merkle_tree.rs

//! Parsers and serializers for Zcash Merkle trees.

use byteorder::{LittleEndian, ReadBytesExt, WriteBytesExt};
use incrementalmerkletree::{
    frontier::{CommitmentTree, Frontier, NonEmptyFrontier},
    witness::IncrementalWitness,
    Address, Hashable, Level, MerklePath, Position,
};
use orchard::tree::MerkleHashOrchard;
use std::io::{self, Read, Write};
use zcash_encoding::{Optional, Vector};

use crate::sapling;

/// A hashable node within a Merkle tree.
pub trait HashSer {
    /// Parses a node from the given byte source.
    fn read<R: Read>(reader: R) -> io::Result<Self>
    where
        Self: Sized;

    /// Serializes this node.
    fn write<W: Write>(&self, writer: W) -> io::Result<()>;
}

impl HashSer for sapling::Node {
    fn read<R: Read>(mut reader: R) -> io::Result<Self> {
        let mut repr = [0u8; 32];
        reader.read_exact(&mut repr)?;
        Option::from(Self::from_bytes(repr)).ok_or_else(|| {
            io::Error::new(
                io::ErrorKind::InvalidData,
                "Non-canonical encoding of Jubjub base field value.",
            )
        })
    }

    fn write<W: Write>(&self, mut writer: W) -> io::Result<()> {
        writer.write_all(&self.to_bytes())
    }
}

impl HashSer for MerkleHashOrchard {
    fn read<R: Read>(mut reader: R) -> io::Result<Self>
    where
        Self: Sized,
    {
        let mut repr = [0u8; 32];
        reader.read_exact(&mut repr)?;
        <Option<_>>::from(Self::from_bytes(&repr)).ok_or_else(|| {
            io::Error::new(
                io::ErrorKind::InvalidData,
                "Non-canonical encoding of Pallas base field value.",
            )
        })
    }

    fn write<W: Write>(&self, mut writer: W) -> io::Result<()> {
        writer.write_all(&self.to_bytes())
    }
}

/// Writes a usize value encoded as a u64 in little-endian order. Since usize
/// is platform-dependent, we consistently represent it as u64 in serialized
/// formats.
pub fn write_usize_leu64<W: Write>(mut writer: W, value: usize) -> io::Result<()> {
    // Panic if we get a usize value that can't fit into a u64.
    writer.write_u64::<LittleEndian>(value.try_into().unwrap())
}

/// Reads a usize value encoded as a u64 in little-endian order. Since usize
/// is platform-dependent, we consistently represent it as u64 in serialized
/// formats.
pub fn read_leu64_usize<R: Read>(mut reader: R) -> io::Result<usize> {
    reader.read_u64::<LittleEndian>()?.try_into().map_err(|e| {
        io::Error::new(
            io::ErrorKind::InvalidData,
            format!(
                "usize could not be decoded from a 64-bit value on this platform: {:?}",
                e
            ),
        )
    })
}

pub fn write_position<W: Write>(mut writer: W, position: Position) -> io::Result<()> {
    writer.write_u64::<LittleEndian>(position.into())
}

pub fn read_position<R: Read>(mut reader: R) -> io::Result<Position> {
    reader.read_u64::<LittleEndian>().map(Position::from)
}

pub fn write_address<W: Write>(mut writer: W, addr: Address) -> io::Result<()> {
    writer.write_u8(addr.level().into())?;
    writer.write_u64::<LittleEndian>(addr.index())
}

pub fn read_address<R: Read>(mut reader: R) -> io::Result<Address> {
    let level = reader.read_u8().map(Level::from)?;
    let index = reader.read_u64::<LittleEndian>()?;
    Ok(Address::from_parts(level, index))
}

pub fn read_frontier_v0<H: Hashable + HashSer + Clone, R: Read>(
    mut reader: R,
) -> io::Result<Frontier<H, { sapling::NOTE_COMMITMENT_TREE_DEPTH }>> {
    let tree = read_commitment_tree(&mut reader)?;

    Ok(tree.to_frontier())
}

pub fn write_nonempty_frontier_v1<H: HashSer, W: Write>(
    mut writer: W,
    frontier: &NonEmptyFrontier<H>,
) -> io::Result<()> {
    write_position(&mut writer, frontier.position())?;
    if frontier.position().is_right_child() {
        // The v1 serialization wrote the sibling of a right-hand leaf as an optional value, rather
        // than as part of the ommers vector.
        frontier
            .ommers()
            .get(0)
            .expect("ommers vector cannot be empty for right-hand nodes")
            .write(&mut writer)?;
        Optional::write(&mut writer, Some(frontier.leaf()), |w, n: &H| n.write(w))?;
        Vector::write(&mut writer, &frontier.ommers()[1..], |w, e| e.write(w))?;
    } else {
        frontier.leaf().write(&mut writer)?;
        Optional::write(&mut writer, None, |w, n: &H| n.write(w))?;
        Vector::write(&mut writer, frontier.ommers(), |w, e| e.write(w))?;
    }

    Ok(())
}

#[allow(clippy::redundant_closure)]
pub fn read_nonempty_frontier_v1<H: HashSer + Clone, R: Read>(
    mut reader: R,
) -> io::Result<NonEmptyFrontier<H>> {
    let position = read_position(&mut reader)?;
    let left = H::read(&mut reader)?;
    let right = Optional::read(&mut reader, H::read)?;
    let mut ommers = Vector::read(&mut reader, |r| H::read(r))?;

    let leaf = if let Some(right) = right {
        // if the frontier has a right leaf, then the left leaf is the first ommer
        ommers.insert(0, left);
        right
    } else {
        left
    };

    NonEmptyFrontier::from_parts(position, leaf, ommers).map_err(|err| {
        io::Error::new(
            io::ErrorKind::InvalidData,
            format!("Parsing resulted in an invalid Merkle frontier: {:?}", err),
        )
    })
}

pub fn write_frontier_v1<H: HashSer, W: Write>(
    writer: W,
    frontier: &Frontier<H, 32>,
) -> io::Result<()> {
    Optional::write(writer, frontier.value(), write_nonempty_frontier_v1)
}

#[allow(clippy::redundant_closure)]
pub fn read_frontier_v1<H: HashSer + Clone, R: Read>(reader: R) -> io::Result<Frontier<H, 32>> {
    match Optional::read(reader, read_nonempty_frontier_v1)? {
        None => Ok(Frontier::empty()),
        Some(f) => Frontier::try_from(f).map_err(|err| {
            io::Error::new(
                io::ErrorKind::InvalidData,
                format!("Parsing resulted in an invalid Merkle frontier: {:?}", err),
            )
        }),
    }
}

/// Reads a legacy `CommitmentTree` from its serialized form.
pub fn read_commitment_tree<Node: HashSer, R: Read, const DEPTH: u8>(
    mut reader: R,
) -> io::Result<CommitmentTree<Node, DEPTH>> {
    let left = Optional::read(&mut reader, Node::read)?;
    let right = Optional::read(&mut reader, Node::read)?;
    let parents = Vector::read(&mut reader, |r| Optional::read(r, Node::read))?;

    CommitmentTree::from_parts(left, right, parents).map_err(|_| {
        io::Error::new(
            io::ErrorKind::InvalidData,
            "parents vector exceeded tree depth",
        )
    })
}

/// Serializes a legacy `CommitmentTree` as an array of bytes.
pub fn write_commitment_tree<Node: HashSer, W: Write, const DEPTH: u8>(
    tree: &CommitmentTree<Node, DEPTH>,
    mut writer: W,
) -> io::Result<()> {
    Optional::write(&mut writer, tree.left().as_ref(), |w, n| n.write(w))?;
    Optional::write(&mut writer, tree.right().as_ref(), |w, n| n.write(w))?;
    Vector::write(&mut writer, tree.parents(), |w, e| {
        Optional::write(w, e.as_ref(), |w, n| n.write(w))
    })
}

/// Reads an `IncrementalWitness` from its serialized form.
#[allow(clippy::redundant_closure)]
pub fn read_incremental_witness<Node: HashSer, R: Read, const DEPTH: u8>(
    mut reader: R,
) -> io::Result<IncrementalWitness<Node, DEPTH>> {
    let tree = read_commitment_tree(&mut reader)?;
    let filled = Vector::read(&mut reader, |r| Node::read(r))?;
    let cursor = Optional::read(&mut reader, read_commitment_tree)?;

