as usize + 1 >= level_size;

            let (left_node, right_node) = if is_last_odd {
                // Node is duplicated - no sibling consumed from proof
                (&computed, &computed)
            } else if position.is_multiple_of(2) {
                // Even position: sibling is to the right
                let sibling = sibling_iter.next().ok_or(Error::UnalignedProof)?;
                (&computed, sibling)
            } else {
                // Odd position: sibling is to the left
                let sibling = sibling_iter.next().ok_or(Error::UnalignedProof)?;
                (sibling, &computed)
            };

            // Compute the parent digest
            hasher.update(left_node);
            hasher.update(right_node);
            computed = hasher.finalize();

            // Move up the tree
            position /= 2;
            level_size = level_size.div_ceil(2);
        }

        // Ensure all siblings were consumed
        if sibling_iter.next().is_some() {
            return Err(Error::UnalignedProof);
        }

        // Finalize the root by incorporating the leaf count: H(leaf_count || tree_root)
        // This binds the proof to the specific tree size, preventing malleability attacks.
        hasher.update(&self.leaf_count.to_be_bytes());
        hasher.update(&computed);
        let finalized = hasher.finalize();

        if finalized == *root {
            Ok(())
        } else {
            Err(Error::InvalidProof(finalized.to_string(), root.to_string()))
        }
    }

    /// Verifies that the given `elements` at their respective positions are included
    /// in a Binary Merkle Tree with `root`.
    ///
    /// Elements can be provided in any order; positions are sorted internally.
    /// Duplicate positions will cause verification to fail.
    ///
    /// The `leaf_count` stored in the proof is incorporated into the finalized root
    /// computation, so any modification to it will cause verification to fail.
    pub fn verify_multi_inclusion<H: Hasher<Digest = D>>(
        &self,
        hasher: &mut H,
        elements: &[(D, u32)],
        root: &D,
    ) -> Result<(), Error> {
        // Handle empty case
        if elements.is_empty() {
            if self.leaf_count == 0 && self.siblings.is_empty() {
                // Compute finalized empty root: H(0 || empty_tree_root)
                let empty_tree_root = hasher.finalize();
                hasher.update(&0u32.to_be_bytes());
                hasher.update(&empty_tree_root);
                let finalized = hasher.finalize();
                if finalized == *root {
                    return Ok(());
                } else {
                    return Err(Error::InvalidProof(finalized.to_string(), root.to_string()));
                }
            }
            return Err(Error::NoLeaves);
        }

        // 1. Sort elements by position and check for duplicates/bounds
        let mut sorted: Vec<(u32, D)> = Vec::with_capacity(elements.len());
        for (leaf, position) in elements {
            if *position >= self.leaf_count {
                return Err(Error::InvalidPosition(*position));
            }
            hasher.update(&position.to_be_bytes());
            hasher.update(leaf);
            sorted.push((*position, hasher.finalize()));
        }
        sorted.sort_unstable_by_key(|(pos, _)| *pos);

        // Check for duplicates (adjacent elements with same position after sorting)
        for i in 1..sorted.len() {
            if sorted[i - 1].0 == sorted[i].0 {
                return Err(Error::DuplicatePosition(sorted[i].0));
            }
        }

        // 2. Iterate up the tree
        // Since we process left-to-right and parent_pos = pos/2, next_level stays sorted.
        let levels = levels_in_tree(self.leaf_count);
        let mut level_size = self.leaf_count;
        let mut sibling_iter = self.siblings.iter();
        let mut current = sorted;
        let mut next_level: Vec<(u32, D)> = Vec::with_capacity(current.len());

        for _ in 0..levels - 1 {
            let mut idx = 0;
            while idx < current.len() {
                let (pos, digest) = current[idx];
                let parent_pos = pos / 2;

                // Determine if we have the left or right child
                let (left, right) = if pos.is_multiple_of(2) {
                    // We are the LEFT child
                    let left = digest;

                    // Check if we have the right child in our current set
                    let right = if idx + 1 < current.len() && current[idx + 1].0 == pos + 1 {
                        idx += 1;
                        current[idx].1
                    } else if pos + 1 >= level_size {
                        // If no right child exists in tree, duplicate left
                        left
                    } else {
                        // Otherwise, must consume a sibling
                        *sibling_iter.next().ok_or(Error::UnalignedProof)?
                    };
                    (left, right)
                } else {
                    // We are the RIGHT child
                    // This implies the LEFT child was missing from 'current', so it must be a sibling.
                    let right = digest;
                    let left = *sibling_iter.next().ok_or(Error::UnalignedProof)?;
                    (left, right)
                };

                // Hash parent
                hasher.update(&left);
                hasher.update(&right);
                next_level.push((parent_pos, hasher.finalize()));

                idx += 1;
            }

            // Prepare for next level
            core::mem::swap(&mut current, &mut next_level);
            next_level.clear();
            level_size = level_size.div_ceil(2);
        }

        // 3. Verify root
        if sibling_iter.next().is_some() {
            return Err(Error::UnalignedProof);
        }

        if current.len() != 1 {
            return Err(Error::UnalignedProof);
        }

        // Finalize the root by incorporating the leaf count: H(leaf_count || tree_root)
        // This binds the proof to the specific tree size, preventing malleability attacks.
        let tree_root = current[0].1;
        hasher.update(&self.leaf_count.to_be_bytes());
        hasher.update(&tree_root);
        let finalized = hasher.finalize();

        if finalized == *root {
            Ok(())
        } else {
            Err(Error::InvalidProof(finalized.to_string(), root.to_string()))
        }
    }

    /// Verifies that a contiguous range of `leaves` starting at `position` are included
    /// in a Binary Merkle Tree with `root`.
    ///
    /// This is a convenience method for verifying range proofs. The leaves must be
    /// in order starting from `position`.
    ///
    /// The `leaf_count` stored in the proof is incorporated into the finalized root
    /// computation, so any modification to it will cause verification to fail.
    pub fn verify_range_inclusion<H: Hasher<Digest = D>>(
        &self,
        hasher: &mut H,
        position: u32,
        leaves: &[D],
        root: &D,
    ) -> Result<(), Error> {
        // For empty trees, only position 0 with empty leaves is valid
        if leaves.is_empty() && position != 0 {
            return Err(Error::InvalidPosition(position));
        }
        if !leaves.is_empty() {
            let leaves_len =
                u32::try_from(leaves.len()).map_err(|_| Error::InvalidPosition(position))?;
            let end = position
                .checked_add(leaves_len - 1)
                .ok_or(Error::InvalidPosition(position))?;
            if end >= self.leaf_count {
                return Err(Error::InvalidPosition(end));
            }
        }

        // Convert to format expected by verify_multi_inclusion
        let elements: Vec<(D, u32)> = leaves
            .iter()
            .enumerate()
            .map(|(i, leaf)| (*leaf, position + i as u32))
            .collect();
        self.verify_multi_inclusion(hasher, &elements, root)
    }
}

#[cfg(test)]
mod tests {
    use super::*;
    use commonware_codec::{Decode, Encode};
    use commonware_cryptography::sha256::{Digest, Sha256};
    use rstest::rstest;

    /// Regression test for https://github.com/commonwarexyz/monorepo/issues/2837
    ///
    /// Before the fix, two proofs with identical siblings but different leaf_count
    /// values would both verify successfully against the same root, enabling
    /// proof malleability attacks.
    #[test]
    fn issue_2837_regression() {
        // Create a tree with 255 leaves (as in the issue report)
        let digests: Vec<Digest> = (0..255u32)
            .map(|i| Sha256::hash(&i.to_be_bytes()))
            .collect();

        let mut builder = Builder::<Sha256>::new(255);
        for digest in &digests {
            builder.add(digest);
        }
        let tree = builder.build();
        let root = tree.root();

        // Get a valid proof for position 0
        let original_proof = tree.proof(0).unwrap();
        assert_eq!(original_proof.leaf_count, 255);

        // Original proof should verify
        let mut hasher = Sha256::default();
        assert!(
            original_proof
                .verify_element_inclusion(&mut hasher, &digests[0], 0, &root)
                .is_ok(),
            "Original proof should verify"
        );

        // Create a malleated proof with leaf_count=254 but same siblings
        // (This is the exact attack from issue #2837)
        let malleated_proof = Proof {
            leaf_count: 254,
            siblings: original_proof.siblings.clone(),
        };

