miden_crypto/merkle/
merkle_tree.rs

1use alloc::{string::String, vec::Vec};
2use core::{fmt, slice};
3
4use super::{InnerNodeInfo, MerkleError, MerklePath, NodeIndex, Poseidon2, Word};
5use crate::utils::{assume_init_vec, uninit_vector, word_to_hex};
6
7// MERKLE TREE
8// ================================================================================================
9
10/// A fully-balanced binary Merkle tree (i.e., a tree where the number of leaves is a power of two).
11#[derive(Debug, Clone, PartialEq, Eq)]
12pub struct MerkleTree {
13    nodes: Vec<Word>,
14}
15
16impl MerkleTree {
17    // CONSTRUCTOR
18    // --------------------------------------------------------------------------------------------
19    /// Returns a Merkle tree instantiated from the provided leaves.
20    ///
21    /// # Errors
22    /// Returns an error if the number of leaves is smaller than two or is not a power of two.
23    pub fn new<T>(leaves: T) -> Result<Self, MerkleError>
24    where
25        T: AsRef<[Word]>,
26    {
27        let leaves = leaves.as_ref();
28        let n = leaves.len();
29        if n <= 1 {
30            return Err(MerkleError::DepthTooSmall(n as u8));
31        } else if !n.is_power_of_two() {
32            return Err(MerkleError::NumLeavesNotPowerOfTwo(n));
33        }
34
35        // Create an uninitialized vector to avoid eagerly zeroing `2 * n` words. This is a
36        // hot path during tree construction; see benches in `miden-crypto/benches/merkle.rs`
37        // (e.g. `merkle_tree_construction`) for performance motivation.
38        // SAFETY: All elements are written before being read (leaves copied, then computed).
39        let mut nodes = uninit_vector::<Word>(2 * n);
40        nodes[0].write(Word::default());
41
42        // copy leaves into the second part of the nodes vector
43        nodes[n..].iter_mut().zip(leaves).for_each(|(node, leaf)| {
44            node.write(*leaf);
45        });
46
47        // calculate all internal tree nodes
48        for i in (1..n).rev() {
49            // SAFETY: We fill leaves first, then iterate from the bottom up. At this point,
50            // nodes[2 * i] and nodes[2 * i + 1] have already been written.
51            let left = unsafe { nodes[2 * i].assume_init_read() };
52            let right = unsafe { nodes[2 * i + 1].assume_init_read() };
53            nodes[i].write(Poseidon2::merge(&[left, right]));
54        }
55
56        // SAFETY: all elements were written above.
57        let nodes = unsafe { assume_init_vec(nodes) };
58
59        Ok(Self { nodes })
60    }
61
62    // PUBLIC ACCESSORS
63    // --------------------------------------------------------------------------------------------
64
65    /// Returns the root of this Merkle tree.
66    pub fn root(&self) -> Word {
67        self.nodes[1]
68    }
69
70    /// Returns the depth of this Merkle tree.
71    ///
72    /// Merkle tree of depth 1 has two leaves, depth 2 has four leaves etc.
73    pub fn depth(&self) -> u8 {
74        (self.nodes.len() / 2).ilog2() as u8
75    }
76
77    /// Returns a node at the specified depth and index value.
78    ///
79    /// # Errors
80    /// Returns an error if:
81    /// * The specified depth is greater than the depth of the tree.
82    /// * The specified index is not valid for the specified depth.
83    pub fn get_node(&self, index: NodeIndex) -> Result<Word, MerkleError> {
84        if index.is_root() {
85            return Err(MerkleError::DepthTooSmall(index.depth()));
86        } else if index.depth() > self.depth() {
87            return Err(MerkleError::DepthTooBig(index.depth() as u64));
88        }
89
90        let pos = index.to_scalar_index()? as usize;
91        Ok(self.nodes[pos])
92    }
93
94    /// Returns a Merkle path to the node at the specified depth and index value. The node itself
95    /// is not included in the path.
96    ///
97    /// # Errors
98    /// Returns an error if:
99    /// * The specified depth is greater than the depth of the tree.
100    /// * The specified value is not valid for the specified depth.