    Ok(IncrementalWitness::from_parts(tree, filled, cursor))
}

/// Serializes an `IncrementalWitness` as an array of bytes.
pub fn write_incremental_witness<Node: HashSer, W: Write, const DEPTH: u8>(
    witness: &IncrementalWitness<Node, DEPTH>,
    mut writer: W,
) -> io::Result<()> {
    write_commitment_tree(witness.tree(), &mut writer)?;
    Vector::write(&mut writer, witness.filled(), |w, n| n.write(w))?;
    Optional::write(&mut writer, witness.cursor().as_ref(), |w, t| {
        write_commitment_tree(t, w)
    })
}

/// Reads a Merkle path from its serialized form.
pub fn merkle_path_from_slice<Node: HashSer, const DEPTH: u8>(
    mut witness: &[u8],
) -> io::Result<MerklePath<Node, DEPTH>> {
    // Skip the first byte, which should be DEPTH to signify the length of
    // the following vector of Pedersen hashes.
    if witness[0] != DEPTH {
        return Err(io::Error::new(
            io::ErrorKind::InvalidData,
            "depth is not as expected",
        ));
    }
    witness = &witness[1..];

    // Begin to construct the authentication path
    let iter = witness.chunks_exact(33);
    witness = iter.remainder();

    // The vector works in reverse
    let auth_path = iter
        .rev()
        .map(|bytes| {
            // Length of inner vector should be the length of a Pedersen hash
            if bytes[0] == 32 {
                // Sibling node should be an element of Fr
                Node::read(&bytes[1..])
            } else {
                Err(io::Error::new(
                    io::ErrorKind::InvalidData,
                    "length of auth path element is not the expected 32 bytes",
                ))
            }
        })
        .collect::<io::Result<Vec<_>>>()?;
    if auth_path.len() != usize::from(DEPTH) {
        return Err(io::Error::new(
            io::ErrorKind::InvalidData,
            format!("length of auth path is not the expected {} elements", DEPTH),
        ));
    }

    // Read the position from the witness
    let position = witness.read_u64::<LittleEndian>().and_then(|p| {
        Position::try_from(p).map_err(|_| {
            io::Error::new(
                io::ErrorKind::InvalidData,
                format!("decoded position {} exceeded the range of a `usize`", p),
            )
        })
    })?;

    // The witness should be empty now; if it wasn't, the caller would
    // have provided more information than they should have, indicating
    // a bug downstream
    if witness.is_empty() {
        let path_len = auth_path.len();
        MerklePath::from_parts(auth_path, position).map_err(|_| {
            io::Error::new(
                io::ErrorKind::InvalidData,
                format!(
                    "auth path expected to contain {} elements, got {}",
                    DEPTH, path_len
                ),
            )
        })
    } else {
        Err(io::Error::new(
            io::ErrorKind::InvalidData,
            "trailing data found in auth path decoding",
        ))
    }
}

#[cfg(any(test, feature = "test-dependencies"))]
pub mod testing {
    use byteorder::{LittleEndian, ReadBytesExt, WriteBytesExt};
    use incrementalmerkletree::frontier::testing::TestNode;
    use std::io::{self, Read, Write};
    use zcash_encoding::Vector;

    use super::HashSer;

    impl HashSer for TestNode {
        fn read<R: Read>(mut reader: R) -> io::Result<TestNode> {
            reader.read_u64::<LittleEndian>().map(TestNode)
        }

        fn write<W: Write>(&self, mut writer: W) -> io::Result<()> {
            writer.write_u64::<LittleEndian>(self.0)
        }
    }

    impl HashSer for String {
        fn read<R: Read>(reader: R) -> io::Result<String> {
            Vector::read(reader, |r| r.read_u8()).and_then(|xs| {
                String::from_utf8(xs).map_err(|e| {
                    io::Error::new(
                        io::ErrorKind::InvalidData,
                        format!("Not a valid utf8 string: {:?}", e),
                    )
                })
            })
        }

        fn write<W: Write>(&self, writer: W) -> io::Result<()> {
            Vector::write(writer, self.as_bytes(), |w, b| w.write_u8(*b))
        }
    }
}

#[cfg(test)]
mod tests {
    use assert_matches::assert_matches;
    use incrementalmerkletree::{
        frontier::{testing::arb_commitment_tree, Frontier, PathFiller},
        witness::IncrementalWitness,
        Hashable,
    };
    use proptest::prelude::*;
    use proptest::strategy::Strategy;

    use super::{
        merkle_path_from_slice, read_commitment_tree, read_frontier_v0, read_frontier_v1,
        read_incremental_witness, write_commitment_tree, write_frontier_v1,
        write_incremental_witness, CommitmentTree, HashSer,
    };
    use crate::sapling::{self, Node};

    proptest! {
        #[test]
        fn frontier_serialization_v0(t in arb_commitment_tree::<_, _, 32>(0, sapling::testing::arb_node()))
        {
            let mut buffer = vec![];
            write_commitment_tree(&t, &mut buffer).unwrap();
            let frontier: Frontier<Node, 32> = read_frontier_v0(&buffer[..]).unwrap();

            let expected: Frontier<Node, 32> = t.to_frontier();
            assert_eq!(frontier, expected);
        }

        #[test]
        fn frontier_serialization_v1(t in arb_commitment_tree::<_, _, 32>(1, sapling::testing::arb_node()))
        {
            let original: Frontier<Node, 32> = t.to_frontier();

            let mut buffer = vec![];
            write_frontier_v1(&mut buffer, &original).unwrap();
            let read: Frontier<Node, 32> = read_frontier_v1(&buffer[..]).unwrap();

            assert_eq!(read, original);
        }
    }

    const HEX_EMPTY_ROOTS: [&str; 33] = [
        "0100000000000000000000000000000000000000000000000000000000000000",
        "817de36ab2d57feb077634bca77819c8e0bd298c04f6fed0e6a83cc1356ca155",
        "ffe9fc03f18b176c998806439ff0bb8ad193afdb27b2ccbc88856916dd804e34",
        "d8283386ef2ef07ebdbb4383c12a739a953a4d6e0d6fb1139a4036d693bfbb6c",
        "e110de65c907b9dea4ae0bd83a4b0a51bea175646a64c12b4c9f931b2cb31b49",
        "912d82b2c2bca231f71efcf61737fbf0a08befa0416215aeef53e8bb6d23390a",
        "8ac9cf9c391e3fd42891d27238a81a8a5c1d3a72b1bcbea8cf44a58ce7389613",
        "d6c639ac24b46bd19341c91b13fdcab31581ddaf7f1411336a271f3d0aa52813",
        "7b99abdc3730991cc9274727d7d82d28cb794edbc7034b4f0053ff7c4b680444",
        "43ff5457f13b926b61df552d4e402ee6dc1463f99a535f9a713439264d5b616b",
        "ba49b659fbd0b7334211ea6a9d9df185c757e70aa81da562fb912b84f49bce72",
        "4777c8776a3b1e69b73a62fa701fa4f7a6282d9aee2c7a6b82e7937d7081c23c",
        "ec677114c27206f5debc1c1ed66f95e2b1885da5b7be3d736b1de98579473048",
        "1b77dac4d24fb7258c3c528704c59430b630718bec486421837021cf75dab651",
        "bd74b25aacb92378a871bf27d225cfc26baca344a1ea35fdd94510f3d157082c",
        "d6acdedf95f608e09fa53fb43dcd0990475726c5131210c9e5caeab97f0e642f",
        "1ea6675f9551eeb9dfaaa9247bc9858270d3d3a4c5afa7177a984d5ed1be2451",
        "6edb16d01907b759977d7650dad7e3ec049af1a3d875380b697c862c9ec5d51c",
        "cd1c8dbf6e3acc7a80439bc4962cf25b9dce7c896f3a5bd70803fc5a0e33cf00",
        "6aca8448d8263e547d5ff2950e2ed3839e998d31cbc6ac9fd57bc6002b159216",
        "8d5fa43e5a10d11605ac7430ba1f5d81fb1b68d29a640405767749e841527673",
        "08eeab0c13abd6069e6310197bf80f9c1ea6de78fd19cbae24d4a520e6cf3023",
        "0769557bc682b1bf308646fd0b22e648e8b9e98f57e29f5af40f6edb833e2c49",
        "4c6937d78f42685f84b43ad3b7b00f81285662f85c6a68ef11d62ad1a3ee0850",
        "fee0e52802cb0c46b1eb4d376c62697f4759f6c8917fa352571202fd778fd712",
        "16d6252968971a83da8521d65382e61f0176646d771c91528e3276ee45383e4a",
        "d2e1642c9a462229289e5b0e3b7f9008e0301cbb93385ee0e21da2545073cb58",
        "a5122c08ff9c161d9ca6fc462073396c7d7d38e8ee48cdb3bea7e2230134ed6a",
        "28e7b841dcbc47cceb69d7cb8d94245fb7cb2ba3a7a6bc18f13f945f7dbd6e2a",
        "e1f34b034d4a3cd28557e2907ebf990c918f64ecb50a94f01d6fda5ca5c7ef72",
        "12935f14b676509b81eb49ef25f39269ed72309238b4c145803544b646dca62d",
        "b2eed031d4d6a4f02a097f80b54cc1541d4163c6b6f5971f88b6e41d35c53814",
        "fbc2f4300c01f0b7820d00e3347c8da4ee614674376cbc45359daa54f9b5493e",
    ];

