1use crate::{crh::FixedLengthCRH, Error, Vec};
  2use algebra_core::{bytes::ToBytes, io::Cursor};
  3use core::fmt;
  4
  5#[cfg(feature = "r1cs")]
  6pub mod constraints;
  7
  8pub trait MerkleTreeConfig {
  9    const HEIGHT: usize;
 10    type H: FixedLengthCRH;
 11}
 12
 13/// Stores the hashes of a particular path (in order) from leaf to root.
 14/// Our path `is_left_child()` if the boolean in `path` is true.
 15#[derive(Derivative)]
 16#[derivative(
 17    Clone(bound = "P: MerkleTreeConfig"),
 18    Debug(bound = "P: MerkleTreeConfig, <P::H as FixedLengthCRH>::Output: fmt::Debug")
 19)]
 20pub struct MerkleTreePath<P: MerkleTreeConfig> {
 21    pub(crate) path: Vec<(
 22        <P::H as FixedLengthCRH>::Output,
 23        <P::H as FixedLengthCRH>::Output,
 24    )>,
 25}
 26
 27pub type MerkleTreeParams<P> = <<P as MerkleTreeConfig>::H as FixedLengthCRH>::Parameters;
 28pub type MerkleTreeDigest<P> = <<P as MerkleTreeConfig>::H as FixedLengthCRH>::Output;
 29
 30impl<P: MerkleTreeConfig> Default for MerkleTreePath<P> {
 31    fn default() -> Self {
 32        let mut path = Vec::with_capacity(P::HEIGHT as usize);
 33        for _i in 1..P::HEIGHT as usize {
 34            path.push((
 35                <P::H as FixedLengthCRH>::Output::default(),
 36                <P::H as FixedLengthCRH>::Output::default(),
 37            ));
 38        }
 39        Self { path }
 40    }
 41}
 42
 43impl<P: MerkleTreeConfig> MerkleTreePath<P> {
 44    pub fn verify<L: ToBytes>(
 45        &self,
 46        parameters: &<P::H as FixedLengthCRH>::Parameters,
 47        root_hash: &<P::H as FixedLengthCRH>::Output,
 48        leaf: &L,
 49    ) -> Result<bool, Error> {
 50        if self.path.len() != (P::HEIGHT - 1) as usize {
 51            return Ok(false);
 52        }
 53        // Check that the given leaf matches the leaf in the membership proof.
 54        let mut buffer = [0u8; 128];
 55
 56        if !self.path.is_empty() {
 57            let claimed_leaf_hash = hash_leaf::<P::H, L>(parameters, leaf, &mut buffer)?;
 58
 59            // Check if leaf is one of the bottom-most siblings.
 60            if claimed_leaf_hash != self.path[0].0 && claimed_leaf_hash != self.path[0].1 {
 61                return Ok(false);
 62            };
 63
 64            let mut prev = claimed_leaf_hash;
 65            // Check levels between leaf level and root.
 66            for &(ref hash, ref sibling_hash) in &self.path {
 67                // Check if the previous hash matches the correct current hash.
 68                if &prev != hash && &prev != sibling_hash {
 69                    return Ok(false);
 70                };
 71                prev = hash_inner_node::<P::H>(parameters, hash, sibling_hash, &mut buffer)?;
 72            }
 73
 74            if root_hash != &prev {
 75                return Ok(false);
 76            }
 77            Ok(true)
 78        } else {
 79            Ok(false)
 80        }
 81    }
 82}
 83
 84pub struct MerkleHashTree<P: MerkleTreeConfig> {
 85    tree: Vec<<P::H as FixedLengthCRH>::Output>,
 86    padding_tree: Vec<(
 87        <P::H as FixedLengthCRH>::Output,
 88        <P::H as FixedLengthCRH>::Output,
 89    )>,
 90    parameters: <P::H as FixedLengthCRH>::Parameters,
 91    root: Option<<P::H as FixedLengthCRH>::Output>,
 92}
 93
 94impl<P: MerkleTreeConfig> MerkleHashTree<P> {
 95    pub const HEIGHT: u8 = P::HEIGHT as u8;
 96
 97    pub fn blank(parameters: <P::H as FixedLengthCRH>::Parameters) -> Self {
 98        MerkleHashTree {
 99            tree: Vec::new(),
100            padding_tree: Vec::new(),
101            root: None,
102            parameters,
103        }
104    }
105
106    pub fn new<L: ToBytes>(
107        parameters: <P::H as FixedLengthCRH>::Parameters,
108        leaves: &[L],
109    ) -> Result<Self, Error> {
110        let new_time = start_timer!(|| "MerkleTree::New");
111
112        let last_level_size = leaves.len().next_power_of_two();
113        let tree_size = 2 * last_level_size - 1;
114        let tree_height = tree_height(tree_size);
115        assert!(tree_height as u8 <= Self::HEIGHT);
116
117        // Initialize the merkle tree.