        // Malleated proof should NOT verify because the root now incorporates
        // the leaf_count: root = H(leaf_count || tree_root)
        let result = malleated_proof.verify_element_inclusion(&mut hasher, &digests[0], 0, &root);
        assert!(
            result.is_err(),
            "Malleated proof with wrong leaf_count must fail verification"
        );
    }

    #[test]
    fn test_tampered_proof_no_siblings() {
        // Create transactions and digests
        let txs = [b"tx1", b"tx2", b"tx3", b"tx4"];
        let digests: Vec<Digest> = txs.iter().map(|tx| Sha256::hash(*tx)).collect();
        let element = &digests[0];

        // Build tree
        let mut builder = Builder::<Sha256>::new(txs.len());
        for digest in &digests {
            builder.add(digest);
        }
        let tree = builder.build();
        let root = tree.root();

        // Build proof
        let mut proof = tree.proof(0).unwrap();

        // Tamper with proof
        proof.siblings = Vec::new();

        // Fail verification with an empty proof.
        let mut hasher = Sha256::default();
        assert!(proof
            .verify_element_inclusion(&mut hasher, element, 0, &root)
            .is_err());
    }

    #[test]
    fn test_tampered_proof_extra_sibling() {
        // Create transactions and digests
        let txs = [b"tx1", b"tx2", b"tx3", b"tx4"];
        let digests: Vec<Digest> = txs.iter().map(|tx| Sha256::hash(*tx)).collect();
        let element = &digests[0];

        // Build tree
        let mut builder = Builder::<Sha256>::new(txs.len());
        for digest in &digests {
            builder.add(digest);
        }
        let tree = builder.build();
        let root = tree.root();

        // Build proof
        let mut proof = tree.proof(0).unwrap();

        // Tamper with proof
        proof.siblings.push(*element);

        // Fail verification with extra sibling
        let mut hasher = Sha256::default();
        assert!(proof
            .verify_element_inclusion(&mut hasher, element, 0, &root)
            .is_err());
    }

    #[test]
    fn test_invalid_proof_wrong_element() {
        // Create transactions and digests
        let txs = [b"tx1", b"tx2", b"tx3", b"tx4"];
        let digests: Vec<Digest> = txs.iter().map(|tx| Sha256::hash(*tx)).collect();

        // Build tree
        let mut builder = Builder::<Sha256>::new(txs.len());
        for digest in &digests {
            builder.add(digest);
        }
        let tree = builder.build();
        let root = tree.root();

        // Generate a valid proof for leaf at index 2.
        let proof = tree.proof(2).unwrap();

        // Use a wrong element (e.g. hash of a different transaction).
        let mut hasher = Sha256::default();
        let wrong_leaf = Sha256::hash(b"wrong_tx");
        assert!(proof
            .verify_element_inclusion(&mut hasher, &wrong_leaf, 2, &root)
            .is_err());
    }

    #[test]
    fn test_invalid_proof_wrong_index() {
        // Create transactions and digests
        let txs = [b"tx1", b"tx2", b"tx3", b"tx4"];
        let digests: Vec<Digest> = txs.iter().map(|tx| Sha256::hash(*tx)).collect();

        // Build tree
        let mut builder = Builder::<Sha256>::new(txs.len());
        for digest in &digests {
            builder.add(digest);
        }
        let tree = builder.build();
        let root = tree.root();

        // Generate a valid proof for leaf at index 1.
        let proof = tree.proof(1).unwrap();

        // Use an incorrect index (e.g. 2 instead of 1).
        let mut hasher = Sha256::default();
        assert!(proof
            .verify_element_inclusion(&mut hasher, &digests[1], 2, &root)
            .is_err());
    }

    #[test]
    fn test_invalid_proof_wrong_root() {
        // Create transactions and digests
        let txs = [b"tx1", b"tx2", b"tx3", b"tx4"];
        let digests: Vec<Digest> = txs.iter().map(|tx| Sha256::hash(*tx)).collect();

        // Build tree
        let mut builder = Builder::<Sha256>::new(txs.len());
        for digest in &digests {
            builder.add(digest);
        }
        let tree = builder.build();

        // Generate a valid proof for leaf at index 0.
        let proof = tree.proof(0).unwrap();

        // Use a wrong root (hash of a different input).
        let mut hasher = Sha256::default();
        let wrong_root = Sha256::hash(b"wrong_root");
        assert!(proof
            .verify_element_inclusion(&mut hasher, &digests[0], 0, &wrong_root)
            .is_err());
    }

    #[test]
    fn test_invalid_proof_serialization_truncated() {
        // Create transactions and digests
        let txs = [b"tx1", b"tx2", b"tx3"];
        let digests: Vec<Digest> = txs.iter().map(|tx| Sha256::hash(*tx)).collect();

        // Build tree
        let mut builder = Builder::<Sha256>::new(txs.len());
        for digest in &digests {
            builder.add(digest);
        }
        let tree = builder.build();

        // Generate a valid proof for leaf at index 1.
        let proof = tree.proof(1).unwrap();
        let mut serialized = proof.encode();

        // Truncate one byte.
        serialized.truncate(serialized.len() - 1);
        assert!(Proof::<Digest>::decode_cfg(&mut serialized, &1).is_err());
    }

    #[test]
    fn test_invalid_proof_serialization_extra() {
        // Create transactions and digests
        let txs = [b"tx1", b"tx2", b"tx3"];
        let digests: Vec<Digest> = txs.iter().map(|tx| Sha256::hash(*tx)).collect();

        // Build tree
        let mut builder = Builder::<Sha256>::new(txs.len());
        for digest in &digests {
            builder.add(digest);
        }
        let tree = builder.build();

        // Generate a valid proof for leaf at index 1.
        let proof = tree.proof(1).unwrap();
        let mut serialized = proof.encode_mut();

        // Append an extra byte.
        serialized.extend_from_slice(&[0u8]);
        assert!(Proof::<Digest>::decode_cfg(&mut serialized, &1).is_err());
    }

    #[test]
    fn test_invalid_proof_modified_hash() {
        // Create transactions and digests
        let txs = [b"tx1", b"tx2", b"tx3", b"tx4"];
        let digests: Vec<Digest> = txs.iter().map(|tx| Sha256::hash(*tx)).collect();

        // Build tree
        let mut builder = Builder::<Sha256>::new(txs.len());
        for digest in &digests {
            builder.add(digest);
        }
        let tree = builder.build();
        let root = tree.root();

        // Generate a valid proof for leaf at index 2.
        let mut proof = tree.proof(2).unwrap();

        // Modify the first hash in the proof.
        let mut hasher = Sha256::default();
        proof.siblings[0] = Sha256::hash(b"modified");
        assert!(proof
            .verify_element_inclusion(&mut hasher, &digests[2], 2, &root)
            .is_err());
    }

    #[test]
    fn test_odd_tree_duplicate_index_proof() {
        // Create transactions and digests
        let txs = [b"tx1", b"tx2", b"tx3"];
        let digests: Vec<Digest> = txs.iter().map(|tx| Sha256::hash(*tx)).collect();

        // Build tree
        let mut builder = Builder::<Sha256>::new(txs.len());
        for digest in &digests {
            builder.add(digest);
        }
        let tree = builder.build();
        let root = tree.root();

        // The tree was built with 3 leaves; index 2 is the last valid index.
        let proof = tree.proof(2).unwrap();

        // Verification should succeed for the proper index 2.
        let mut hasher = Sha256::default();
        assert!(proof
            .verify_element_inclusion(&mut hasher, &digests[2], 2, &root)
            .is_ok());

        // Should not be able to generate a proof for an out-of-range index (e.g. 3).
        assert!(tree.proof(3).is_err());

        // Attempting to verify using an out-of-range index (e.g. 3, which would correspond
        // to a duplicate leaf that doesn't actually exist) should fail.
        assert!(proof
            .verify_element_inclusion(&mut hasher, &digests[2], 3, &root)
            .is_err());
    }

    #[test]
    fn test_range_proof_basic() {
        // Create test data
        let digests: Vec<Digest> = (0..8u32).map(|i| Sha256::hash(&i.to_be_bytes())).collect();

        // Build tree
        let mut builder = Builder::<Sha256>::new(digests.len());
        for digest in &digests {
            builder.add(digest);
        }
        let tree = builder.build();
        let root = tree.root();

        // Test range proof for elements 2-5
        let range_proof = tree.range_proof(2, 5).unwrap();
        let mut hasher = Sha256::default();
        let range_leaves = &digests[2..6];

        assert!(range_proof
            .verify_range_inclusion(&mut hasher, 2, range_leaves, &root)
            .is_ok());