    #[test]
    fn empty_root_test_vectors() {
        let mut tmp = [0u8; 32];
        for (&expected, i) in HEX_EMPTY_ROOTS.iter().zip(0u8..) {
            Node::empty_root(i.into())
                .write(&mut tmp[..])
                .expect("length is 32 bytes");
            assert_eq!(hex::encode(tmp), expected);
        }
    }

    #[test]
    fn sapling_empty_root() {
        let mut tmp = [0u8; 32];
        sapling::CommitmentTree::empty()
            .root()
            .write(&mut tmp[..])
            .expect("length is 32 bytes");
        assert_eq!(
            hex::encode(tmp),
            "fbc2f4300c01f0b7820d00e3347c8da4ee614674376cbc45359daa54f9b5493e"
        );
    }

    #[test]
    fn empty_commitment_tree_roots() {
        let tree = sapling::CommitmentTree::empty();
        let mut tmp = [0u8; 32];
        for (&expected, i) in HEX_EMPTY_ROOTS.iter().zip(0u8..).skip(1) {
            tree.root_at_depth(i, PathFiller::empty())
                .write(&mut tmp[..])
                .expect("length is 32 bytes");
            assert_eq!(hex::encode(tmp), expected);
        }
    }

    #[test]
    fn test_sapling_tree() {
        // From https://github.com/zcash/zcash/blob/master/src/test/data/merkle_commitments_sapling.json
        // Byte-reversed because the original test vectors are loaded using uint256S()
        let commitments = [
            "b02310f2e087e55bfd07ef5e242e3b87ee5d00c9ab52f61e6bd42542f93a6f55",
            "225747f3b5d5dab4e5a424f81f85c904ff43286e0f3fd07ef0b8c6a627b11458",
            "7c3ea01a6e3a3d90cf59cd789e467044b5cd78eb2c84cc6816f960746d0e036c",
            "50421d6c2c94571dfaaa135a4ff15bf916681ebd62c0e43e69e3b90684d0a030",
            "aaec63863aaa0b2e3b8009429bdddd455e59be6f40ccab887a32eb98723efc12",
            "f76748d40d5ee5f9a608512e7954dd515f86e8f6d009141c89163de1cf351a02",
            "bc8a5ec71647415c380203b681f7717366f3501661512225b6dc3e121efc0b2e",
            "da1adda2ccde9381e11151686c121e7f52d19a990439161c7eb5a9f94be5a511",
            "3a27fed5dbbc475d3880360e38638c882fd9b273b618fc433106896083f77446",
            "c7ca8f7df8fd997931d33985d935ee2d696856cc09cc516d419ea6365f163008",
            "f0fa37e8063b139d342246142fc48e7c0c50d0a62c97768589e06466742c3702",
            "e6d4d7685894d01b32f7e081ab188930be6c2b9f76d6847b7f382e3dddd7c608",
            "8cebb73be883466d18d3b0c06990520e80b936440a2c9fd184d92a1f06c4e826",
            "22fab8bcdb88154dbf5877ad1e2d7f1b541bc8a5ec1b52266095381339c27c03",
            "f43e3aac61e5a753062d4d0508c26ceaf5e4c0c58ba3c956e104b5d2cf67c41c",
            "3a3661bc12b72646c94bc6c92796e81953985ee62d80a9ec3645a9a95740ac15",
        ];

        // From https://github.com/zcash/zcash/blob/master/src/test/data/merkle_roots_sapling.json
        let roots = [
            "8c3daa300c9710bf24d2595536e7c80ff8d147faca726636d28e8683a0c27703",
            "8611f17378eb55e8c3c3f0a5f002e2b0a7ca39442fc928322b8072d1079c213d",
            "3db73b998d536be0e1c2ec124df8e0f383ae7b602968ff6a5276ca0695023c46",
            "7ac2e6442fec5970e116dfa4f2ee606f395366cafb1fa7dfd6c3de3ce18c4363",
            "6a8f11ab2a11c262e39ed4ea3825ae6c94739ccf94479cb69402c5722b034532",
            "149595eed0b54a7e694cc8a68372525b9ae2c7b102514f527460db91eb690565",
            "8c0432f1994a2381a7a4b5fda770336011f9e0b30784f9a5597901619c797045",
            "e780c48d70420601f3313ff8488d7766b70c059c53aa3cda2ff1ef57ff62383c",
            "f919f03caaed8a2c60f58c0d43838f83e670dc7e8ccd25daa04a13f3e8f45541",
            "74f32b36629724038e71cbd6823b5a666440205a7d1a9242e95870b53d81f34a",
            "a4af205a4e1ee02102866b23a68930ac33efda9235832f49b17fcc4939be4525",
            "a946a42f1636045a16e65b2308e036d9da70089686c87c692e45912bd1cab772",
            "a1db2dbac055364c1cb43cbeb49c7e2815bff855122602a2ad0fb981a91e0e39",
            "16329b3ba4f0640f4d306532d9ea6ba0fbf0e70e44ed57d27b4277ed9cda6849",
            "7b6523b2d9b23f72fec6234aa6a1f8fae3dba1c6a266023ea8b1826feba7a25c",
            "5c0bea7e17bde5bee4eb795c2eec3d389a68da587b36dd687b134826ecc09308",
        ];

        // From https://github.com/zcash/zcash/blob/master/src/test/data/merkle_serialization_sapling.json
        let tree_ser = [
            "01b02310f2e087e55bfd07ef5e242e3b87ee5d00c9ab52f61e6bd42542f93a6f550000",
            "01b02310f2e087e55bfd07ef5e242e3b87ee5d00c9ab52f61e6bd42542f93a6f5501225747f3b5d5dab4e5a424f81f85c904ff43286e0f3fd07ef0b8c6a627b1145800",
            "017c3ea01a6e3a3d90cf59cd789e467044b5cd78eb2c84cc6816f960746d0e036c00010162324ff2c329e99193a74d28a585a3c167a93bf41a255135529c913bd9b1e666",
            "017c3ea01a6e3a3d90cf59cd789e467044b5cd78eb2c84cc6816f960746d0e036c0150421d6c2c94571dfaaa135a4ff15bf916681ebd62c0e43e69e3b90684d0a030010162324ff2c329e99193a74d28a585a3c167a93bf41a255135529c913bd9b1e666",
            "01aaec63863aaa0b2e3b8009429bdddd455e59be6f40ccab887a32eb98723efc12000200011fb189b02ad2f7c6b0d09bd5691c4896c28269da3d4ba768b1b446f655186564",
            "01aaec63863aaa0b2e3b8009429bdddd455e59be6f40ccab887a32eb98723efc1201f76748d40d5ee5f9a608512e7954dd515f86e8f6d009141c89163de1cf351a020200011fb189b02ad2f7c6b0d09bd5691c4896c28269da3d4ba768b1b446f655186564",
            "01bc8a5ec71647415c380203b681f7717366f3501661512225b6dc3e121efc0b2e000201eb97b35d826f55a65e23ea7febf38fadea8517312ca79346c129a277260fd724011fb189b02ad2f7c6b0d09bd5691c4896c28269da3d4ba768b1b446f655186564",
            "01bc8a5ec71647415c380203b681f7717366f3501661512225b6dc3e121efc0b2e01da1adda2ccde9381e11151686c121e7f52d19a990439161c7eb5a9f94be5a5110201eb97b35d826f55a65e23ea7febf38fadea8517312ca79346c129a277260fd724011fb189b02ad2f7c6b0d09bd5691c4896c28269da3d4ba768b1b446f655186564",
            "013a27fed5dbbc475d3880360e38638c882fd9b273b618fc433106896083f7744600030000010d6b42350c11df4fcc17987c13d8492ba4e8b3f31eb9baff9be5d8890cfa512d",
            "013a27fed5dbbc475d3880360e38638c882fd9b273b618fc433106896083f7744601c7ca8f7df8fd997931d33985d935ee2d696856cc09cc516d419ea6365f163008030000010d6b42350c11df4fcc17987c13d8492ba4e8b3f31eb9baff9be5d8890cfa512d",
            "01f0fa37e8063b139d342246142fc48e7c0c50d0a62c97768589e06466742c3702000301cca46d2249e0d79669b8ad2e8c3fc5e67a8501112aa4e572fe03a1868ef3173200010d6b42350c11df4fcc17987c13d8492ba4e8b3f31eb9baff9be5d8890cfa512d",
            "01f0fa37e8063b139d342246142fc48e7c0c50d0a62c97768589e06466742c370201e6d4d7685894d01b32f7e081ab188930be6c2b9f76d6847b7f382e3dddd7c6080301cca46d2249e0d79669b8ad2e8c3fc5e67a8501112aa4e572fe03a1868ef3173200010d6b42350c11df4fcc17987c13d8492ba4e8b3f31eb9baff9be5d8890cfa512d",
            "018cebb73be883466d18d3b0c06990520e80b936440a2c9fd184d92a1f06c4e82600030001002df68503da9247dfde6585cb8c9fa94897cf21735f8fc1b32116ef474de05c010d6b42350c11df4fcc17987c13d8492ba4e8b3f31eb9baff9be5d8890cfa512d",
            "018cebb73be883466d18d3b0c06990520e80b936440a2c9fd184d92a1f06c4e8260122fab8bcdb88154dbf5877ad1e2d7f1b541bc8a5ec1b52266095381339c27c03030001002df68503da9247dfde6585cb8c9fa94897cf21735f8fc1b32116ef474de05c010d6b42350c11df4fcc17987c13d8492ba4e8b3f31eb9baff9be5d8890cfa512d",
            "01f43e3aac61e5a753062d4d0508c26ceaf5e4c0c58ba3c956e104b5d2cf67c41c0003015991131c5c25911b35fcea2a8343e2dfd7a4d5b45493390e0cb184394d91c34901002df68503da9247dfde6585cb8c9fa94897cf21735f8fc1b32116ef474de05c010d6b42350c11df4fcc17987c13d8492ba4e8b3f31eb9baff9be5d8890cfa512d",
            "01f43e3aac61e5a753062d4d0508c26ceaf5e4c0c58ba3c956e104b5d2cf67c41c013a3661bc12b72646c94bc6c92796e81953985ee62d80a9ec3645a9a95740ac1503015991131c5c25911b35fcea2a8343e2dfd7a4d5b45493390e0cb184394d91c34901002df68503da9247dfde6585cb8c9fa94897cf21735f8fc1b32116ef474de05c010d6b42350c11df4fcc17987c13d8492ba4e8b3f31eb9baff9be5d8890cfa512d",
        ];