118        let mut tree = Vec::with_capacity(tree_size);
119        let empty_hash = hash_empty::<P::H>(&parameters)?;
120        for _ in 0..tree_size {
121            tree.push(empty_hash.clone());
122        }
123
124        // Compute the starting indices for each level of the tree.
125        let mut index = 0;
126        let mut level_indices = Vec::with_capacity(tree_height);
127        for _ in 0..tree_height {
128            level_indices.push(index);
129            index = left_child(index);
130        }
131
132        // Compute and store the hash values for each leaf.
133        let last_level_index = level_indices.pop().unwrap_or(0);
134        let mut buffer = [0u8; 128];
135        for (i, leaf) in leaves.iter().enumerate() {
136            tree[last_level_index + i] = hash_leaf::<P::H, _>(&parameters, leaf, &mut buffer)?;
137        }
138
139        // Compute the hash values for every node in the tree.
140        let mut upper_bound = last_level_index;
141        let mut buffer = [0u8; 128];
142        level_indices.reverse();
143        for &start_index in &level_indices {
144            // Iterate over the current level.
145            for current_index in start_index..upper_bound {
146                let left_index = left_child(current_index);
147                let right_index = right_child(current_index);
148
149                // Compute Hash(left || right).
150                tree[current_index] = hash_inner_node::<P::H>(
151                    &parameters,
152                    &tree[left_index],
153                    &tree[right_index],
154                    &mut buffer,
155                )?;
156            }
157            upper_bound = start_index;
158        }
159        // Finished computing actual tree.
160        // Now, we compute the dummy nodes until we hit our HEIGHT goal.
161        let mut cur_height = tree_height;
162        let mut padding_tree = Vec::new();
163        let mut cur_hash = tree[0].clone();
164        let root_hash = if cur_height < Self::HEIGHT as usize {
165            while cur_height < (Self::HEIGHT - 1) as usize {
166                cur_hash = hash_inner_node::<P::H>(&parameters, &cur_hash, &empty_hash, &mut buffer)?;
167                padding_tree.push((cur_hash.clone(), empty_hash.clone()));
168                cur_height += 1;
169            }
170            hash_inner_node::<P::H>(&parameters, &cur_hash, &empty_hash, &mut buffer)?
171        } else {
172            cur_hash
173        };
174        end_timer!(new_time);
175
176        Ok(MerkleHashTree {
177            tree,
178            padding_tree,
179            parameters,
180            root: Some(root_hash),
181        })
182    }
183
184    #[inline]
185    pub fn root(&self) -> <P::H as FixedLengthCRH>::Output {
186        self.root.clone().unwrap()
187    }
188
189    pub fn generate_proof<L: ToBytes>(
190        &self,
191        index: usize,
192        leaf: &L,
193    ) -> Result<MerkleTreePath<P>, Error> {
194        let prove_time = start_timer!(|| "MerkleTree::GenProof");
195        let mut path = Vec::new();
196
197        let mut buffer = [0u8; 128];
198        let leaf_hash = hash_leaf::<P::H, _>(&self.parameters, leaf, &mut buffer)?;
199        let tree_height = tree_height(self.tree.len());
200        let tree_index = convert_index_to_last_level(index, tree_height);
201        let empty_hash = hash_empty::<P::H>(&self.parameters)?;
202
203        // Check that the given index corresponds to the correct leaf.
204        if leaf_hash != self.tree[tree_index] {
205            return Err(MerkleTreeError::IncorrectLeafIndex(tree_index).into());
206        }
207
208        // Iterate from the leaf up to the root, storing all intermediate hash values.