        // Serialize and deserialize
        let mut serialized = range_proof.encode();
        let deserialized = Proof::<Digest>::decode_cfg(&mut serialized, &4).unwrap();
        assert!(deserialized
            .verify_range_inclusion(&mut hasher, 2, range_leaves, &root)
            .is_ok());
    }

    #[test]
    fn test_range_proof_single_element() {
        // Create test data
        let digests: Vec<Digest> = (0..8u32).map(|i| Sha256::hash(&i.to_be_bytes())).collect();

        // Build tree
        let mut builder = Builder::<Sha256>::new(digests.len());
        for digest in &digests {
            builder.add(digest);
        }
        let tree = builder.build();
        let root = tree.root();

        // Test single element range proof
        for (i, digest) in digests.iter().enumerate() {
            let range_proof = tree.range_proof(i as u32, i as u32).unwrap();
            let mut hasher = Sha256::default();

            let result =
                range_proof.verify_range_inclusion(&mut hasher, i as u32, &[*digest], &root);
            assert!(result.is_ok());
        }
    }

    #[test]
    fn test_range_proof_full_tree() {
        // Create test data
        let digests: Vec<Digest> = (0..7u32).map(|i| Sha256::hash(&i.to_be_bytes())).collect();

        // Build tree
        let mut builder = Builder::<Sha256>::new(digests.len());
        for digest in &digests {
            builder.add(digest);
        }
        let tree = builder.build();
        let root = tree.root();

        // Test full tree range proof
        let range_proof = tree.range_proof(0, (digests.len() - 1) as u32).unwrap();
        let mut hasher = Sha256::default();
        assert!(range_proof
            .verify_range_inclusion(&mut hasher, 0, &digests, &root)
            .is_ok());
    }

    #[test]
    fn test_range_proof_edge_cases() {
        // Create test data
        let digests: Vec<Digest> = (0..15u32).map(|i| Sha256::hash(&i.to_be_bytes())).collect();

        // Build tree
        let mut builder = Builder::<Sha256>::new(digests.len());
        for digest in &digests {
            builder.add(digest);
        }
        let tree = builder.build();
        let root = tree.root();
        let mut hasher = Sha256::default();

        // Test first half
        let range_proof = tree.range_proof(0, 7).unwrap();
        assert!(range_proof
            .verify_range_inclusion(&mut hasher, 0, &digests[0..8], &root)
            .is_ok());

        // Test second half
        let range_proof = tree.range_proof(8, 14).unwrap();
        assert!(range_proof
            .verify_range_inclusion(&mut hasher, 8, &digests[8..15], &root)
            .is_ok());

        // Test last elements
        let range_proof = tree.range_proof(13, 14).unwrap();
        assert!(range_proof
            .verify_range_inclusion(&mut hasher, 13, &digests[13..15], &root)
            .is_ok());
    }

    #[test]
    fn test_range_proof_invalid_range() {
        // Create test data
        let digests: Vec<Digest> = (0..8u32).map(|i| Sha256::hash(&i.to_be_bytes())).collect();

        // Build tree
        let mut builder = Builder::<Sha256>::new(digests.len());
        for digest in &digests {
            builder.add(digest);
        }
        let tree = builder.build();

        // Test invalid ranges
        assert!(tree.range_proof(8, 8).is_err()); // Start out of bounds
        assert!(tree.range_proof(0, 8).is_err()); // End out of bounds
        assert!(tree.range_proof(5, 8).is_err()); // End out of bounds
        assert!(tree.range_proof(2, 1).is_err()); // Start > end
    }

    #[test]
    fn test_range_proof_tampering() {
        // Create test data
        let digests: Vec<Digest> = (0..8u32).map(|i| Sha256::hash(&i.to_be_bytes())).collect();

        // Build tree
        let mut builder = Builder::<Sha256>::new(digests.len());
        for digest in &digests {
            builder.add(digest);
        }
        let tree = builder.build();
        let root = tree.root();

        // Get valid range proof
        let range_proof = tree.range_proof(2, 4).unwrap();
        let mut hasher = Sha256::default();
        let range_leaves = &digests[2..5];

        // Test with wrong leaves
        let wrong_leaves = vec![
            Sha256::hash(b"wrong1"),
            Sha256::hash(b"wrong2"),
            Sha256::hash(b"wrong3"),
        ];
        assert!(range_proof
            .verify_range_inclusion(&mut hasher, 2, &wrong_leaves, &root)
            .is_err());

        // Test with wrong number of leaves
        assert!(range_proof
            .verify_range_inclusion(&mut hasher, 2, &digests[2..4], &root)
            .is_err());

        // Test with tampered proof
        let mut tampered_proof = range_proof.clone();
        assert!(!tampered_proof.siblings.is_empty());
        // Tamper with the first sibling
        tampered_proof.siblings[0] = Sha256::hash(b"tampered");
        assert!(tampered_proof
            .verify_range_inclusion(&mut hasher, 2, range_leaves, &root)
            .is_err());

        // Test with wrong root
        let wrong_root = Sha256::hash(b"wrong_root");
        assert!(range_proof
            .verify_range_inclusion(&mut hasher, 2, range_leaves, &wrong_root)
            .is_err());
    }

    #[test]
    fn test_range_proof_various_sizes() {
        // Test range proofs for trees of various sizes
        for tree_size in [1, 2, 3, 4, 5, 7, 8, 15, 16, 31, 32, 63, 64] {
            let digests: Vec<Digest> = (0..tree_size as u32)
                .map(|i| Sha256::hash(&i.to_be_bytes()))
                .collect();

            // Build tree
            let mut builder = Builder::<Sha256>::new(digests.len());
            for digest in &digests {
                builder.add(digest);
            }
            let tree = builder.build();
            let root = tree.root();
            let mut hasher = Sha256::default();

            // Test various range sizes
            for range_size in 1..=tree_size.min(8) {
                for start in 0..=(tree_size - range_size) {
                    let range_proof = tree
                        .range_proof(start as u32, (start + range_size - 1) as u32)
                        .unwrap();
                    let end = start + range_size;
                    assert!(
                        range_proof
                            .verify_range_inclusion(
                                &mut hasher,
                                start as u32,
                                &digests[start..end],
                                &root
                            )
                            .is_ok(),
                        "Failed for tree_size={tree_size}, start={start}, range_size={range_size}"
                    );
                }
            }
        }
    }

    #[test]
    fn test_range_proof_malicious_wrong_position() {
        // Create test data
        let digests: Vec<Digest> = (0..8u32).map(|i| Sha256::hash(&i.to_be_bytes())).collect();

        // Build tree
        let mut builder = Builder::<Sha256>::new(digests.len());
        for digest in &digests {
            builder.add(digest);
        }
        let tree = builder.build();
        let root = tree.root();

        // Get valid range proof for position 2 to 4
        let range_proof = tree.range_proof(2, 4).unwrap();
        let mut hasher = Sha256::default();
        let range_leaves = &digests[2..5];

        // Try to verify with wrong position
        assert!(range_proof
            .verify_range_inclusion(&mut hasher, 3, range_leaves, &root)
            .is_err());
        assert!(range_proof
            .verify_range_inclusion(&mut hasher, 1, range_leaves, &root)
            .is_err());
    }

    #[test]
    fn test_range_proof_malicious_reordered_leaves() {
        // Create test data
        let digests: Vec<Digest> = (0..8u32).map(|i| Sha256::hash(&i.to_be_bytes())).collect();

        // Build tree
        let mut builder = Builder::<Sha256>::new(digests.len());
        for digest in &digests {
            builder.add(digest);
        }
        let tree = builder.build();
        let root = tree.root();

        // Get valid range proof for position 2 to 4
        let range_proof = tree.range_proof(2, 4).unwrap();
        let mut hasher = Sha256::default();

        // Try to verify with reordered leaves
        let reordered_leaves = vec![digests[3], digests[2], digests[4]];
        assert!(range_proof
            .verify_range_inclusion(&mut hasher, 2, &reordered_leaves, &root)
            .is_err());
    }

    #[test]
    fn test_range_proof_malicious_extra_siblings() {
        // Create test data
        let digests: Vec<Digest> = (0..8u32).map(|i| Sha256::hash(&i.to_be_bytes())).collect();

        // Build tree
        let mut builder = Builder::<Sha256>::new(digests.len());
        for digest in &digests {
            builder.add(digest);
        }
        let tree = builder.build();
        let root = tree.root();