        // From https://github.com/zcash/zcash/blob/master/src/test/data/merkle_path_sapling.json
        let paths = [
            "0420d8283386ef2ef07ebdbb4383c12a739a953a4d6e0d6fb1139a4036d693bfbb6c20ffe9fc03f18b176c998806439ff0bb8ad193afdb27b2ccbc88856916dd804e3420817de36ab2d57feb077634bca77819c8e0bd298c04f6fed0e6a83cc1356ca15520225747f3b5d5dab4e5a424f81f85c904ff43286e0f3fd07ef0b8c6a627b114580000000000000000",
            "0420d8283386ef2ef07ebdbb4383c12a739a953a4d6e0d6fb1139a4036d693bfbb6c20ffe9fc03f18b176c998806439ff0bb8ad193afdb27b2ccbc88856916dd804e342037b3a0921a4047e617bde62b8958f86c010e6af6cc650959b9f50af8c7e8392620225747f3b5d5dab4e5a424f81f85c904ff43286e0f3fd07ef0b8c6a627b114580000000000000000",
            "0420d8283386ef2ef07ebdbb4383c12a739a953a4d6e0d6fb1139a4036d693bfbb6c20ffe9fc03f18b176c998806439ff0bb8ad193afdb27b2ccbc88856916dd804e342037b3a0921a4047e617bde62b8958f86c010e6af6cc650959b9f50af8c7e8392620b02310f2e087e55bfd07ef5e242e3b87ee5d00c9ab52f61e6bd42542f93a6f550100000000000000",
            "0420d8283386ef2ef07ebdbb4383c12a739a953a4d6e0d6fb1139a4036d693bfbb6c20ffe9fc03f18b176c998806439ff0bb8ad193afdb27b2ccbc88856916dd804e3420f2c6ff34520c4ed63159b5ad4e99712fe64e3b4add73c66218e9797ac15a826420225747f3b5d5dab4e5a424f81f85c904ff43286e0f3fd07ef0b8c6a627b114580000000000000000",
            "0420d8283386ef2ef07ebdbb4383c12a739a953a4d6e0d6fb1139a4036d693bfbb6c20ffe9fc03f18b176c998806439ff0bb8ad193afdb27b2ccbc88856916dd804e3420f2c6ff34520c4ed63159b5ad4e99712fe64e3b4add73c66218e9797ac15a826420b02310f2e087e55bfd07ef5e242e3b87ee5d00c9ab52f61e6bd42542f93a6f550100000000000000",
            "0420d8283386ef2ef07ebdbb4383c12a739a953a4d6e0d6fb1139a4036d693bfbb6c20ffe9fc03f18b176c998806439ff0bb8ad193afdb27b2ccbc88856916dd804e342062324ff2c329e99193a74d28a585a3c167a93bf41a255135529c913bd9b1e6662050421d6c2c94571dfaaa135a4ff15bf916681ebd62c0e43e69e3b90684d0a0300200000000000000",
            "0420d8283386ef2ef07ebdbb4383c12a739a953a4d6e0d6fb1139a4036d693bfbb6c2031d39685384e4ea322594d99a15aa8bdd8cc5cd6724410fa385b8d5447f1740220f2c6ff34520c4ed63159b5ad4e99712fe64e3b4add73c66218e9797ac15a826420225747f3b5d5dab4e5a424f81f85c904ff43286e0f3fd07ef0b8c6a627b114580000000000000000",
            "0420d8283386ef2ef07ebdbb4383c12a739a953a4d6e0d6fb1139a4036d693bfbb6c2031d39685384e4ea322594d99a15aa8bdd8cc5cd6724410fa385b8d5447f1740220f2c6ff34520c4ed63159b5ad4e99712fe64e3b4add73c66218e9797ac15a826420b02310f2e087e55bfd07ef5e242e3b87ee5d00c9ab52f61e6bd42542f93a6f550100000000000000",
            "0420d8283386ef2ef07ebdbb4383c12a739a953a4d6e0d6fb1139a4036d693bfbb6c2031d39685384e4ea322594d99a15aa8bdd8cc5cd6724410fa385b8d5447f174022062324ff2c329e99193a74d28a585a3c167a93bf41a255135529c913bd9b1e6662050421d6c2c94571dfaaa135a4ff15bf916681ebd62c0e43e69e3b90684d0a0300200000000000000",
            "0420d8283386ef2ef07ebdbb4383c12a739a953a4d6e0d6fb1139a4036d693bfbb6c2031d39685384e4ea322594d99a15aa8bdd8cc5cd6724410fa385b8d5447f174022062324ff2c329e99193a74d28a585a3c167a93bf41a255135529c913bd9b1e666207c3ea01a6e3a3d90cf59cd789e467044b5cd78eb2c84cc6816f960746d0e036c0300000000000000",
            "0420d8283386ef2ef07ebdbb4383c12a739a953a4d6e0d6fb1139a4036d693bfbb6c20f0321eea8e13c2f3a567f894c9738759d9d01e64ec259caf2cecca61374c157320f2c6ff34520c4ed63159b5ad4e99712fe64e3b4add73c66218e9797ac15a826420225747f3b5d5dab4e5a424f81f85c904ff43286e0f3fd07ef0b8c6a627b114580000000000000000",
            "0420d8283386ef2ef07ebdbb4383c12a739a953a4d6e0d6fb1139a4036d693bfbb6c20f0321eea8e13c2f3a567f894c9738759d9d01e64ec259caf2cecca61374c157320f2c6ff34520c4ed63159b5ad4e99712fe64e3b4add73c66218e9797ac15a826420b02310f2e087e55bfd07ef5e242e3b87ee5d00c9ab52f61e6bd42542f93a6f550100000000000000",
            "0420d8283386ef2ef07ebdbb4383c12a739a953a4d6e0d6fb1139a4036d693bfbb6c20f0321eea8e13c2f3a567f894c9738759d9d01e64ec259caf2cecca61374c15732062324ff2c329e99193a74d28a585a3c167a93bf41a255135529c913bd9b1e6662050421d6c2c94571dfaaa135a4ff15bf916681ebd62c0e43e69e3b90684d0a0300200000000000000",
            "0420d8283386ef2ef07ebdbb4383c12a739a953a4d6e0d6fb1139a4036d693bfbb6c20f0321eea8e13c2f3a567f894c9738759d9d01e64ec259caf2cecca61374c15732062324ff2c329e99193a74d28a585a3c167a93bf41a255135529c913bd9b1e666207c3ea01a6e3a3d90cf59cd789e467044b5cd78eb2c84cc6816f960746d0e036c0300000000000000",
            "0420d8283386ef2ef07ebdbb4383c12a739a953a4d6e0d6fb1139a4036d693bfbb6c201fb189b02ad2f7c6b0d09bd5691c4896c28269da3d4ba768b1b446f65518656420817de36ab2d57feb077634bca77819c8e0bd298c04f6fed0e6a83cc1356ca15520f76748d40d5ee5f9a608512e7954dd515f86e8f6d009141c89163de1cf351a020400000000000000",
            "0420d8283386ef2ef07ebdbb4383c12a739a953a4d6e0d6fb1139a4036d693bfbb6c2082c424de0185a63f6ce0aa65d3d55890748af44bb4bb5822a9a21df34546d32220f2c6ff34520c4ed63159b5ad4e99712fe64e3b4add73c66218e9797ac15a826420225747f3b5d5dab4e5a424f81f85c904ff43286e0f3fd07ef0b8c6a627b114580000000000000000",
            "0420d8283386ef2ef07ebdbb4383c12a739a953a4d6e0d6fb1139a4036d693bfbb6c2082c424de0185a63f6ce0aa65d3d55890748af44bb4bb5822a9a21df34546d32220f2c6ff34520c4ed63159b5ad4e99712fe64e3b4add73c66218e9797ac15a826420b02310f2e087e55bfd07ef5e242e3b87ee5d00c9ab52f61e6bd42542f93a6f550100000000000000",
            "0420d8283386ef2ef07ebdbb4383c12a739a953a4d6e0d6fb1139a4036d693bfbb6c2082c424de0185a63f6ce0aa65d3d55890748af44bb4bb5822a9a21df34546d3222062324ff2c329e99193a74d28a585a3c167a93bf41a255135529c913bd9b1e6662050421d6c2c94571dfaaa135a4ff15bf916681ebd62c0e43e69e3b90684d0a0300200000000000000",
            "0420d8283386ef2ef07ebdbb4383c12a739a953a4d6e0d6fb1139a4036d693bfbb6c2082c424de0185a63f6ce0aa65d3d55890748af44bb4bb5822a9a21df34546d3222062324ff2c329e99193a74d28a585a3c167a93bf41a255135529c913bd9b1e666207c3ea01a6e3a3d90cf59cd789e467044b5cd78eb2c84cc6816f960746d0e036c0300000000000000",
            "0420d8283386ef2ef07ebdbb4383c12a739a953a4d6e0d6fb1139a4036d693bfbb6c201fb189b02ad2f7c6b0d09bd5691c4896c28269da3d4ba768b1b446f655186564206ab2e08286c36f6fe4374baebdc28b97e2f1f4ea3544fafd8a6489f42824bf0e20f76748d40d5ee5f9a608512e7954dd515f86e8f6d009141c89163de1cf351a020400000000000000",
            "0420d8283386ef2ef07ebdbb4383c12a739a953a4d6e0d6fb1139a4036d693bfbb6c201fb189b02ad2f7c6b0d09bd5691c4896c28269da3d4ba768b1b446f655186564206ab2e08286c36f6fe4374baebdc28b97e2f1f4ea3544fafd8a6489f42824bf0e20aaec63863aaa0b2e3b8009429bdddd455e59be6f40ccab887a32eb98723efc120500000000000000",
            "0420d8283386ef2ef07ebdbb4383c12a739a953a4d6e0d6fb1139a4036d693bfbb6c20130adab3afe0931c42f058efb1381c2dce6cc768ad7964330146bf88b2b34f2420f2c6ff34520c4ed63159b5ad4e99712fe64e3b4add73c66218e9797ac15a826420225747f3b5d5dab4e5a424f81f85c904ff43286e0f3fd07ef0b8c6a627b114580000000000000000",
            "0420d8283386ef2ef07ebdbb4383c12a739a953a4d6e0d6fb1139a4036d693bfbb6c20130adab3afe0931c42f058efb1381c2dce6cc768ad7964330146bf88b2b34f2420f2c6ff34520c4ed63159b5ad4e99712fe64e3b4add73c66218e9797ac15a826420b02310f2e087e55bfd07ef5e242e3b87ee5d00c9ab52f61e6bd42542f93a6f550100000000000000",