101    pub fn get_path(&self, index: NodeIndex) -> Result<MerklePath, MerkleError> {
102        if index.is_root() {
103            return Err(MerkleError::DepthTooSmall(index.depth()));
104        } else if index.depth() > self.depth() {
105            return Err(MerkleError::DepthTooBig(index.depth() as u64));
106        }
107
108        Ok(MerklePath::from(Vec::from_iter(
109            index.proof_indices().map(|index| self.get_node(index).unwrap()),
110        )))
111    }
112
113    // ITERATORS
114    // --------------------------------------------------------------------------------------------
115
116    /// Returns an iterator over the leaves of this [MerkleTree].
117    pub fn leaves(&self) -> impl Iterator<Item = (u64, &Word)> {
118        let leaves_start = self.nodes.len() / 2;
119        self.nodes.iter().skip(leaves_start).enumerate().map(|(i, v)| (i as u64, v))
120    }
121
122    /// Returns n iterator over every inner node of this [MerkleTree].
123    ///
124    /// The iterator order is unspecified.
125    pub fn inner_nodes(&self) -> InnerNodeIterator<'_> {
126        InnerNodeIterator {
127            nodes: &self.nodes,
128            index: 1, // index 0 is just padding, start at 1
129        }
130    }
131
132    // STATE MUTATORS
133    // --------------------------------------------------------------------------------------------
134
135    /// Replaces the leaf at the specified index with the provided value.
136    ///
137    /// # Errors
138    /// Returns an error if the specified index value is not a valid leaf value for this tree.
139    pub fn update_leaf<'a>(&'a mut self, index_value: u64, value: Word) -> Result<(), MerkleError> {
140        let mut index = NodeIndex::new(self.depth(), index_value)?;
141
142        // Performance note: We use unsafe pointer casts here for ~2-2.5% performance improvement
143        // at scale. See benches/merkle.rs for benchmarks. The safe alternative uses index
144        // arithmetic (`nodes[pos*2]`, `nodes[pos*2+1]`) which is measurably slower on large
145        // trees.
146
147        // we don't need to copy the pairs into a new address as we are logically guaranteed to not
148        // overlap write instructions. however, it's important to bind the lifetime of pairs to
149        // `self.nodes` so the compiler will never move one without moving the other.
150        debug_assert_eq!(self.nodes.len() & 1, 0);
151        let n = self.nodes.len() / 2;
152
153        // Safety: the length of nodes is guaranteed to contain pairs of words; hence, pairs of
154        // digests. we explicitly bind the lifetime here so we add an extra layer of guarantee that
155        // `self.nodes` will be moved only if `pairs` is moved as well. also, the algorithm is
156        // logically guaranteed to not overlap write positions as the write index is always half
157        // the index from which we read the digest input.
158        let ptr = self.nodes.as_ptr() as *const [Word; 2];
159        let pairs: &'a [[Word; 2]] = unsafe { slice::from_raw_parts(ptr, n) };
160
161        // update the current node
162        let pos = index.to_scalar_index()? as usize;
163        self.nodes[pos] = value;
164
165        // traverse to the root, updating each node with the merged values of its parents
166        for _ in 0..index.depth() {
167            index.move_up();
168            let pos = index.to_scalar_index()? as usize;
169            let value = Poseidon2::merge(&pairs[pos]);
170            self.nodes[pos] = value;
171        }
172
173        Ok(())
174    }
175}
176
177// CONVERSIONS
178// ================================================================================================
179
180impl TryFrom<&[Word]> for MerkleTree {
181    type Error = MerkleError;
182
183    fn try_from(value: &[Word]) -> Result<Self, Self::Error> {
184        MerkleTree::new(value)
185    }
186}
187
188// ITERATORS
189// ================================================================================================
190
191/// An iterator over every inner node of the [MerkleTree].
192///
193/// Use this to extract the data of the tree, there is no guarantee on the order of the elements.
194pub struct InnerNodeIterator<'a> {
195    nodes: &'a Vec<Word>,
196    index: usize,
197}
198
199impl Iterator for InnerNodeIterator<'_> {
200    type Item = InnerNodeInfo;
201
202    fn next(&mut self) -> Option<Self::Item> {
203        if self.index < self.nodes.len() / 2 {
204            let value = self.index;
205            let left = self.index * 2;
206            let right = left + 1;
207
208            self.index += 1;
209
210            Some(InnerNodeInfo {
211                value: self.nodes[value],
212                left: self.nodes[left],
213                right: self.nodes[right],
214            })
215        } else {
216            None
217        }
218    }
219}
220
221// UTILITY FUNCTIONS
222// ================================================================================================
223
224/// Utility to visualize a [MerkleTree] in text.
