miden-crypto/src/merkle/merkle_tree.rs
src/merkle/merkle_tree.rsRaw
1use super::{InnerNodeInfo, MerkleError, MerklePath, NodeIndex, Rpo256, RpoDigest, Vec, Word};
2use crate::utils::{string::String, uninit_vector, word_to_hex};
3use core::{fmt, ops::Deref, slice};
4use winter_math::log2;
5
6// MERKLE TREE
7// ================================================================================================
8
9/// A fully-balanced binary Merkle tree (i.e., a tree where the number of leaves is a power of two).
10#[derive(Debug, Clone, PartialEq, Eq)]
11pub struct MerkleTree {
12 nodes: Vec<RpoDigest>,
13}
14
15impl MerkleTree {
16 // CONSTRUCTOR
17 // --------------------------------------------------------------------------------------------
18 /// Returns a Merkle tree instantiated from the provided leaves.
19 ///
20 /// # Errors
21 /// Returns an error if the number of leaves is smaller than two or is not a power of two.
22 pub fn new(leaves: Vec<Word>) -> Result<Self, MerkleError> {
23 let n = leaves.len();
24 if n <= 1 {
25 return Err(MerkleError::DepthTooSmall(n as u8));
26 } else if !n.is_power_of_two() {
27 return Err(MerkleError::NumLeavesNotPowerOfTwo(n));
28 }
29
30 // create un-initialized vector to hold all tree nodes
31 let mut nodes = unsafe { uninit_vector(2 * n) };
32 nodes[0] = RpoDigest::default();
33
34 // copy leaves into the second part of the nodes vector
35 nodes[n..].iter_mut().zip(leaves).for_each(|(node, leaf)| {
36 *node = RpoDigest::from(leaf);
37 });
38
39 // re-interpret nodes as an array of two nodes fused together
40 // Safety: `nodes` will never move here as it is not bound to an external lifetime (i.e.
41 // `self`).
42 let ptr = nodes.as_ptr() as *const [RpoDigest; 2];
43 let pairs = unsafe { slice::from_raw_parts(ptr, n) };
44
45 // calculate all internal tree nodes
46 for i in (1..n).rev() {
47 nodes[i] = Rpo256::merge(&pairs[i]);
48 }
49
50 Ok(Self { nodes })
51 }
52
53 // PUBLIC ACCESSORS
54 // --------------------------------------------------------------------------------------------
55
56 /// Returns the root of this Merkle tree.
57 pub fn root(&self) -> RpoDigest {
58 self.nodes[1]
59 }
60
61 /// Returns the depth of this Merkle tree.
62 ///
63 /// Merkle tree of depth 1 has two leaves, depth 2 has four leaves etc.
64 pub fn depth(&self) -> u8 {
65 log2(self.nodes.len() / 2) as u8
66 }
67
68 /// Returns a node at the specified depth and index value.
69 ///
70 /// # Errors
71 /// Returns an error if:
72 /// * The specified depth is greater than the depth of the tree.
73 /// * The specified index is not valid for the specified depth.
74 pub fn get_node(&self, index: NodeIndex) -> Result<RpoDigest, MerkleError> {
75 if index.is_root() {
76 return Err(MerkleError::DepthTooSmall(index.depth()));
77 } else if index.depth() > self.depth() {
78 return Err(MerkleError::DepthTooBig(index.depth() as u64));
79 }
80
81 let pos = index.to_scalar_index() as usize;
82 Ok(self.nodes[pos])
83 }
84
85 /// Returns a Merkle path to the node at the specified depth and index value. The node itself
86 /// is not included in the path.
87 ///
88 /// # Errors
89 /// Returns an error if:
90 /// * The specified depth is greater than the depth of the tree.
91 /// * The specified value is not valid for the specified depth.