            "0420d8283386ef2ef07ebdbb4383c12a739a953a4d6e0d6fb1139a4036d693bfbb6c20130adab3afe0931c42f058efb1381c2dce6cc768ad7964330146bf88b2b34f242062324ff2c329e99193a74d28a585a3c167a93bf41a255135529c913bd9b1e6662050421d6c2c94571dfaaa135a4ff15bf916681ebd62c0e43e69e3b90684d0a0300200000000000000",
            "0420d8283386ef2ef07ebdbb4383c12a739a953a4d6e0d6fb1139a4036d693bfbb6c20130adab3afe0931c42f058efb1381c2dce6cc768ad7964330146bf88b2b34f242062324ff2c329e99193a74d28a585a3c167a93bf41a255135529c913bd9b1e666207c3ea01a6e3a3d90cf59cd789e467044b5cd78eb2c84cc6816f960746d0e036c0300000000000000",
            "0420d8283386ef2ef07ebdbb4383c12a739a953a4d6e0d6fb1139a4036d693bfbb6c201fb189b02ad2f7c6b0d09bd5691c4896c28269da3d4ba768b1b446f65518656420d0c26e22b78df58552b4fd61e8883a70f9011556b2e14b80ff23c591db7dbc4c20f76748d40d5ee5f9a608512e7954dd515f86e8f6d009141c89163de1cf351a020400000000000000",
            "0420d8283386ef2ef07ebdbb4383c12a739a953a4d6e0d6fb1139a4036d693bfbb6c201fb189b02ad2f7c6b0d09bd5691c4896c28269da3d4ba768b1b446f65518656420d0c26e22b78df58552b4fd61e8883a70f9011556b2e14b80ff23c591db7dbc4c20aaec63863aaa0b2e3b8009429bdddd455e59be6f40ccab887a32eb98723efc120500000000000000",
            "0420d8283386ef2ef07ebdbb4383c12a739a953a4d6e0d6fb1139a4036d693bfbb6c201fb189b02ad2f7c6b0d09bd5691c4896c28269da3d4ba768b1b446f65518656420eb97b35d826f55a65e23ea7febf38fadea8517312ca79346c129a277260fd72420da1adda2ccde9381e11151686c121e7f52d19a990439161c7eb5a9f94be5a5110600000000000000",
            "0420109713c6c346ab0b17904ae18d101d92a98a612116a3f787043c802b55d5573120130adab3afe0931c42f058efb1381c2dce6cc768ad7964330146bf88b2b34f2420f2c6ff34520c4ed63159b5ad4e99712fe64e3b4add73c66218e9797ac15a826420225747f3b5d5dab4e5a424f81f85c904ff43286e0f3fd07ef0b8c6a627b114580000000000000000",
            "0420109713c6c346ab0b17904ae18d101d92a98a612116a3f787043c802b55d5573120130adab3afe0931c42f058efb1381c2dce6cc768ad7964330146bf88b2b34f2420f2c6ff34520c4ed63159b5ad4e99712fe64e3b4add73c66218e9797ac15a826420b02310f2e087e55bfd07ef5e242e3b87ee5d00c9ab52f61e6bd42542f93a6f550100000000000000",
            "0420109713c6c346ab0b17904ae18d101d92a98a612116a3f787043c802b55d5573120130adab3afe0931c42f058efb1381c2dce6cc768ad7964330146bf88b2b34f242062324ff2c329e99193a74d28a585a3c167a93bf41a255135529c913bd9b1e6662050421d6c2c94571dfaaa135a4ff15bf916681ebd62c0e43e69e3b90684d0a0300200000000000000",
            "0420109713c6c346ab0b17904ae18d101d92a98a612116a3f787043c802b55d5573120130adab3afe0931c42f058efb1381c2dce6cc768ad7964330146bf88b2b34f242062324ff2c329e99193a74d28a585a3c167a93bf41a255135529c913bd9b1e666207c3ea01a6e3a3d90cf59cd789e467044b5cd78eb2c84cc6816f960746d0e036c0300000000000000",
            "0420109713c6c346ab0b17904ae18d101d92a98a612116a3f787043c802b55d55731201fb189b02ad2f7c6b0d09bd5691c4896c28269da3d4ba768b1b446f65518656420d0c26e22b78df58552b4fd61e8883a70f9011556b2e14b80ff23c591db7dbc4c20f76748d40d5ee5f9a608512e7954dd515f86e8f6d009141c89163de1cf351a020400000000000000",
            "0420109713c6c346ab0b17904ae18d101d92a98a612116a3f787043c802b55d55731201fb189b02ad2f7c6b0d09bd5691c4896c28269da3d4ba768b1b446f65518656420d0c26e22b78df58552b4fd61e8883a70f9011556b2e14b80ff23c591db7dbc4c20aaec63863aaa0b2e3b8009429bdddd455e59be6f40ccab887a32eb98723efc120500000000000000",
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            "0420c9cd5269cd697706cb0745d57f66e5ba4a5051fb910127318d283f751910ac71201fb189b02ad2f7c6b0d09bd5691c4896c28269da3d4ba768b1b446f65518656420d0c26e22b78df58552b4fd61e8883a70f9011556b2e14b80ff23c591db7dbc4c20aaec63863aaa0b2e3b8009429bdddd455e59be6f40ccab887a32eb98723efc120500000000000000",
            "0420c9cd5269cd697706cb0745d57f66e5ba4a5051fb910127318d283f751910ac71201fb189b02ad2f7c6b0d09bd5691c4896c28269da3d4ba768b1b446f65518656420eb97b35d826f55a65e23ea7febf38fadea8517312ca79346c129a277260fd72420da1adda2ccde9381e11151686c121e7f52d19a990439161c7eb5a9f94be5a5110600000000000000",
            "0420c9cd5269cd697706cb0745d57f66e5ba4a5051fb910127318d283f751910ac71201fb189b02ad2f7c6b0d09bd5691c4896c28269da3d4ba768b1b446f65518656420eb97b35d826f55a65e23ea7febf38fadea8517312ca79346c129a277260fd72420bc8a5ec71647415c380203b681f7717366f3501661512225b6dc3e121efc0b2e0700000000000000",
            "04200d6b42350c11df4fcc17987c13d8492ba4e8b3f31eb9baff9be5d8890cfa512d20c2b786e4ab72ae4f01c7241bc056817b19d42bc85107f42c3fd3a9b9e98f156420635c0b1b8035705127dc3f672191b4958ad331f9134117e3ba7d721f712b614420c7ca8f7df8fd997931d33985d935ee2d696856cc09cc516d419ea6365f1630080800000000000000",
            "04200d6b42350c11df4fcc17987c13d8492ba4e8b3f31eb9baff9be5d8890cfa512d20c2b786e4ab72ae4f01c7241bc056817b19d42bc85107f42c3fd3a9b9e98f156420635c0b1b8035705127dc3f672191b4958ad331f9134117e3ba7d721f712b6144203a27fed5dbbc475d3880360e38638c882fd9b273b618fc433106896083f774460900000000000000",
            "04200d6b42350c11df4fcc17987c13d8492ba4e8b3f31eb9baff9be5d8890cfa512d20c2b786e4ab72ae4f01c7241bc056817b19d42bc85107f42c3fd3a9b9e98f156420cca46d2249e0d79669b8ad2e8c3fc5e67a8501112aa4e572fe03a1868ef3173220e6d4d7685894d01b32f7e081ab188930be6c2b9f76d6847b7f382e3dddd7c6080a00000000000000",
            "04200d6b42350c11df4fcc17987c13d8492ba4e8b3f31eb9baff9be5d8890cfa512d20c2b786e4ab72ae4f01c7241bc056817b19d42bc85107f42c3fd3a9b9e98f156420cca46d2249e0d79669b8ad2e8c3fc5e67a8501112aa4e572fe03a1868ef3173220f0fa37e8063b139d342246142fc48e7c0c50d0a62c97768589e06466742c37020b00000000000000",
            "04200d6b42350c11df4fcc17987c13d8492ba4e8b3f31eb9baff9be5d8890cfa512d20002df68503da9247dfde6585cb8c9fa94897cf21735f8fc1b32116ef474de05c20817de36ab2d57feb077634bca77819c8e0bd298c04f6fed0e6a83cc1356ca1552022fab8bcdb88154dbf5877ad1e2d7f1b541bc8a5ec1b52266095381339c27c030c00000000000000",
            "04203cf9ea50bea2cebf829213d91c098813d11dbe5c6696cdaefab3249dbf892f5e20130adab3afe0931c42f058efb1381c2dce6cc768ad7964330146bf88b2b34f2420f2c6ff34520c4ed63159b5ad4e99712fe64e3b4add73c66218e9797ac15a826420225747f3b5d5dab4e5a424f81f85c904ff43286e0f3fd07ef0b8c6a627b114580000000000000000",
            "04203cf9ea50bea2cebf829213d91c098813d11dbe5c6696cdaefab3249dbf892f5e20130adab3afe0931c42f058efb1381c2dce6cc768ad7964330146bf88b2b34f2420f2c6ff34520c4ed63159b5ad4e99712fe64e3b4add73c66218e9797ac15a826420b02310f2e087e55bfd07ef5e242e3b87ee5d00c9ab52f61e6bd42542f93a6f550100000000000000",
            "04203cf9ea50bea2cebf829213d91c098813d11dbe5c6696cdaefab3249dbf892f5e20130adab3afe0931c42f058efb1381c2dce6cc768ad7964330146bf88b2b34f242062324ff2c329e99193a74d28a585a3c167a93bf41a255135529c913bd9b1e6662050421d6c2c94571dfaaa135a4ff15bf916681ebd62c0e43e69e3b90684d0a0300200000000000000",
            "04203cf9ea50bea2cebf829213d91c098813d11dbe5c6696cdaefab3249dbf892f5e20130adab3afe0931c42f058efb1381c2dce6cc768ad7964330146bf88b2b34f242062324ff2c329e99193a74d28a585a3c167a93bf41a255135529c913bd9b1e666207c3ea01a6e3a3d90cf59cd789e467044b5cd78eb2c84cc6816f960746d0e036c0300000000000000",
            "04203cf9ea50bea2cebf829213d91c098813d11dbe5c6696cdaefab3249dbf892f5e201fb189b02ad2f7c6b0d09bd5691c4896c28269da3d4ba768b1b446f65518656420d0c26e22b78df58552b4fd61e8883a70f9011556b2e14b80ff23c591db7dbc4c20f76748d40d5ee5f9a608512e7954dd515f86e8f6d009141c89163de1cf351a020400000000000000",