        // Get valid range proof
        let mut range_proof = tree.range_proof(2, 3).unwrap();
        let mut hasher = Sha256::default();
        let range_leaves = &digests[2..4];

        // Tamper by adding extra siblings
        range_proof.siblings.push(Sha256::hash(b"extra"));
        assert!(range_proof
            .verify_range_inclusion(&mut hasher, 2, range_leaves, &root)
            .is_err());
    }

    #[test]
    fn test_range_proof_malicious_missing_siblings() {
        // Create test data
        let digests: Vec<Digest> = (0..8u32).map(|i| Sha256::hash(&i.to_be_bytes())).collect();

        // Build tree
        let mut builder = Builder::<Sha256>::new(digests.len());
        for digest in &digests {
            builder.add(digest);
        }
        let tree = builder.build();
        let root = tree.root();

        // Get valid range proof for a single element (which needs siblings)
        let mut range_proof = tree.range_proof(2, 2).unwrap();
        let mut hasher = Sha256::default();
        let range_leaves = &digests[2..3];

        // The proof should have siblings
        assert!(!range_proof.siblings.is_empty());

        // Remove a sibling
        range_proof.siblings.pop();
        assert!(range_proof
            .verify_range_inclusion(&mut hasher, 2, range_leaves, &root)
            .is_err());
    }

    #[test]
    fn test_range_proof_integer_overflow_protection() {
        // Create test data
        let digests: Vec<Digest> = (0..8u32).map(|i| Sha256::hash(&i.to_be_bytes())).collect();

        // Build tree
        let mut builder = Builder::<Sha256>::new(digests.len());
        for digest in &digests {
            builder.add(digest);
        }
        let tree = builder.build();

        // Test overflow in range_proof generation
        assert!(tree.range_proof(u32::MAX, u32::MAX).is_err());
        assert!(tree.range_proof(u32::MAX - 1, u32::MAX).is_err());
        assert!(tree.range_proof(7, u32::MAX).is_err());
    }

    #[test]
    fn test_range_proof_malicious_wrong_tree_structure() {
        // Create test data
        let digests: Vec<Digest> = (0..8u32).map(|i| Sha256::hash(&i.to_be_bytes())).collect();

        // Build tree
        let mut builder = Builder::<Sha256>::new(digests.len());
        for digest in &digests {
            builder.add(digest);
        }
        let tree = builder.build();
        let root = tree.root();

        // Get valid range proof
        let mut range_proof = tree.range_proof(2, 3).unwrap();
        let mut hasher = Sha256::default();
        let range_leaves = &digests[2..4];

        // Add extra sibling (simulating proof from different tree structure)
        range_proof.siblings.push(Sha256::hash(b"fake_level"));
        assert!(range_proof
            .verify_range_inclusion(&mut hasher, 2, range_leaves, &root)
            .is_err());

        // Remove a sibling
        let mut range_proof = tree.range_proof(2, 2).unwrap();
        let range_leaves = &digests[2..3];
        assert!(!range_proof.siblings.is_empty());
        range_proof.siblings.pop();
        assert!(range_proof
            .verify_range_inclusion(&mut hasher, 2, range_leaves, &root)
            .is_err());
    }

    #[test]
    fn test_range_proof_boundary_conditions() {
        // Test various power-of-2 boundary conditions
        for tree_size in [1, 2, 4, 8, 16, 32] {
            let digests: Vec<Digest> = (0..tree_size as u32)
                .map(|i| Sha256::hash(&i.to_be_bytes()))
                .collect();

            // Build tree
            let mut builder = Builder::<Sha256>::new(digests.len());
            for digest in &digests {
                builder.add(digest);
            }
            let tree = builder.build();
            let root = tree.root();
            let mut hasher = Sha256::default();

            // Test edge cases
            // First element only
            let proof = tree.range_proof(0, 0).unwrap();
            assert!(proof
                .verify_range_inclusion(&mut hasher, 0, &digests[0..1], &root)
                .is_ok());

            // Last element only
            let last_idx = tree_size - 1;
            let proof = tree.range_proof(last_idx as u32, last_idx as u32).unwrap();
            assert!(proof
                .verify_range_inclusion(
                    &mut hasher,
                    last_idx as u32,
                    &digests[last_idx..tree_size],
                    &root
                )
                .is_ok());

            // Full tree
            let proof = tree.range_proof(0, (tree_size - 1) as u32).unwrap();
            assert!(proof
                .verify_range_inclusion(&mut hasher, 0, &digests, &root)
                .is_ok());
        }
    }

    #[test]
    fn test_empty_tree_proof() {
        // Build an empty tree
        let builder = Builder::<Sha256>::new(0);
        let tree = builder.build();

        // Empty tree should fail for any position since there are no elements
        assert!(tree.proof(0).is_err());
        assert!(tree.proof(1).is_err());
        assert!(tree.proof(100).is_err());
    }

    #[test]
    fn test_empty_tree_range_proof() {
        // Build an empty tree
        let builder = Builder::<Sha256>::new(0);
        let tree = builder.build();
        let root = tree.root();

        // Empty tree should return default proof only for (0, 0)
        let range_proof = tree.range_proof(0, 0).unwrap();
        assert!(range_proof.siblings.is_empty());
        assert_eq!(range_proof, Proof::default());

        // All other combinations should fail
        let invalid_ranges = vec![
            (0, 1),
            (0, 10),
            (1, 1),
            (1, 2),
            (5, 5),
            (10, 10),
            (0, u32::MAX),
            (u32::MAX, u32::MAX),
        ];
        for (start, end) in invalid_ranges {
            assert!(tree.range_proof(start, end).is_err());
        }

        // Verify empty range proof against empty tree root
        let mut hasher = Sha256::default();
        let empty_leaves: &[Digest] = &[];
        assert!(range_proof
            .verify_range_inclusion(&mut hasher, 0, empty_leaves, &root)
            .is_ok());

        // Should fail with non-empty leaves
        let non_empty_leaves = vec![Sha256::hash(b"leaf")];
        assert!(range_proof
            .verify_range_inclusion(&mut hasher, 0, &non_empty_leaves, &root)
            .is_err());

        // Should fail with wrong root
        let wrong_root = Sha256::hash(b"wrong");
        assert!(range_proof
            .verify_range_inclusion(&mut hasher, 0, empty_leaves, &wrong_root)
            .is_err());

        // Should fail with wrong position
        assert!(range_proof
            .verify_range_inclusion(&mut hasher, 1, empty_leaves, &root)
            .is_err());
    }

    #[test]
    fn test_empty_range_proof_serialization() {
        let proof = Proof::<Digest>::default();
        let mut serialized = proof.encode();
        let deserialized = Proof::<Digest>::decode_cfg(&mut serialized, &0).unwrap();
        assert_eq!(proof, deserialized);
    }

    #[test]
    fn test_empty_tree_root_consistency() {
        // Create multiple empty trees and verify they have the same root
        let mut roots = Vec::new();
        for _ in 0..5 {
            let builder = Builder::<Sha256>::new(0);
            let tree = builder.build();
            roots.push(tree.root());
        }

        // All empty trees should have the same root
        for i in 1..roots.len() {
            assert_eq!(roots[0], roots[i]);
        }

        // The root should be the hash of empty data
        let mut hasher = Sha256::default();
        hasher.update(0u32.to_be_bytes().as_slice());
        hasher.update(Sha256::hash(b"").as_ref());
        let expected_root = hasher.finalize();
        assert_eq!(roots[0], expected_root);
    }

    #[rstest]
    #[case::need_left_sibling(1, 2)] // Range starting at odd index (needs left sibling)
    #[case::need_right_sibling(4, 4)] // Range starting at even index
    #[case::full_tree(0, 16)] // Full tree (no siblings needed at leaf level)
    fn test_range_proof_siblings_usage(#[case] start: u32, #[case] count: u32) {
        // This test ensures that all siblings in a range proof are actually used during verification
        let digests: Vec<Digest> = (0..16u32).map(|i| Sha256::hash(&i.to_be_bytes())).collect();

        // Build tree
        let mut builder = Builder::<Sha256>::new(digests.len());
        for digest in &digests {
            builder.add(digest);
        }
        let tree = builder.build();
        let root = tree.root();
        let mut hasher = Sha256::default();

        let range_proof = tree.range_proof(start, start + count - 1).unwrap();
        let end = start as usize + count as usize;