92 pub fn get_path(&self, mut index: NodeIndex) -> Result<MerklePath, MerkleError> {
93 if index.is_root() {
94 return Err(MerkleError::DepthTooSmall(index.depth()));
95 } else if index.depth() > self.depth() {
96 return Err(MerkleError::DepthTooBig(index.depth() as u64));
97 }
98
99 // TODO should we create a helper in `NodeIndex` that will encapsulate traversal to root so
100 // we always use inlined `for` instead of `while`? the reason to use `for` is because its
101 // easier for the compiler to vectorize.
102 let mut path = Vec::with_capacity(index.depth() as usize);
103 for _ in 0..index.depth() {
104 let sibling = index.sibling().to_scalar_index() as usize;
105 path.push(self.nodes[sibling]);
106 index.move_up();
107 }
108
109 debug_assert!(index.is_root(), "the path walk must go all the way to the root");
110
111 Ok(path.into())
112 }
113
114 // ITERATORS
115 // --------------------------------------------------------------------------------------------
116
117 /// Returns an iterator over the leaves of this [MerkleTree].
118 pub fn leaves(&self) -> impl Iterator<Item = (u64, &Word)> {
119 let leaves_start = self.nodes.len() / 2;
120 self.nodes
121 .iter()
122 .skip(leaves_start)
123 .enumerate()
124 .map(|(i, v)| (i as u64, v.deref()))
125 }
126
127 /// Returns n iterator over every inner node of this [MerkleTree].
128 ///
129 /// The iterator order is unspecified.
130 pub fn inner_nodes(&self) -> InnerNodeIterator {
131 InnerNodeIterator {
132 nodes: &self.nodes,
133 index: 1, // index 0 is just padding, start at 1
134 }
135 }
136
137 // STATE MUTATORS
138 // --------------------------------------------------------------------------------------------
139
140 /// Replaces the leaf at the specified index with the provided value.
141 ///
142 /// # Errors
143 /// Returns an error if the specified index value is not a valid leaf value for this tree.
144 pub fn update_leaf<'a>(&'a mut self, index_value: u64, value: Word) -> Result<(), MerkleError> {
145 let mut index = NodeIndex::new(self.depth(), index_value)?;
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 [RpoDigest; 2];
159 let pairs: &'a [[RpoDigest; 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.into();
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 = Rpo256::merge(&pairs[pos]);
170 self.nodes[pos] = value;
171 }
172
173 Ok(())
174 }
175}
176
177// ITERATORS
178// ================================================================================================
179
180/// An iterator over every inner node of the [MerkleTree].
181///
182/// Use this to extract the data of the tree, there is no guarantee on the order of the elements.
183pub struct InnerNodeIterator<'a> {
184 nodes: &'a Vec<RpoDigest>,
185 index: usize,
186}
187
188impl<'a> Iterator for InnerNodeIterator<'a> {
189 type Item = InnerNodeInfo;
190
191 fn next(&mut self) -> Option<Self::Item> {
192 if self.index < self.nodes.len() / 2 {
193 let value = self.index;
194 let left = self.index * 2;
195 let right = left + 1;
196
197 self.index += 1;
198
199 Some(InnerNodeInfo {
200 value: self.nodes[value],
201 left: self.nodes[left],
202 right: self.nodes[right],
203 })
204 } else {
205 None
206 }
207 }
208}
209
210// UTILITY FUNCTIONS
211// ================================================================================================
212
213/// Utility to visualize a [MerkleTree] in text.
214pub fn tree_to_text(tree: &MerkleTree) -> Result<String, fmt::Error> {
215 let indent = " ";
216 let mut s = String::new();
217 s.push_str(&word_to_hex(&tree.root())?);
218 s.push('\n');
219 for d in 1..=tree.depth() {
220 let entries = 2u64.pow(d.into());
221 for i in 0..entries {
222 let index = NodeIndex::new(d, i).expect("The index must always be valid");
223 let node = tree.get_node(index).expect("The node must always be found");
224
225 for _ in 0..d {
226 s.push_str(indent);
227 }
228 s.push_str(&word_to_hex(&node)?);
229 s.push('\n');
230 }
231 }
232
233 Ok(s)
234}
235
236/// Utility to visualize a [MerklePath] in text.