209        let mut current_node = tree_index;
210        while !is_root(current_node) {
211            let sibling_node = sibling(current_node).unwrap();
212            let (curr_hash, sibling_hash) = (
213                self.tree[current_node].clone(),
214                self.tree[sibling_node].clone(),
215            );
216            if is_left_child(current_node) {
217                path.push((curr_hash, sibling_hash));
218            } else {
219                path.push((sibling_hash, curr_hash));
220            }
221            current_node = parent(current_node).unwrap();
222        }
223
224        // Store the root node. Set boolean as true for consistency with digest
225        // location.
226        assert!(path.len() < Self::HEIGHT as usize);
227        if path.len() != (Self::HEIGHT - 1) as usize {
228            path.push((self.tree[0].clone(), empty_hash));
229            for &(ref hash, ref sibling_hash) in &self.padding_tree {
230                path.push((hash.clone(), sibling_hash.clone()));
231            }
232        }
233        end_timer!(prove_time);
234        if path.len() != (Self::HEIGHT - 1) as usize {
235            return Err(MerkleTreeError::IncorrectPathLength(path.len()).into());
236        } else {
237            Ok(MerkleTreePath { path })
238        }
239    }
240}
241
242#[derive(Debug)]
243pub enum MerkleTreeError {
244    IncorrectLeafIndex(usize),
245    IncorrectPathLength(usize),
246}
247
248impl core::fmt::Display for MerkleTreeError {
249    fn fmt(&self, f: &mut core::fmt::Formatter<'_>) -> core::fmt::Result {
250        let msg = match self {
251            MerkleTreeError::IncorrectLeafIndex(index) => {
252                format!("incorrect leaf index: {}", index)
253            }
254            MerkleTreeError::IncorrectPathLength(len) => format!("incorrect path length: {}", len),
255        };
256        write!(f, "{}", msg)
257    }
258}
259
260impl algebra_core::Error for MerkleTreeError {}
261
262/// Returns the log2 value of the given number.
263#[inline]
264fn log2(number: usize) -> usize {
265    algebra_core::log2(number) as usize
266}
267
268/// Returns the height of the tree, given the size of the tree.
269#[inline]
270fn tree_height(tree_size: usize) -> usize {
271    log2(tree_size)
272}
273
274/// Returns true iff the index represents the root.
275#[inline]
276fn is_root(index: usize) -> bool {
277    index == 0
278}
279
280/// Returns the index of the left child, given an index.
281#[inline]
282fn left_child(index: usize) -> usize {
283    2 * index + 1
284}
285
286/// Returns the index of the right child, given an index.
287#[inline]
288fn right_child(index: usize) -> usize {
289    2 * index + 2
290}
291
292/// Returns the index of the sibling, given an index.
293#[inline]
294fn sibling(index: usize) -> Option<usize> {
295    if index == 0 {
296        None
297    } else if is_left_child(index) {
298        Some(index + 1)
299    } else {
300        Some(index - 1)
301    }
302}
303
304/// Returns true iff the given index represents a left child.
305#[inline]
306fn is_left_child(index: usize) -> bool {
307    index % 2 == 1
308}
309
310/// Returns the index of the parent, given an index.
311#[inline]
312fn parent(index: usize) -> Option<usize> {
313    if index > 0 {
314        Some((index - 1) >> 1)
315    } else {
316        None
317    }
318}
319
320#[inline]
321fn convert_index_to_last_level(index: usize, tree_height: usize) -> usize {
322    index + (1 << (tree_height - 1)) - 1
323}
324
325/// Returns the output hash, given a left and right hash value.
326pub(crate) fn hash_inner_node<H: FixedLengthCRH>(
327    parameters: &H::Parameters,
328    left: &H::Output,
329    right: &H::Output,
330    buffer: &mut [u8],
331) -> Result<H::Output, Error> {
332    let mut writer = Cursor::new(&mut *buffer);
333    // Construct left input.
334    left.write(&mut writer)?;
335
336    // Construct right input.
337    right.write(&mut writer)?;
338
339    H::evaluate(parameters, &buffer[..(H::INPUT_SIZE_BITS / 8)])
340}
341
342/// Returns the hash of a leaf.