            "04203cf9ea50bea2cebf829213d91c098813d11dbe5c6696cdaefab3249dbf892f5e201fb189b02ad2f7c6b0d09bd5691c4896c28269da3d4ba768b1b446f65518656420d0c26e22b78df58552b4fd61e8883a70f9011556b2e14b80ff23c591db7dbc4c20aaec63863aaa0b2e3b8009429bdddd455e59be6f40ccab887a32eb98723efc120500000000000000",
            "04203cf9ea50bea2cebf829213d91c098813d11dbe5c6696cdaefab3249dbf892f5e201fb189b02ad2f7c6b0d09bd5691c4896c28269da3d4ba768b1b446f65518656420eb97b35d826f55a65e23ea7febf38fadea8517312ca79346c129a277260fd72420da1adda2ccde9381e11151686c121e7f52d19a990439161c7eb5a9f94be5a5110600000000000000",
            "04203cf9ea50bea2cebf829213d91c098813d11dbe5c6696cdaefab3249dbf892f5e201fb189b02ad2f7c6b0d09bd5691c4896c28269da3d4ba768b1b446f65518656420eb97b35d826f55a65e23ea7febf38fadea8517312ca79346c129a277260fd72420bc8a5ec71647415c380203b681f7717366f3501661512225b6dc3e121efc0b2e0700000000000000",
            "04200d6b42350c11df4fcc17987c13d8492ba4e8b3f31eb9baff9be5d8890cfa512d20cd6db4bcd77d6ca695b9579f9ec5791d106f83b69118bb3a2a2a99f63779e06720635c0b1b8035705127dc3f672191b4958ad331f9134117e3ba7d721f712b614420c7ca8f7df8fd997931d33985d935ee2d696856cc09cc516d419ea6365f1630080800000000000000",
            "04200d6b42350c11df4fcc17987c13d8492ba4e8b3f31eb9baff9be5d8890cfa512d20cd6db4bcd77d6ca695b9579f9ec5791d106f83b69118bb3a2a2a99f63779e06720635c0b1b8035705127dc3f672191b4958ad331f9134117e3ba7d721f712b6144203a27fed5dbbc475d3880360e38638c882fd9b273b618fc433106896083f774460900000000000000",
            "04200d6b42350c11df4fcc17987c13d8492ba4e8b3f31eb9baff9be5d8890cfa512d20cd6db4bcd77d6ca695b9579f9ec5791d106f83b69118bb3a2a2a99f63779e06720cca46d2249e0d79669b8ad2e8c3fc5e67a8501112aa4e572fe03a1868ef3173220e6d4d7685894d01b32f7e081ab188930be6c2b9f76d6847b7f382e3dddd7c6080a00000000000000",
            "04200d6b42350c11df4fcc17987c13d8492ba4e8b3f31eb9baff9be5d8890cfa512d20cd6db4bcd77d6ca695b9579f9ec5791d106f83b69118bb3a2a2a99f63779e06720cca46d2249e0d79669b8ad2e8c3fc5e67a8501112aa4e572fe03a1868ef3173220f0fa37e8063b139d342246142fc48e7c0c50d0a62c97768589e06466742c37020b00000000000000",
            "04200d6b42350c11df4fcc17987c13d8492ba4e8b3f31eb9baff9be5d8890cfa512d20002df68503da9247dfde6585cb8c9fa94897cf21735f8fc1b32116ef474de05c2045d573e80606a552974215e13b5d3e7b4dd8675c77b8d612d293475ee139b9472022fab8bcdb88154dbf5877ad1e2d7f1b541bc8a5ec1b52266095381339c27c030c00000000000000",
            "04200d6b42350c11df4fcc17987c13d8492ba4e8b3f31eb9baff9be5d8890cfa512d20002df68503da9247dfde6585cb8c9fa94897cf21735f8fc1b32116ef474de05c2045d573e80606a552974215e13b5d3e7b4dd8675c77b8d612d293475ee139b947208cebb73be883466d18d3b0c06990520e80b936440a2c9fd184d92a1f06c4e8260d00000000000000",
            "04201d73ff8e39cff60ff0d6402cc752a3351f1b434dccfa1941da3b1e422b73a33c20130adab3afe0931c42f058efb1381c2dce6cc768ad7964330146bf88b2b34f2420f2c6ff34520c4ed63159b5ad4e99712fe64e3b4add73c66218e9797ac15a826420225747f3b5d5dab4e5a424f81f85c904ff43286e0f3fd07ef0b8c6a627b114580000000000000000",
            "04201d73ff8e39cff60ff0d6402cc752a3351f1b434dccfa1941da3b1e422b73a33c20130adab3afe0931c42f058efb1381c2dce6cc768ad7964330146bf88b2b34f2420f2c6ff34520c4ed63159b5ad4e99712fe64e3b4add73c66218e9797ac15a826420b02310f2e087e55bfd07ef5e242e3b87ee5d00c9ab52f61e6bd42542f93a6f550100000000000000",
            "04201d73ff8e39cff60ff0d6402cc752a3351f1b434dccfa1941da3b1e422b73a33c20130adab3afe0931c42f058efb1381c2dce6cc768ad7964330146bf88b2b34f242062324ff2c329e99193a74d28a585a3c167a93bf41a255135529c913bd9b1e6662050421d6c2c94571dfaaa135a4ff15bf916681ebd62c0e43e69e3b90684d0a0300200000000000000",
            "04201d73ff8e39cff60ff0d6402cc752a3351f1b434dccfa1941da3b1e422b73a33c20130adab3afe0931c42f058efb1381c2dce6cc768ad7964330146bf88b2b34f242062324ff2c329e99193a74d28a585a3c167a93bf41a255135529c913bd9b1e666207c3ea01a6e3a3d90cf59cd789e467044b5cd78eb2c84cc6816f960746d0e036c0300000000000000",
            "04201d73ff8e39cff60ff0d6402cc752a3351f1b434dccfa1941da3b1e422b73a33c201fb189b02ad2f7c6b0d09bd5691c4896c28269da3d4ba768b1b446f65518656420d0c26e22b78df58552b4fd61e8883a70f9011556b2e14b80ff23c591db7dbc4c20f76748d40d5ee5f9a608512e7954dd515f86e8f6d009141c89163de1cf351a020400000000000000",
            "04201d73ff8e39cff60ff0d6402cc752a3351f1b434dccfa1941da3b1e422b73a33c201fb189b02ad2f7c6b0d09bd5691c4896c28269da3d4ba768b1b446f65518656420d0c26e22b78df58552b4fd61e8883a70f9011556b2e14b80ff23c591db7dbc4c20aaec63863aaa0b2e3b8009429bdddd455e59be6f40ccab887a32eb98723efc120500000000000000",
            "04201d73ff8e39cff60ff0d6402cc752a3351f1b434dccfa1941da3b1e422b73a33c201fb189b02ad2f7c6b0d09bd5691c4896c28269da3d4ba768b1b446f65518656420eb97b35d826f55a65e23ea7febf38fadea8517312ca79346c129a277260fd72420da1adda2ccde9381e11151686c121e7f52d19a990439161c7eb5a9f94be5a5110600000000000000",
            "04201d73ff8e39cff60ff0d6402cc752a3351f1b434dccfa1941da3b1e422b73a33c201fb189b02ad2f7c6b0d09bd5691c4896c28269da3d4ba768b1b446f65518656420eb97b35d826f55a65e23ea7febf38fadea8517312ca79346c129a277260fd72420bc8a5ec71647415c380203b681f7717366f3501661512225b6dc3e121efc0b2e0700000000000000",
            "04200d6b42350c11df4fcc17987c13d8492ba4e8b3f31eb9baff9be5d8890cfa512d20076795f3651049c8895a7d127eb9bb4a17698da400430b33fdd06b1d8160394020635c0b1b8035705127dc3f672191b4958ad331f9134117e3ba7d721f712b614420c7ca8f7df8fd997931d33985d935ee2d696856cc09cc516d419ea6365f1630080800000000000000",
            "04200d6b42350c11df4fcc17987c13d8492ba4e8b3f31eb9baff9be5d8890cfa512d20076795f3651049c8895a7d127eb9bb4a17698da400430b33fdd06b1d8160394020635c0b1b8035705127dc3f672191b4958ad331f9134117e3ba7d721f712b6144203a27fed5dbbc475d3880360e38638c882fd9b273b618fc433106896083f774460900000000000000",
            "04200d6b42350c11df4fcc17987c13d8492ba4e8b3f31eb9baff9be5d8890cfa512d20076795f3651049c8895a7d127eb9bb4a17698da400430b33fdd06b1d8160394020cca46d2249e0d79669b8ad2e8c3fc5e67a8501112aa4e572fe03a1868ef3173220e6d4d7685894d01b32f7e081ab188930be6c2b9f76d6847b7f382e3dddd7c6080a00000000000000",
            "04200d6b42350c11df4fcc17987c13d8492ba4e8b3f31eb9baff9be5d8890cfa512d20076795f3651049c8895a7d127eb9bb4a17698da400430b33fdd06b1d8160394020cca46d2249e0d79669b8ad2e8c3fc5e67a8501112aa4e572fe03a1868ef3173220f0fa37e8063b139d342246142fc48e7c0c50d0a62c97768589e06466742c37020b00000000000000",
            "04200d6b42350c11df4fcc17987c13d8492ba4e8b3f31eb9baff9be5d8890cfa512d20002df68503da9247dfde6585cb8c9fa94897cf21735f8fc1b32116ef474de05c20afa80a9a1bb8b6aad144cfb53e0bab004dd541c8b72025ae694bb60d6050a5322022fab8bcdb88154dbf5877ad1e2d7f1b541bc8a5ec1b52266095381339c27c030c00000000000000",
            "04200d6b42350c11df4fcc17987c13d8492ba4e8b3f31eb9baff9be5d8890cfa512d20002df68503da9247dfde6585cb8c9fa94897cf21735f8fc1b32116ef474de05c20afa80a9a1bb8b6aad144cfb53e0bab004dd541c8b72025ae694bb60d6050a532208cebb73be883466d18d3b0c06990520e80b936440a2c9fd184d92a1f06c4e8260d00000000000000",
            "04200d6b42350c11df4fcc17987c13d8492ba4e8b3f31eb9baff9be5d8890cfa512d20002df68503da9247dfde6585cb8c9fa94897cf21735f8fc1b32116ef474de05c205991131c5c25911b35fcea2a8343e2dfd7a4d5b45493390e0cb184394d91c349203a3661bc12b72646c94bc6c92796e81953985ee62d80a9ec3645a9a95740ac150e00000000000000",
        ];