237pub fn path_to_text(path: &MerklePath) -> Result<String, fmt::Error> {
238 let mut s = String::new();
239 s.push('[');
240
241 for el in path.iter() {
242 s.push_str(&word_to_hex(el)?);
243 s.push_str(", ");
244 }
245
246 // remove the last ", "
247 if path.len() != 0 {
248 s.pop();
249 s.pop();
250 }
251 s.push(']');
252
253 Ok(s)
254}
255
256// TESTS
257// ================================================================================================
258
259#[cfg(test)]
260mod tests {
261 use super::*;
262 use crate::{
263 merkle::{digests_to_words, int_to_leaf, int_to_node, InnerNodeInfo},
264 Felt, Word, WORD_SIZE,
265 };
266 use core::mem::size_of;
267 use proptest::prelude::*;
268
269 const LEAVES4: [RpoDigest; WORD_SIZE] =
270 [int_to_node(1), int_to_node(2), int_to_node(3), int_to_node(4)];
271
272 const LEAVES8: [RpoDigest; 8] = [
273 int_to_node(1),
274 int_to_node(2),
275 int_to_node(3),
276 int_to_node(4),
277 int_to_node(5),
278 int_to_node(6),
279 int_to_node(7),
280 int_to_node(8),
281 ];
282
283 #[test]
284 fn build_merkle_tree() {
285 let tree = super::MerkleTree::new(digests_to_words(&LEAVES4)).unwrap();
286 assert_eq!(8, tree.nodes.len());
287
288 // leaves were copied correctly
289 for (a, b) in tree.nodes.iter().skip(4).zip(LEAVES4.iter()) {
290 assert_eq!(*a, RpoDigest::from(*b));
291 }
292
293 let (root, node2, node3) = compute_internal_nodes();
294
295 assert_eq!(root, tree.nodes[1]);
296 assert_eq!(node2, tree.nodes[2]);
297 assert_eq!(node3, tree.nodes[3]);
298
299 assert_eq!(root, tree.root());
300 }
301
302 #[test]
303 fn get_leaf() {
304 let tree = super::MerkleTree::new(digests_to_words(&LEAVES4)).unwrap();
305
306 // check depth 2
307 assert_eq!(LEAVES4[0], tree.get_node(NodeIndex::make(2, 0)).unwrap());
308 assert_eq!(LEAVES4[1], tree.get_node(NodeIndex::make(2, 1)).unwrap());
309 assert_eq!(LEAVES4[2], tree.get_node(NodeIndex::make(2, 2)).unwrap());
310 assert_eq!(LEAVES4[3], tree.get_node(NodeIndex::make(2, 3)).unwrap());
311
312 // check depth 1
313 let (_, node2, node3) = compute_internal_nodes();
314
315 assert_eq!(node2, tree.get_node(NodeIndex::make(1, 0)).unwrap());
316 assert_eq!(node3, tree.get_node(NodeIndex::make(1, 1)).unwrap());
317 }
318
319 #[test]
320 fn get_path() {
321 let tree = super::MerkleTree::new(digests_to_words(&LEAVES4)).unwrap();
322
323 let (_, node2, node3) = compute_internal_nodes();
324
325 // check depth 2
326 assert_eq!(vec![LEAVES4[1], node3], *tree.get_path(NodeIndex::make(2, 0)).unwrap());
327 assert_eq!(vec![LEAVES4[0], node3], *tree.get_path(NodeIndex::make(2, 1)).unwrap());
328 assert_eq!(vec![LEAVES4[3], node2], *tree.get_path(NodeIndex::make(2, 2)).unwrap());
329 assert_eq!(vec![LEAVES4[2], node2], *tree.get_path(NodeIndex::make(2, 3)).unwrap());
330
331 // check depth 1
332 assert_eq!(vec![node3], *tree.get_path(NodeIndex::make(1, 0)).unwrap());
333 assert_eq!(vec![node2], *tree.get_path(NodeIndex::make(1, 1)).unwrap());
334 }
335
336 #[test]
337 fn update_leaf() {
338 let mut tree = super::MerkleTree::new(digests_to_words(&LEAVES8)).unwrap();
339
340 // update one leaf