343pub(crate) fn hash_leaf<H: FixedLengthCRH, L: ToBytes>(
344    parameters: &H::Parameters,
345    leaf: &L,
346    buffer: &mut [u8],
347) -> Result<H::Output, Error> {
348    let mut writer = Cursor::new(&mut *buffer);
349    leaf.write(&mut writer)?;
350
351    H::evaluate(parameters, &buffer[..(H::INPUT_SIZE_BITS / 8)])
352}
353
354pub(crate) fn hash_empty<H: FixedLengthCRH>(
355    parameters: &H::Parameters,
356) -> Result<H::Output, Error> {
357    let empty_buffer = vec![0u8; H::INPUT_SIZE_BITS / 8];
358    H::evaluate(parameters, &empty_buffer)
359}
360
361#[cfg(test)]
362mod test {
363    use crate::{
364        crh::{pedersen::*, *},
365        merkle_tree::*,
366    };
367    use algebra::{jubjub::JubJubAffine as JubJub, Zero};
368    use rand::SeedableRng;
369    use rand_xorshift::XorShiftRng;
370
371    #[derive(Clone)]
372    pub(super) struct Window4x256;
373    impl PedersenWindow for Window4x256 {
374        const WINDOW_SIZE: usize = 4;
375        const NUM_WINDOWS: usize = 256;
376    }
377
378    type H = PedersenCRH<JubJub, Window4x256>;
379
380    struct JubJubMerkleTreeParams;
381
382    impl MerkleTreeConfig for JubJubMerkleTreeParams {
383        const HEIGHT: usize = 8;
384        type H = H;
385    }
386    type JubJubMerkleTree = MerkleHashTree<JubJubMerkleTreeParams>;
387
388    fn generate_merkle_tree<L: ToBytes + Clone + Eq>(leaves: &[L]) -> () {
389        let mut rng = XorShiftRng::seed_from_u64(9174123u64);
390
391        let crh_parameters = H::setup(&mut rng).unwrap();
392        let tree = JubJubMerkleTree::new(crh_parameters.clone(), &leaves).unwrap();
393        let root = tree.root();
394        for (i, leaf) in leaves.iter().enumerate() {
395            let proof = tree.generate_proof(i, &leaf).unwrap();
396            assert!(proof.verify(&crh_parameters, &root, &leaf).unwrap());
397        }
398    }
399
400    #[test]
401    fn good_root_test() {
402        let mut leaves = Vec::new();
403        for i in 0..4u8 {
404            leaves.push([i, i, i, i, i, i, i, i]);
405        }
406        generate_merkle_tree(&leaves);
407        let mut leaves = Vec::new();
408        for i in 0..100u8 {
409            leaves.push([i, i, i, i, i, i, i, i]);
410        }
411        generate_merkle_tree(&leaves);
412    }
413
414    #[test]
415    fn no_dummy_nodes_test() {
416        let mut leaves = Vec::new();
417        for i in 0..(1u8 << JubJubMerkleTree::HEIGHT - 1) {
418            leaves.push([i, i, i, i, i, i, i, i]);
419        }
420        generate_merkle_tree(&leaves);
421    }
422
423    #[test]
424    fn single_leaf_test() {
425        generate_merkle_tree(&[[1u8; 8]]);
426    }
427
428    fn bad_merkle_tree_verify<L: ToBytes + Clone + Eq>(leaves: &[L]) -> () {
429        let mut rng = XorShiftRng::seed_from_u64(13423423u64);
430
431        let crh_parameters = H::setup(&mut rng).unwrap();
432        let tree = JubJubMerkleTree::new(crh_parameters.clone(), &leaves).unwrap();
433        let root = JubJub::zero();
434        for (i, leaf) in leaves.iter().enumerate() {
435            let proof = tree.generate_proof(i, &leaf).unwrap();
436            assert!(proof.verify(&crh_parameters, &root, &leaf).unwrap());
437        }
438    }
439
440    #[should_panic]
441    #[test]
442    fn bad_root_test() {
443        let mut leaves = Vec::new();
444        for i in 0..4u8 {
445            leaves.push([i, i, i, i, i, i, i, i]);
446        }
447        generate_merkle_tree(&leaves);
448        let mut leaves = Vec::new();
449        for i in 0..100u8 {
450            leaves.push([i, i, i, i, i, i, i, i]);
451        }
452        bad_merkle_tree_verify(&leaves);
453    }
454}