        // Verify the proof works
        assert!(range_proof
            .verify_range_inclusion(&mut hasher, start, &digests[start as usize..end], &root)
            .is_ok());

        // For each sibling, try tampering with it and verify the proof fails
        for sibling_idx in 0..range_proof.siblings.len() {
            let mut tampered_proof = range_proof.clone();
            tampered_proof.siblings[sibling_idx] = Sha256::hash(b"tampered");
            assert!(tampered_proof
                .verify_range_inclusion(&mut hasher, start, &digests[start as usize..end], &root)
                .is_err());
        }
    }

    // Test trees with odd sizes that require duplicate nodes
    #[rstest]
    fn test_range_proof_duplicate_node_edge_cases(
        #[values(3, 5, 7, 9, 11, 13, 15)] tree_size: usize,
    ) {
        let digests: Vec<Digest> = (0..tree_size as u32)
            .map(|i| Sha256::hash(&i.to_be_bytes()))
            .collect();

        // Build tree
        let mut builder = Builder::<Sha256>::new(digests.len());
        for digest in &digests {
            builder.add(digest);
        }
        let tree = builder.build();
        let root = tree.root();
        let mut hasher = Sha256::default();

        // Test range including the last element (which may require duplicate handling)
        let start = tree_size - 2;
        let proof = tree
            .range_proof(start as u32, (tree_size - 1) as u32)
            .unwrap();
        assert!(proof
            .verify_range_inclusion(&mut hasher, start as u32, &digests[start..tree_size], &root)
            .is_ok());
    }

    #[test]
    fn test_multi_proof_basic() {
        // Create test data
        let digests: Vec<Digest> = (0..8u32).map(|i| Sha256::hash(&i.to_be_bytes())).collect();

        // Build tree
        let mut builder = Builder::<Sha256>::new(digests.len());
        for digest in &digests {
            builder.add(digest);
        }
        let tree = builder.build();
        let root = tree.root();

        // Test multi-proof for non-contiguous positions [0, 3, 5]
        let positions = [0, 3, 5];
        let multi_proof = tree.multi_proof(positions).unwrap();
        let mut hasher = Sha256::default();

        let elements: Vec<(Digest, u32)> = positions
            .iter()
            .map(|&p| (digests[p as usize], p))
            .collect();
        assert!(multi_proof
            .verify_multi_inclusion(&mut hasher, &elements, &root)
            .is_ok());
    }

    #[test]
    fn test_multi_proof_single_element() {
        // Create test data
        let digests: Vec<Digest> = (0..8u32).map(|i| Sha256::hash(&i.to_be_bytes())).collect();

        // Build tree
        let mut builder = Builder::<Sha256>::new(digests.len());
        for digest in &digests {
            builder.add(digest);
        }
        let tree = builder.build();
        let root = tree.root();
        let mut hasher = Sha256::default();

        // Test single element multi-proof for each position
        for (i, digest) in digests.iter().enumerate() {
            let multi_proof = tree.multi_proof([i as u32]).unwrap();
            let elements = [(*digest, i as u32)];
            assert!(
                multi_proof
                    .verify_multi_inclusion(&mut hasher, &elements, &root)
                    .is_ok(),
                "Failed for position {i}"
            );
        }
    }

    #[test]
    fn test_multi_proof_all_elements() {
        // Create test data
        let digests: Vec<Digest> = (0..8u32).map(|i| Sha256::hash(&i.to_be_bytes())).collect();

        // Build tree
        let mut builder = Builder::<Sha256>::new(digests.len());
        for digest in &digests {
            builder.add(digest);
        }
        let tree = builder.build();
        let root = tree.root();
        let mut hasher = Sha256::default();

        // Test multi-proof for all elements
        let positions: Vec<u32> = (0..digests.len() as u32).collect();
        let multi_proof = tree.multi_proof(&positions).unwrap();

        let elements: Vec<(Digest, u32)> = positions
            .iter()
            .map(|&p| (digests[p as usize], p))
            .collect();
        assert!(multi_proof
            .verify_multi_inclusion(&mut hasher, &elements, &root)
            .is_ok());

        // When proving all elements, we shouldn't need any siblings (all can be computed)
        assert!(multi_proof.siblings.is_empty());
    }

    #[test]
    fn test_multi_proof_adjacent_elements() {
        // Create test data
        let digests: Vec<Digest> = (0..8u32).map(|i| Sha256::hash(&i.to_be_bytes())).collect();

        // Build tree
        let mut builder = Builder::<Sha256>::new(digests.len());
        for digest in &digests {
            builder.add(digest);
        }
        let tree = builder.build();
        let root = tree.root();
        let mut hasher = Sha256::default();

        // Test adjacent positions (should deduplicate shared siblings)
        let positions = [2, 3];
        let multi_proof = tree.multi_proof(positions).unwrap();

        let elements: Vec<(Digest, u32)> = positions
            .iter()
            .map(|&p| (digests[p as usize], p))
            .collect();
        assert!(multi_proof
            .verify_multi_inclusion(&mut hasher, &elements, &root)
            .is_ok());
    }

    #[test]
    fn test_multi_proof_sparse_positions() {
        // Create test data
        let digests: Vec<Digest> = (0..16u32).map(|i| Sha256::hash(&i.to_be_bytes())).collect();

        // Build tree
        let mut builder = Builder::<Sha256>::new(digests.len());
        for digest in &digests {
            builder.add(digest);
        }
        let tree = builder.build();
        let root = tree.root();
        let mut hasher = Sha256::default();

        // Test widely separated positions
        let positions = [0, 7, 8, 15];
        let multi_proof = tree.multi_proof(positions).unwrap();

        let elements: Vec<(Digest, u32)> = positions
            .iter()
            .map(|&p| (digests[p as usize], p))
            .collect();
        assert!(multi_proof
            .verify_multi_inclusion(&mut hasher, &elements, &root)
            .is_ok());
    }

    #[test]
    fn test_multi_proof_empty_tree() {
        // Build empty tree
        let builder = Builder::<Sha256>::new(0);
        let tree = builder.build();

        // Empty tree with empty positions should return NoLeaves error
        // (we can't prove zero elements)
        assert!(matches!(
            tree.multi_proof(std::iter::empty::<u32>()),
            Err(Error::NoLeaves)
        ));

        // Empty tree with any position should fail with InvalidPosition
        assert!(matches!(
            tree.multi_proof([0]),
            Err(Error::InvalidPosition(0))
        ));
    }

    #[test]
    fn test_multi_proof_empty_positions() {
        // Create test data
        let digests: Vec<Digest> = (0..8u32).map(|i| Sha256::hash(&i.to_be_bytes())).collect();

        // Build tree
        let mut builder = Builder::<Sha256>::new(digests.len());
        for digest in &digests {
            builder.add(digest);
        }
        let tree = builder.build();

        // Empty positions should return error
        assert!(matches!(
            tree.multi_proof(std::iter::empty::<u32>()),
            Err(Error::NoLeaves)
        ));
    }

    #[test]
    fn test_multi_proof_duplicate_positions_error() {
        // Create test data
        let digests: Vec<Digest> = (0..8u32).map(|i| Sha256::hash(&i.to_be_bytes())).collect();

        // Build tree
        let mut builder = Builder::<Sha256>::new(digests.len());
        for digest in &digests {
            builder.add(digest);
        }
        let tree = builder.build();

        // Duplicate positions should return error
        assert!(matches!(
            tree.multi_proof([1, 1]),
            Err(Error::DuplicatePosition(1))
        ));
        assert!(matches!(
            tree.multi_proof([0, 2, 2, 5]),
            Err(Error::DuplicatePosition(2))
        ));
    }

    #[test]
    fn test_multi_proof_unsorted_input() {
        // Create test data
        let digests: Vec<Digest> = (0..8u32).map(|i| Sha256::hash(&i.to_be_bytes())).collect();

        // Build tree
        let mut builder = Builder::<Sha256>::new(digests.len());
        for digest in &digests {
            builder.add(digest);
        }
        let tree = builder.build();
        let root = tree.root();
        let mut hasher = Sha256::default();

        // Test with unsorted positions (should work - internal sorting)
        let positions = [5, 0, 3];
        let multi_proof = tree.multi_proof(positions).unwrap();

        // Verify with unsorted elements (should work - internal sorting)
        let unsorted_elements = [(digests[5], 5), (digests[0], 0), (digests[3], 3)];
        assert!(multi_proof
            .verify_multi_inclusion(&mut hasher, &unsorted_elements, &root)
            .is_ok());
    }