341 let value = 3;
342 let new_node = int_to_leaf(9);
343 let mut expected_leaves = digests_to_words(&LEAVES8);
344 expected_leaves[value as usize] = new_node.into();
345 let expected_tree = super::MerkleTree::new(expected_leaves.clone()).unwrap();
346
347 tree.update_leaf(value, new_node).unwrap();
348 assert_eq!(expected_tree.nodes, tree.nodes);
349
350 // update another leaf
351 let value = 6;
352 let new_node = int_to_leaf(10);
353 expected_leaves[value as usize] = new_node;
354 let expected_tree = super::MerkleTree::new(expected_leaves.clone()).unwrap();
355
356 tree.update_leaf(value, new_node).unwrap();
357 assert_eq!(expected_tree.nodes, tree.nodes);
358 }
359
360 #[test]
361 fn nodes() -> Result<(), MerkleError> {
362 let tree = super::MerkleTree::new(digests_to_words(&LEAVES4)).unwrap();
363 let root = tree.root();
364 let l1n0 = tree.get_node(NodeIndex::make(1, 0))?;
365 let l1n1 = tree.get_node(NodeIndex::make(1, 1))?;
366 let l2n0 = tree.get_node(NodeIndex::make(2, 0))?;
367 let l2n1 = tree.get_node(NodeIndex::make(2, 1))?;
368 let l2n2 = tree.get_node(NodeIndex::make(2, 2))?;
369 let l2n3 = tree.get_node(NodeIndex::make(2, 3))?;
370
371 let nodes: Vec<InnerNodeInfo> = tree.inner_nodes().collect();
372 let expected = vec![
373 InnerNodeInfo {
374 value: root,
375 left: l1n0,
376 right: l1n1,
377 },
378 InnerNodeInfo {
379 value: l1n0,
380 left: l2n0,
381 right: l2n1,
382 },
383 InnerNodeInfo {
384 value: l1n1,
385 left: l2n2,
386 right: l2n3,
387 },
388 ];
389 assert_eq!(nodes, expected);
390
391 Ok(())
392 }
393
394 proptest! {
395 #[test]
396 fn arbitrary_word_can_be_represented_as_digest(
397 a in prop::num::u64::ANY,
398 b in prop::num::u64::ANY,
399 c in prop::num::u64::ANY,
400 d in prop::num::u64::ANY,
401 ) {
402 // this test will assert the memory equivalence between word and digest.
403 // it is used to safeguard the `[MerkleTee::update_leaf]` implementation
404 // that assumes this equivalence.
405
406 // build a word and copy it to another address as digest
407 let word = [Felt::new(a), Felt::new(b), Felt::new(c), Felt::new(d)];
408 let digest = RpoDigest::from(word);
409
410 // assert the addresses are different
411 let word_ptr = (&word).as_ptr() as *const u8;
412 let digest_ptr = (&digest).as_ptr() as *const u8;
413 assert_ne!(word_ptr, digest_ptr);
414
415 // compare the bytes representation
416 let word_bytes = unsafe { slice::from_raw_parts(word_ptr, size_of::<Word>()) };
417 let digest_bytes = unsafe { slice::from_raw_parts(digest_ptr, size_of::<RpoDigest>()) };
418 assert_eq!(word_bytes, digest_bytes);
419 }
420 }
421
422 // HELPER FUNCTIONS
423 // --------------------------------------------------------------------------------------------
424
425 fn compute_internal_nodes() -> (RpoDigest, RpoDigest, RpoDigest) {
426 let node2 =
427 Rpo256::hash_elements(&[Word::from(LEAVES4[0]), Word::from(LEAVES4[1])].concat());
428 let node3 =
429 Rpo256::hash_elements(&[Word::from(LEAVES4[2]), Word::from(LEAVES4[3])].concat());
430 let root = Rpo256::merge(&[node2, node3]);
431
432 (root, node2, node3)
433 }
434}