        // From https://github.com/zcash/zcash/blob/master/src/test/data/merkle_witness_serialization_sapling.json
        let witness_ser = [
            "00000001b02310f2e087e55bfd07ef5e242e3b87ee5d00c9ab52f61e6bd42542f93a6f5500",
            "00000002b02310f2e087e55bfd07ef5e242e3b87ee5d00c9ab52f61e6bd42542f93a6f55225747f3b5d5dab4e5a424f81f85c904ff43286e0f3fd07ef0b8c6a627b1145800",
            "01b02310f2e087e55bfd07ef5e242e3b87ee5d00c9ab52f61e6bd42542f93a6f55000001225747f3b5d5dab4e5a424f81f85c904ff43286e0f3fd07ef0b8c6a627b1145800",
            "00000002b02310f2e087e55bfd07ef5e242e3b87ee5d00c9ab52f61e6bd42542f93a6f55225747f3b5d5dab4e5a424f81f85c904ff43286e0f3fd07ef0b8c6a627b1145801017c3ea01a6e3a3d90cf59cd789e467044b5cd78eb2c84cc6816f960746d0e036c0000",
            "01b02310f2e087e55bfd07ef5e242e3b87ee5d00c9ab52f61e6bd42542f93a6f55000001225747f3b5d5dab4e5a424f81f85c904ff43286e0f3fd07ef0b8c6a627b1145801017c3ea01a6e3a3d90cf59cd789e467044b5cd78eb2c84cc6816f960746d0e036c0000",
            "01b02310f2e087e55bfd07ef5e242e3b87ee5d00c9ab52f61e6bd42542f93a6f5501225747f3b5d5dab4e5a424f81f85c904ff43286e0f3fd07ef0b8c6a627b11458000001017c3ea01a6e3a3d90cf59cd789e467044b5cd78eb2c84cc6816f960746d0e036c0000",
            "00000003b02310f2e087e55bfd07ef5e242e3b87ee5d00c9ab52f61e6bd42542f93a6f55225747f3b5d5dab4e5a424f81f85c904ff43286e0f3fd07ef0b8c6a627b11458f2c6ff34520c4ed63159b5ad4e99712fe64e3b4add73c66218e9797ac15a826400",
            "01b02310f2e087e55bfd07ef5e242e3b87ee5d00c9ab52f61e6bd42542f93a6f55000002225747f3b5d5dab4e5a424f81f85c904ff43286e0f3fd07ef0b8c6a627b11458f2c6ff34520c4ed63159b5ad4e99712fe64e3b4add73c66218e9797ac15a826400",
            "01b02310f2e087e55bfd07ef5e242e3b87ee5d00c9ab52f61e6bd42542f93a6f5501225747f3b5d5dab4e5a424f81f85c904ff43286e0f3fd07ef0b8c6a627b114580001f2c6ff34520c4ed63159b5ad4e99712fe64e3b4add73c66218e9797ac15a826400",
            "017c3ea01a6e3a3d90cf59cd789e467044b5cd78eb2c84cc6816f960746d0e036c00010162324ff2c329e99193a74d28a585a3c167a93bf41a255135529c913bd9b1e6660150421d6c2c94571dfaaa135a4ff15bf916681ebd62c0e43e69e3b90684d0a03000",
            "00000003b02310f2e087e55bfd07ef5e242e3b87ee5d00c9ab52f61e6bd42542f93a6f55225747f3b5d5dab4e5a424f81f85c904ff43286e0f3fd07ef0b8c6a627b11458f2c6ff34520c4ed63159b5ad4e99712fe64e3b4add73c66218e9797ac15a82640101aaec63863aaa0b2e3b8009429bdddd455e59be6f40ccab887a32eb98723efc120000",
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        ];