    #[test]
    fn test_multi_proof_various_sizes() {
        // Test multi-proofs for trees of various sizes
        for tree_size in [1, 2, 3, 4, 5, 7, 8, 15, 16, 31, 32] {
            let digests: Vec<Digest> = (0..tree_size as u32)
                .map(|i| Sha256::hash(&i.to_be_bytes()))
                .collect();

            // Build tree
            let mut builder = Builder::<Sha256>::new(digests.len());
            for digest in &digests {
                builder.add(digest);
            }
            let tree = builder.build();
            let root = tree.root();
            let mut hasher = Sha256::default();

            // Test various position combinations
            // First and last
            if tree_size >= 2 {
                let positions = [0, (tree_size - 1) as u32];
                let multi_proof = tree.multi_proof(positions).unwrap();
                let elements: Vec<(Digest, u32)> = positions
                    .iter()
                    .map(|&p| (digests[p as usize], p))
                    .collect();
                assert!(
                    multi_proof
                        .verify_multi_inclusion(&mut hasher, &elements, &root)
                        .is_ok(),
                    "Failed for tree_size={tree_size}, positions=[0, {}]",
                    tree_size - 1
                );
            }

            // Every other element
            if tree_size >= 4 {
                let positions: Vec<u32> = (0..tree_size as u32).step_by(2).collect();
                let multi_proof = tree.multi_proof(&positions).unwrap();
                let elements: Vec<(Digest, u32)> = positions
                    .iter()
                    .map(|&p| (digests[p as usize], p))
                    .collect();
                assert!(
                    multi_proof
                        .verify_multi_inclusion(&mut hasher, &elements, &root)
                        .is_ok(),
                    "Failed for tree_size={tree_size}, every other element"
                );
            }
        }
    }

    #[test]
    fn test_multi_proof_wrong_elements() {
        // Create test data
        let digests: Vec<Digest> = (0..8u32).map(|i| Sha256::hash(&i.to_be_bytes())).collect();

        // Build tree
        let mut builder = Builder::<Sha256>::new(digests.len());
        for digest in &digests {
            builder.add(digest);
        }
        let tree = builder.build();
        let root = tree.root();
        let mut hasher = Sha256::default();

        // Generate valid proof
        let positions = [0, 3, 5];
        let multi_proof = tree.multi_proof(positions).unwrap();

        // Verify with wrong elements
        let wrong_elements = [
            (Sha256::hash(b"wrong1"), 0),
            (digests[3], 3),
            (digests[5], 5),
        ];
        assert!(multi_proof
            .verify_multi_inclusion(&mut hasher, &wrong_elements, &root)
            .is_err());
    }

    #[test]
    fn test_multi_proof_wrong_positions() {
        // Create test data
        let digests: Vec<Digest> = (0..8u32).map(|i| Sha256::hash(&i.to_be_bytes())).collect();

        // Build tree
        let mut builder = Builder::<Sha256>::new(digests.len());
        for digest in &digests {
            builder.add(digest);
        }
        let tree = builder.build();
        let root = tree.root();
        let mut hasher = Sha256::default();

        // Generate valid proof
        let positions = [0, 3, 5];
        let multi_proof = tree.multi_proof(positions).unwrap();

        // Verify with wrong positions (same elements, different positions)
        let wrong_positions = [
            (digests[0], 1), // wrong position
            (digests[3], 3),
            (digests[5], 5),
        ];
        assert!(multi_proof
            .verify_multi_inclusion(&mut hasher, &wrong_positions, &root)
            .is_err());
    }

    #[test]
    fn test_multi_proof_wrong_root() {
        // Create test data
        let digests: Vec<Digest> = (0..8u32).map(|i| Sha256::hash(&i.to_be_bytes())).collect();

        // Build tree
        let mut builder = Builder::<Sha256>::new(digests.len());
        for digest in &digests {
            builder.add(digest);
        }
        let tree = builder.build();
        let mut hasher = Sha256::default();

        // Generate valid proof
        let positions = [0, 3, 5];
        let multi_proof = tree.multi_proof(positions).unwrap();

        let elements: Vec<(Digest, u32)> = positions
            .iter()
            .map(|&p| (digests[p as usize], p))
            .collect();

        // Verify with wrong root
        let wrong_root = Sha256::hash(b"wrong_root");
        assert!(multi_proof
            .verify_multi_inclusion(&mut hasher, &elements, &wrong_root)
            .is_err());
    }

    #[test]
    fn test_multi_proof_tampering() {
        // Create test data
        let digests: Vec<Digest> = (0..8u32).map(|i| Sha256::hash(&i.to_be_bytes())).collect();

        // Build tree
        let mut builder = Builder::<Sha256>::new(digests.len());
        for digest in &digests {
            builder.add(digest);
        }
        let tree = builder.build();
        let root = tree.root();
        let mut hasher = Sha256::default();

        // Generate valid proof
        let positions = [0, 5];
        let multi_proof = tree.multi_proof(positions).unwrap();

        let elements: Vec<(Digest, u32)> = positions
            .iter()
            .map(|&p| (digests[p as usize], p))
            .collect();

        // Tamper with sibling
        assert!(!multi_proof.siblings.is_empty());
        let mut modified = multi_proof.clone();
        modified.siblings[0] = Sha256::hash(b"tampered");
        assert!(modified
            .verify_multi_inclusion(&mut hasher, &elements, &root)
            .is_err());

        // Add extra sibling
        let mut extra = multi_proof.clone();
        extra.siblings.push(Sha256::hash(b"extra"));
        assert!(extra
            .verify_multi_inclusion(&mut hasher, &elements, &root)
            .is_err());

        // Remove a sibling
        let mut missing = multi_proof;
        missing.siblings.pop();
        assert!(missing
            .verify_multi_inclusion(&mut hasher, &elements, &root)
            .is_err());
    }

    #[test]
    fn test_multi_proof_deduplication() {
        // Create test data
        let digests: Vec<Digest> = (0..16u32).map(|i| Sha256::hash(&i.to_be_bytes())).collect();

        // Build tree
        let mut builder = Builder::<Sha256>::new(digests.len());
        for digest in &digests {
            builder.add(digest);
        }
        let tree = builder.build();

        // Get individual proofs
        let individual_siblings: usize = [0u32, 1, 8, 9]
            .iter()
            .map(|&p| tree.proof(p).unwrap().siblings.len())
            .sum();

        // Get multi-proof for same positions
        let multi_proof = tree.multi_proof([0, 1, 8, 9]).unwrap();

        // Multi-proof should have fewer siblings due to deduplication
        assert!(
            multi_proof.siblings.len() < individual_siblings,
            "Multi-proof ({}) should have fewer siblings than sum of individual proofs ({})",
            multi_proof.siblings.len(),
            individual_siblings
        );
    }

    #[test]
    fn test_multi_proof_serialization() {
        // Create test data
        let digests: Vec<Digest> = (0..8u32).map(|i| Sha256::hash(&i.to_be_bytes())).collect();

        // Build tree
        let mut builder = Builder::<Sha256>::new(digests.len());
        for digest in &digests {
            builder.add(digest);
        }
        let tree = builder.build();
        let root = tree.root();
        let mut hasher = Sha256::default();

        // Generate proof
        let positions = [0, 3, 5];
        let multi_proof = tree.multi_proof(positions).unwrap();

        // Serialize and deserialize
        let serialized = multi_proof.encode();
        let deserialized = Proof::<Digest>::decode_cfg(serialized, &positions.len()).unwrap();

        assert_eq!(multi_proof, deserialized);

        // Verify deserialized proof works
        let elements: Vec<(Digest, u32)> = positions
            .iter()
            .map(|&p| (digests[p as usize], p))
            .collect();
        assert!(deserialized
            .verify_multi_inclusion(&mut hasher, &elements, &root)
            .is_ok());
    }

    #[test]
    fn test_multi_proof_serialization_truncated() {
        // Create test data
        let digests: Vec<Digest> = (0..8u32).map(|i| Sha256::hash(&i.to_be_bytes())).collect();

        // Build tree
        let mut builder = Builder::<Sha256>::new(digests.len());
        for digest in &digests {
            builder.add(digest);
        }
        let tree = builder.build();

        // Generate proof
        let positions = [0, 3, 5];
        let multi_proof = tree.multi_proof(positions).unwrap();

        // Serialize and truncate
        let mut serialized = multi_proof.encode();
        serialized.truncate(serialized.len() - 1);