225pub fn tree_to_text(tree: &MerkleTree) -> Result<String, fmt::Error> {
226    let indent = "  ";
227    let mut s = String::new();
228    s.push_str(&word_to_hex(&tree.root())?);
229    s.push('\n');
230    for d in 1..=tree.depth() {
231        let entries = 2u64.pow(d.into());
232        for i in 0..entries {
233            let index = NodeIndex::new(d, i).expect("The index must always be valid");
234            let node = tree.get_node(index).expect("The node must always be found");
235
236            for _ in 0..d {
237                s.push_str(indent);
238            }
239            s.push_str(&word_to_hex(&node)?);
240            s.push('\n');
241        }
242    }
243
244    Ok(s)
245}
246
247/// Utility to visualize a [MerklePath] in text.
248pub fn path_to_text(path: &MerklePath) -> Result<String, fmt::Error> {
249    let mut s = String::new();
250    s.push('[');
251
252    for el in path.iter() {
253        s.push_str(&word_to_hex(el)?);
254        s.push_str(", ");
255    }
256
257    // remove the last ", "
258    if !path.is_empty() {
259        s.pop();
260        s.pop();
261    }
262    s.push(']');
263
264    Ok(s)
265}
266
267// TESTS
268// ================================================================================================
269
270#[cfg(test)]
271mod tests {
272    use core::mem::size_of;
273
274    use proptest::prelude::*;
275
276    use super::*;
277    use crate::{
278        Felt,
279        merkle::{int_to_leaf, int_to_node},
280    };
281
282    const LEAVES4: [Word; Word::NUM_ELEMENTS] =
283        [int_to_node(1), int_to_node(2), int_to_node(3), int_to_node(4)];
284
285    const LEAVES8: [Word; 8] = [
286        int_to_node(1),
287        int_to_node(2),
288        int_to_node(3),
289        int_to_node(4),
290        int_to_node(5),
291        int_to_node(6),
292        int_to_node(7),
293        int_to_node(8),
294    ];
295
296    #[test]
297    fn build_merkle_tree() {
298        let tree = MerkleTree::new(LEAVES4).unwrap();
299        assert_eq!(8, tree.nodes.len());
300
301        // leaves were copied correctly
302        for (a, b) in tree.nodes.iter().skip(4).zip(LEAVES4.iter()) {
303            assert_eq!(a, b);
304        }
305
306        let (root, node2, node3) = compute_internal_nodes();
307
308        assert_eq!(root, tree.nodes[1]);
309        assert_eq!(node2, tree.nodes[2]);
310        assert_eq!(node3, tree.nodes[3]);
311
312        assert_eq!(root, tree.root());
313    }
314
315    #[test]
316    fn get_leaf() {
317        let tree = MerkleTree::new(LEAVES4).unwrap();
318
319        // check depth 2
320        assert_eq!(LEAVES4[0], tree.get_node(NodeIndex::make(2, 0)).unwrap());
321        assert_eq!(LEAVES4[1], tree.get_node(NodeIndex::make(2, 1)).unwrap());
322        assert_eq!(LEAVES4[2], tree.get_node(NodeIndex::make(2, 2)).unwrap());
323        assert_eq!(LEAVES4[3], tree.get_node(NodeIndex::make(2, 3)).unwrap());
324
325        // check depth 1
326        let (_, node2, node3) = compute_internal_nodes();
327
328        assert_eq!(node2, tree.get_node(NodeIndex::make(1, 0)).unwrap());
329        assert_eq!(node3, tree.get_node(NodeIndex::make(1, 1)).unwrap());
330    }
331
332    #[test]
333    fn get_path() {
334        let tree = MerkleTree::new(LEAVES4).unwrap();
335
336        let (_, node2, node3) = compute_internal_nodes();
337
338        // check depth 2
339        assert_eq!(vec![LEAVES4[1], node3], *tree.get_path(NodeIndex::make(2, 0)).unwrap());
340        assert_eq!(vec![LEAVES4[0], node3], *tree.get_path(NodeIndex::make(2, 1)).unwrap());
341        assert_eq!(vec![LEAVES4[3], node2], *tree.get_path(NodeIndex::make(2, 2)).unwrap());
342        assert_eq!(vec![LEAVES4[2], node2], *tree.get_path(NodeIndex::make(2, 3)).unwrap());
343
344        // check depth 1