        const TESTING_DEPTH: u8 = 4;

        fn assert_root_eq(root: Node, expected: &str) {
            let mut tmp = [0u8; 32];
            root.write(&mut tmp[..]).expect("length is 32 bytes");
            assert_eq!(hex::encode(tmp), expected);
        }

        fn assert_tree_ser_eq(tree: &CommitmentTree<Node, TESTING_DEPTH>, expected: &str) {
            // Check that the tree matches its encoding
            let mut tmp = Vec::new();
            write_commitment_tree(tree, &mut tmp).unwrap();
            assert_eq!(hex::encode(&tmp[..]), expected);

            // Check round-trip encoding
            let decoded: CommitmentTree<Node, TESTING_DEPTH> =
                read_commitment_tree(&hex::decode(expected).unwrap()[..]).unwrap();
            tmp.clear();
            write_commitment_tree(&decoded, &mut tmp).unwrap();
            assert_eq!(hex::encode(tmp), expected);
        }

        fn assert_witness_ser_eq(
            witness: &IncrementalWitness<Node, TESTING_DEPTH>,
            expected: &str,
        ) {
            // Check that the witness matches its encoding
            let mut tmp = Vec::new();
            write_incremental_witness(witness, &mut tmp).unwrap();
            assert_eq!(hex::encode(&tmp[..]), expected);

            // Check round-trip encoding
            let decoded: IncrementalWitness<Node, TESTING_DEPTH> =
                read_incremental_witness(&hex::decode(expected).unwrap()[..]).unwrap();
            tmp.clear();
            write_incremental_witness(&decoded, &mut tmp).unwrap();
            assert_eq!(hex::encode(tmp), expected);
        }

        let mut tree = CommitmentTree::<Node, TESTING_DEPTH>::empty();
        assert_eq!(tree.size(), 0);

        let mut witnesses = vec![];
        let mut last_cmu = None;
        let mut paths_i = 0;
        let mut witness_ser_i = 0;
        for i in 0..16 {
            let cmu = hex::decode(commitments[i]).unwrap();

            let cmu = Node::from_bytes(cmu[..].try_into().unwrap()).unwrap();

            // Witness here
            witnesses.push((IncrementalWitness::from_tree(tree.clone()), last_cmu));

            // Now append a commitment to the tree
            assert!(tree.append(cmu).is_ok());

            // Size incremented by one.
            assert_eq!(tree.size(), i + 1);

            // Check tree root consistency
            assert_root_eq(tree.root(), roots[i]);

            // Check serialization of tree
            assert_tree_ser_eq(&tree, tree_ser[i]);

            for (witness, leaf) in witnesses.as_mut_slice() {
                // Append the same commitment to all the witnesses
                assert!(witness.append(cmu).is_ok());

                if let Some(leaf) = leaf {
                    let path = witness.path().expect("should be able to create a path");
                    let expected =
                        merkle_path_from_slice(&hex::decode(paths[paths_i]).unwrap()).unwrap();
                    assert_eq!(path, expected);

                    assert_eq!(path.root(*leaf), witness.root());
                    paths_i += 1;
                } else {
                    // The first witness can never form a path
                    assert!(witness.path().is_none());
                }

                // Check witness serialization
                assert_witness_ser_eq(witness, witness_ser[witness_ser_i]);
                witness_ser_i += 1;

                assert_eq!(witness.root(), tree.root());
            }

            last_cmu = Some(cmu);
        }

        // Tree should be full now
        let node = Node::empty_leaf();
        assert!(tree.append(node).is_err());
        for (witness, _) in witnesses.as_mut_slice() {
            assert!(witness.append(node).is_err());
        }
    }

    proptest! {
        #[test]
        fn prop_commitment_tree_roundtrip_str(ct in arb_commitment_tree::<_, _, 8>(32, any::<char>().prop_map(|c| c.to_string()))) {
            let frontier: Frontier<String, 8> = ct.to_frontier();
            let ct0 = CommitmentTree::from_frontier(&frontier);
            assert_eq!(ct, ct0);
            let frontier0: Frontier<String, 8> = ct0.to_frontier();
            assert_eq!(frontier, frontier0);
        }

        #[test]
        fn prop_commitment_tree_roundtrip_node(ct in arb_commitment_tree::<_, _, 8>(32, sapling::testing::arb_node())) {
            let frontier: Frontier<Node, 8> = ct.to_frontier();
            let ct0 = CommitmentTree::from_frontier(&frontier);
            assert_eq!(ct, ct0);
            let frontier0: Frontier<Node, 8> = ct0.to_frontier();
            assert_eq!(frontier, frontier0);
        }

        #[test]
        fn prop_commitment_tree_roundtrip_ser(ct in arb_commitment_tree::<_, _, 8>(32, sapling::testing::arb_node())) {
            let mut serialized = vec![];
            assert_matches!(write_commitment_tree(&ct, &mut serialized), Ok(()));
            assert_matches!(read_commitment_tree::<_, _, 8>(&serialized[..]), Ok(ct_out) if ct == ct_out);
        }
    }
}