        // Should fail to deserialize
        assert!(Proof::<Digest>::decode_cfg(&mut serialized, &positions.len()).is_err());
    }

    #[test]
    fn test_multi_proof_serialization_extra() {
        // Create test data
        let digests: Vec<Digest> = (0..8u32).map(|i| Sha256::hash(&i.to_be_bytes())).collect();

        // Build tree
        let mut builder = Builder::<Sha256>::new(digests.len());
        for digest in &digests {
            builder.add(digest);
        }
        let tree = builder.build();

        // Generate proof
        let positions = [0, 3, 5];
        let multi_proof = tree.multi_proof(positions).unwrap();

        // Serialize and add extra byte
        let mut serialized = multi_proof.encode_mut();
        serialized.extend_from_slice(&[0u8]);

        // Should fail to deserialize
        assert!(Proof::<Digest>::decode_cfg(&mut serialized, &positions.len()).is_err());
    }

    #[test]
    fn test_multi_proof_decode_insufficient_data() {
        let mut serialized = Vec::new();
        serialized.extend_from_slice(&8u32.encode()); // leaf_count
        serialized.extend_from_slice(&1usize.encode()); // claims 1 sibling but no data follows

        // Should fail because the buffer claims 1 sibling but doesn't have the data
        let err = Proof::<Digest>::decode_cfg(serialized.as_slice(), &1).unwrap_err();
        assert!(matches!(err, commonware_codec::Error::EndOfBuffer));
    }

    #[test]
    fn test_multi_proof_invalid_position() {
        // Create test data
        let digests: Vec<Digest> = (0..8u32).map(|i| Sha256::hash(&i.to_be_bytes())).collect();

        // Build tree
        let mut builder = Builder::<Sha256>::new(digests.len());
        for digest in &digests {
            builder.add(digest);
        }
        let tree = builder.build();

        // Test out of bounds position
        assert!(matches!(
            tree.multi_proof([0, 8]),
            Err(Error::InvalidPosition(8))
        ));
        assert!(matches!(
            tree.multi_proof([100]),
            Err(Error::InvalidPosition(100))
        ));
    }

    #[test]
    fn test_multi_proof_verify_invalid_position() {
        // Create test data
        let digests: Vec<Digest> = (0..8u32).map(|i| Sha256::hash(&i.to_be_bytes())).collect();

        // Build tree
        let mut builder = Builder::<Sha256>::new(digests.len());
        for digest in &digests {
            builder.add(digest);
        }
        let tree = builder.build();
        let root = tree.root();
        let mut hasher = Sha256::default();

        // Generate valid proof
        let positions = [0, 3];
        let multi_proof = tree.multi_proof(positions).unwrap();

        // Try to verify with out of bounds position
        let invalid_elements = [(digests[0], 0), (digests[3], 100)];
        assert!(multi_proof
            .verify_multi_inclusion(&mut hasher, &invalid_elements, &root)
            .is_err());
    }

    #[test]
    fn test_multi_proof_odd_tree_sizes() {
        // Test odd-sized trees that require node duplication
        for tree_size in [3, 5, 7, 9, 11, 13, 15] {
            let digests: Vec<Digest> = (0..tree_size as u32)
                .map(|i| Sha256::hash(&i.to_be_bytes()))
                .collect();

            // Build tree
            let mut builder = Builder::<Sha256>::new(digests.len());
            for digest in &digests {
                builder.add(digest);
            }
            let tree = builder.build();
            let root = tree.root();
            let mut hasher = Sha256::default();

            // Test with positions including the last element
            let positions = [0, (tree_size - 1) as u32];
            let multi_proof = tree.multi_proof(positions).unwrap();

            let elements: Vec<(Digest, u32)> = positions
                .iter()
                .map(|&p| (digests[p as usize], p))
                .collect();
            assert!(
                multi_proof
                    .verify_multi_inclusion(&mut hasher, &elements, &root)
                    .is_ok(),
                "Failed for tree_size={tree_size}"
            );
        }
    }

    #[test]
    fn test_multi_proof_verify_empty_elements() {
        // Create a valid proof and try to verify with empty elements
        let digests: Vec<Digest> = (0..8u32).map(|i| Sha256::hash(&i.to_be_bytes())).collect();

        let mut builder = Builder::<Sha256>::new(digests.len());
        for digest in &digests {
            builder.add(digest);
        }
        let tree = builder.build();
        let root = tree.root();
        let mut hasher = Sha256::default();

        // Generate valid proof
        let positions = [0, 3];
        let multi_proof = tree.multi_proof(positions).unwrap();

        // Try to verify with empty elements
        let empty_elements: &[(Digest, u32)] = &[];
        assert!(multi_proof
            .verify_multi_inclusion(&mut hasher, empty_elements, &root)
            .is_err());
    }

    #[test]
    fn test_multi_proof_default_verify() {
        // Default (empty) proof should only verify against empty tree
        let mut hasher = Sha256::default();
        let default_proof = Proof::<Digest>::default();

        // Empty elements against default proof
        let empty_elements: &[(Digest, u32)] = &[];

        // Build empty tree to get the empty root
        let builder = Builder::<Sha256>::new(0);
        let empty_tree = builder.build();
        let empty_root = empty_tree.root();

        assert!(default_proof
            .verify_multi_inclusion(&mut hasher, empty_elements, &empty_root)
            .is_ok());

        // Should fail with wrong root
        let wrong_root = Sha256::hash(b"not_empty");
        assert!(default_proof
            .verify_multi_inclusion(&mut hasher, empty_elements, &wrong_root)
            .is_err());
    }

    #[test]
    fn test_multi_proof_single_leaf_tree() {
        // Edge case: tree with exactly one leaf
        let digest = Sha256::hash(b"only_leaf");

        // Build single-leaf tree
        let mut builder = Builder::<Sha256>::new(1);
        builder.add(&digest);
        let tree = builder.build();
        let root = tree.root();
        let mut hasher = Sha256::default();

        // Generate multi-proof for the only leaf
        let multi_proof = tree.multi_proof([0]).unwrap();

        // Single leaf tree: leaf_count should be 1
        assert_eq!(multi_proof.leaf_count, 1);

        // Single leaf tree: no siblings needed (leaf is the root after position hashing)
        assert!(
            multi_proof.siblings.is_empty(),
            "Single leaf tree should have no siblings"
        );

        // Verify the proof
        let elements = [(digest, 0u32)];
        assert!(
            multi_proof
                .verify_multi_inclusion(&mut hasher, &elements, &root)
                .is_ok(),
            "Single leaf multi-proof verification failed"
        );

        // Verify with wrong digest fails
        let wrong_digest = Sha256::hash(b"wrong");
        let wrong_elements = [(wrong_digest, 0u32)];
        assert!(
            multi_proof
                .verify_multi_inclusion(&mut hasher, &wrong_elements, &root)
                .is_err(),
            "Should fail with wrong digest"
        );

        // Verify with wrong position fails
        let wrong_position_elements = [(digest, 1u32)];
        assert!(
            multi_proof
                .verify_multi_inclusion(&mut hasher, &wrong_position_elements, &root)
                .is_err(),
            "Should fail with invalid position"
        );
    }

    #[test]
    fn test_multi_proof_malicious_leaf_count_zero() {
        // Attacker sets leaf_count = 0 but provides siblings
        let digests: Vec<Digest> = (0..8u32).map(|i| Sha256::hash(&i.to_be_bytes())).collect();

        let mut builder = Builder::<Sha256>::new(digests.len());
        for digest in &digests {
            builder.add(digest);
        }
        let tree = builder.build();
        let root = tree.root();
        let mut hasher = Sha256::default();

        // Generate valid proof and tamper with leaf_count
        let positions = [0, 3];
        let mut multi_proof = tree.multi_proof(positions).unwrap();
        multi_proof.leaf_count = 0;

        let elements: Vec<(Digest, u32)> = positions
            .iter()
            .map(|&p| (digests[p as usize], p))
            .collect();

        // Should fail - leaf_count=0 but we have elements
        assert!(multi_proof
            .verify_multi_inclusion(&mut hasher, &elements, &root)
            .is_err());
    }

    #[test]
    fn test_multi_proof_malicious_leaf_count_larger() {
        // Attacker inflates leaf_count to claim proof is for larger tree
        let digests: Vec<Digest> = (0..8u32).map(|i| Sha256::hash(&i.to_be_bytes())).collect();

        let mut builder = Builder::<Sha256>::new(digests.len());
        for digest in &digests {
            builder.add(digest);
        }
        let tree = builder.build();
        let root = tree.root();
        let mut hasher = Sha256::default();