345        assert_eq!(vec![node3], *tree.get_path(NodeIndex::make(1, 0)).unwrap());
346        assert_eq!(vec![node2], *tree.get_path(NodeIndex::make(1, 1)).unwrap());
347    }
348
349    #[test]
350    fn update_leaf() {
351        let mut tree = MerkleTree::new(LEAVES8).unwrap();
352
353        // update one leaf
354        let value = 3;
355        let new_node = int_to_leaf(9);
356        let mut expected_leaves = LEAVES8.to_vec();
357        expected_leaves[value as usize] = new_node;
358        let expected_tree = MerkleTree::new(expected_leaves.clone()).unwrap();
359
360        tree.update_leaf(value, new_node).unwrap();
361        assert_eq!(expected_tree.nodes, tree.nodes);
362
363        // update another leaf
364        let value = 6;
365        let new_node = int_to_leaf(10);
366        expected_leaves[value as usize] = new_node;
367        let expected_tree = MerkleTree::new(expected_leaves.clone()).unwrap();
368
369        tree.update_leaf(value, new_node).unwrap();
370        assert_eq!(expected_tree.nodes, tree.nodes);
371    }
372
373    #[test]
374    fn nodes() -> Result<(), MerkleError> {
375        let tree = MerkleTree::new(LEAVES4).unwrap();
376        let root = tree.root();
377        let l1n0 = tree.get_node(NodeIndex::make(1, 0))?;
378        let l1n1 = tree.get_node(NodeIndex::make(1, 1))?;
379        let l2n0 = tree.get_node(NodeIndex::make(2, 0))?;
380        let l2n1 = tree.get_node(NodeIndex::make(2, 1))?;
381        let l2n2 = tree.get_node(NodeIndex::make(2, 2))?;
382        let l2n3 = tree.get_node(NodeIndex::make(2, 3))?;
383
384        let nodes: Vec<InnerNodeInfo> = tree.inner_nodes().collect();
385        let expected = vec![
386            InnerNodeInfo { value: root, left: l1n0, right: l1n1 },
387            InnerNodeInfo { value: l1n0, left: l2n0, right: l2n1 },
388            InnerNodeInfo { value: l1n1, left: l2n2, right: l2n3 },
389        ];
390        assert_eq!(nodes, expected);
391
392        Ok(())
393    }
394
395    proptest! {
396        #[test]
397        fn arbitrary_word_can_be_represented_as_digest(
398            a in prop::num::u64::ANY,
399            b in prop::num::u64::ANY,
400            c in prop::num::u64::ANY,
401            d in prop::num::u64::ANY,
402        ) {
403            // this test will assert the memory equivalence between word and digest.
404            // it is used to safeguard the `[MerkleTee::update_leaf]` implementation
405            // that assumes this equivalence.
406
407            // build a word and copy it to another address as digest
408            let word = [Felt::new_unchecked(a), Felt::new_unchecked(b), Felt::new_unchecked(c), Felt::new_unchecked(d)];
409            let digest = Word::from(word);
410
411            // assert the addresses are different
412            let word_ptr = word.as_ptr() as *const u8;
413            let digest_ptr = digest.as_ptr() as *const u8;
414            assert_ne!(word_ptr, digest_ptr);
415
416            // compare the bytes representation
417            let word_bytes = unsafe { slice::from_raw_parts(word_ptr, size_of::<Word>()) };
418            let digest_bytes = unsafe { slice::from_raw_parts(digest_ptr, size_of::<Word>()) };
419            assert_eq!(word_bytes, digest_bytes);
420        }
421    }
422
423    // HELPER FUNCTIONS
424    // --------------------------------------------------------------------------------------------
425
426    fn compute_internal_nodes() -> (Word, Word, Word) {
427        let node2 = Poseidon2::hash_elements(&[*LEAVES4[0], *LEAVES4[1]].concat());
428        let node3 = Poseidon2::hash_elements(&[*LEAVES4[2], *LEAVES4[3]].concat());
429        let root = Poseidon2::merge(&[node2, node3]);
430
431        (root, node2, node3)
432    }
433}
miden_crypto/merkle/merkle_tree.rs

miden_crypto/merkle/
merkle_tree.rs