        // Generate valid proof and inflate leaf_count
        let positions = [0, 3];
        let mut multi_proof = tree.multi_proof(positions).unwrap();
        let original_leaf_count = multi_proof.leaf_count;
        multi_proof.leaf_count = 1000;

        let elements: Vec<(Digest, u32)> = positions
            .iter()
            .map(|&p| (digests[p as usize], p))
            .collect();

        // Should fail - inflated leaf_count changes required siblings
        assert!(
            multi_proof
                .verify_multi_inclusion(&mut hasher, &elements, &root)
                .is_err(),
            "Should reject proof with inflated leaf_count ({} -> {})",
            original_leaf_count,
            multi_proof.leaf_count
        );
    }

    #[test]
    fn test_multi_proof_malicious_leaf_count_smaller() {
        // Attacker deflates leaf_count to claim proof is for smaller tree
        let digests: Vec<Digest> = (0..8u32).map(|i| Sha256::hash(&i.to_be_bytes())).collect();

        let mut builder = Builder::<Sha256>::new(digests.len());
        for digest in &digests {
            builder.add(digest);
        }
        let tree = builder.build();
        let root = tree.root();
        let mut hasher = Sha256::default();

        // Generate valid proof and deflate leaf_count
        let positions = [0, 3];
        let mut multi_proof = tree.multi_proof(positions).unwrap();
        multi_proof.leaf_count = 4; // Smaller than actual tree

        let elements: Vec<(Digest, u32)> = positions
            .iter()
            .map(|&p| (digests[p as usize], p))
            .collect();

        // Should fail - deflated leaf_count changes tree structure
        assert!(
            multi_proof
                .verify_multi_inclusion(&mut hasher, &elements, &root)
                .is_err(),
            "Should reject proof with deflated leaf_count"
        );
    }

    #[test]
    fn test_multi_proof_mismatched_element_count() {
        // Provide more or fewer elements than the proof was generated for
        let digests: Vec<Digest> = (0..8u32).map(|i| Sha256::hash(&i.to_be_bytes())).collect();

        let mut builder = Builder::<Sha256>::new(digests.len());
        for digest in &digests {
            builder.add(digest);
        }
        let tree = builder.build();
        let root = tree.root();
        let mut hasher = Sha256::default();

        // Generate proof for 2 positions
        let positions = [0, 3];
        let multi_proof = tree.multi_proof(positions).unwrap();

        // Try to verify with only 1 element (too few)
        let too_few = [(digests[0], 0u32)];
        assert!(
            multi_proof
                .verify_multi_inclusion(&mut hasher, &too_few, &root)
                .is_err(),
            "Should reject when fewer elements provided than proof was generated for"
        );

        // Try to verify with 3 elements (too many)
        let too_many = [(digests[0], 0u32), (digests[3], 3), (digests[5], 5)];
        assert!(
            multi_proof
                .verify_multi_inclusion(&mut hasher, &too_many, &root)
                .is_err(),
            "Should reject when more elements provided than proof was generated for"
        );
    }

    #[test]
    fn test_multi_proof_swapped_siblings() {
        // Swap the order of siblings in the proof
        let digests: Vec<Digest> = (0..8u32).map(|i| Sha256::hash(&i.to_be_bytes())).collect();

        let mut builder = Builder::<Sha256>::new(digests.len());
        for digest in &digests {
            builder.add(digest);
        }
        let tree = builder.build();
        let root = tree.root();
        let mut hasher = Sha256::default();

        // Generate valid proof with multiple siblings
        let positions = [0, 5];
        let mut multi_proof = tree.multi_proof(positions).unwrap();

        // Ensure we have at least 2 siblings to swap
        if multi_proof.siblings.len() >= 2 {
            // Swap first two siblings
            multi_proof.siblings.swap(0, 1);

            let elements: Vec<(Digest, u32)> = positions
                .iter()
                .map(|&p| (digests[p as usize], p))
                .collect();

            assert!(
                multi_proof
                    .verify_multi_inclusion(&mut hasher, &elements, &root)
                    .is_err(),
                "Should reject proof with swapped siblings"
            );
        }
    }

    #[test]
    fn test_multi_proof_dos_large_leaf_count() {
        // Attacker sets massive leaf_count trying to cause DoS via memory allocation
        // The verify function should NOT allocate proportional to leaf_count
        let digests: Vec<Digest> = (0..4u32).map(|i| Sha256::hash(&i.to_be_bytes())).collect();

        let mut builder = Builder::<Sha256>::new(digests.len());
        for digest in &digests {
            builder.add(digest);
        }
        let tree = builder.build();
        let root = tree.root();
        let mut hasher = Sha256::default();

        // Generate valid proof
        let positions = [0, 2];
        let mut multi_proof = tree.multi_proof(positions).unwrap();

        // Set massive leaf_count (attacker trying to exhaust memory)
        multi_proof.leaf_count = u32::MAX;

        let elements: Vec<(Digest, u32)> = positions
            .iter()
            .map(|&p| (digests[p as usize], p))
            .collect();

        // This should fail quickly without allocating massive memory
        // The function is O(elements * levels), not O(leaf_count)
        let result = multi_proof.verify_multi_inclusion(&mut hasher, &elements, &root);
        assert!(result.is_err(), "Should reject malicious large leaf_count");
    }

    #[cfg(feature = "arbitrary")]
    mod conformance {
        use super::*;
        use commonware_codec::conformance::CodecConformance;
        use commonware_conformance::Conformance;
        use commonware_cryptography::sha256::Digest as Sha256Digest;

        fn test_merkle_tree(n: usize) -> Digest {
            // Build tree
            let mut digests = Vec::with_capacity(n);
            let mut builder = Builder::<Sha256>::new(n);
            for i in 0..n {
                let digest = Sha256::hash(&i.to_be_bytes());
                builder.add(&digest);
                digests.push(digest);
            }
            let tree = builder.build();
            let root = tree.root();

            // For each leaf, generate and verify its proof
            let mut hasher = Sha256::default();
            for (i, leaf) in digests.iter().enumerate() {
                // Generate proof
                let proof = tree.proof(i as u32).unwrap();
                assert!(
                    proof
                        .verify_element_inclusion(&mut hasher, leaf, i as u32, &root)
                        .is_ok(),
                    "correct fail for size={n} leaf={i}"
                );

                // Serialize and deserialize the proof
                let serialized = proof.encode();
                let deserialized = Proof::<Digest>::decode_cfg(serialized, &1).unwrap();
                assert!(
                    deserialized
                        .verify_element_inclusion(&mut hasher, leaf, i as u32, &root)
                        .is_ok(),
                    "deserialize fail for size={n} leaf={i}"
                );

                // Modify a sibling hash and ensure the proof fails
                if !proof.siblings.is_empty() {
                    let mut update_tamper = proof.clone();
                    update_tamper.siblings[0] = Sha256::hash(b"tampered");
                    assert!(
                        update_tamper
                            .verify_element_inclusion(&mut hasher, leaf, i as u32, &root)
                            .is_err(),
                        "modify fail for size={n} leaf={i}"
                    );
                }

                // Add a sibling hash and ensure the proof fails
                let mut add_tamper = proof.clone();
                add_tamper.siblings.push(Sha256::hash(b"tampered"));
                assert!(
                    add_tamper
                        .verify_element_inclusion(&mut hasher, leaf, i as u32, &root)
                        .is_err(),
                    "add fail for size={n} leaf={i}"
                );

                // Remove a sibling hash and ensure the proof fails
                if !proof.siblings.is_empty() {
                    let mut remove_tamper = proof.clone();
                    remove_tamper.siblings.pop();
                    assert!(
                        remove_tamper
                            .verify_element_inclusion(&mut hasher, leaf, i as u32, &root)
                            .is_err(),
                        "remove fail for size={n} leaf={i}"
                    );
                }
            }

            // Test proof for larger than size
            assert!(tree.proof(n as u32).is_err());

            // Return the root so we can ensure we don't silently change.
            root
        }

        struct RootConformance;

        impl Conformance for RootConformance {
            async fn commit(seed: u64) -> Vec<u8> {
                let root = test_merkle_tree(seed as usize);
                root.to_vec()
            }
        }

        commonware_conformance::conformance_tests! {
            CodecConformance<Proof<Sha256Digest>>,
            RootConformance => 200
        }
    }
}