miden-crypto/src/merkle/merkle_tree.rs
src/merkle/merkle_tree.rsRaw
1use super::{
2 Felt, InnerNodeInfo, MerkleError, MerklePath, NodeIndex, Rpo256, RpoDigest, Vec, Word,
3};
4use crate::{
5 utils::{string::String, uninit_vector, word_to_hex},
6 FieldElement,
7};
8use core::{fmt, slice};
9use winter_math::log2;
10
11// MERKLE TREE
12// ================================================================================================
13
14/// A fully-balanced binary Merkle tree (i.e., a tree where the number of leaves is a power of two).
15#[derive(Debug, Clone, PartialEq, Eq)]
16pub struct MerkleTree {
17 nodes: Vec<Word>,
18}
19
20impl MerkleTree {
21 // CONSTRUCTOR
22 // --------------------------------------------------------------------------------------------
23 /// Returns a Merkle tree instantiated from the provided leaves.
24 ///
25 /// # Errors
26 /// Returns an error if the number of leaves is smaller than two or is not a power of two.
27 pub fn new(leaves: Vec<Word>) -> Result<Self, MerkleError> {
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 un-initialized vector to hold all tree nodes
36 let mut nodes = unsafe { uninit_vector(2 * n) };
37 nodes[0] = [Felt::ZERO; 4];
38
39 // copy leaves into the second part of the nodes vector
40 nodes[n..].copy_from_slice(&leaves);
41
42 // re-interpret nodes as an array of two nodes fused together
43 // Safety: `nodes` will never move here as it is not bound to an external lifetime (i.e.
44 // `self`).
45 let ptr = nodes.as_ptr() as *const [RpoDigest; 2];
46 let pairs = unsafe { slice::from_raw_parts(ptr, n) };
47
48 // calculate all internal tree nodes
49 for i in (1..n).rev() {
50 nodes[i] = Rpo256::merge(&pairs[i]).into();
51 }
52
53 Ok(Self { nodes })
54 }
55
56 // PUBLIC ACCESSORS
57 // --------------------------------------------------------------------------------------------
58
59 /// Returns the root of this Merkle tree.
60 pub fn root(&self) -> Word {
61 self.nodes[1]
62 }
63
64 /// Returns the depth of this Merkle tree.
65 ///
66 /// Merkle tree of depth 1 has two leaves, depth 2 has four leaves etc.
67 pub fn depth(&self) -> u8 {
68 log2(self.nodes.len() / 2) as u8
69 }
70
71 /// Returns a node at the specified depth and index value.
72 ///
73 /// # Errors
74 /// Returns an error if:
75 /// * The specified depth is greater than the depth of the tree.
76 /// * The specified index is not valid for the specified depth.
77 pub fn get_node(&self, index: NodeIndex) -> Result<Word, MerkleError> {
78 if index.is_root() {
79 return Err(MerkleError::DepthTooSmall(index.depth()));
80 } else if index.depth() > self.depth() {
81 return Err(MerkleError::DepthTooBig(index.depth() as u64));
82 }
83
84 let pos = index.to_scalar_index() as usize;
85 Ok(self.nodes[pos])
86 }
87
88 /// Returns a Merkle path to the node at the specified depth and index value. The node itself
89 /// is not included in the path.
90 ///
91 /// # Errors
92 /// Returns an error if:
93 /// * The specified depth is greater than the depth of the tree.
94 /// * The specified value is not valid for the specified depth.
95 pub fn get_path(&self, mut index: NodeIndex) -> Result<MerklePath, MerkleError> {
96 if index.is_root() {
97 return Err(MerkleError::DepthTooSmall(index.depth()));
98 } else if index.depth() > self.depth() {
99 return Err(MerkleError::DepthTooBig(index.depth() as u64));
100 }
101
102 // TODO should we create a helper in `NodeIndex` that will encapsulate traversal to root so
103 // we always use inlined `for` instead of `while`? the reason to use `for` is because its
104 // easier for the compiler to vectorize.
105 let mut path = Vec::with_capacity(index.depth() as usize);
106 for _ in 0..index.depth() {
107 let sibling = index.sibling().to_scalar_index() as usize;
108 path.push(self.nodes[sibling]);
109 index.move_up();
110 }
111
112 debug_assert!(index.is_root(), "the path walk must go all the way to the root");
113
114 Ok(path.into())
115 }
116
117 /// Replaces the leaf at the specified index with the provided value.
118 ///
119 /// # Errors
120 /// Returns an error if the specified index value is not a valid leaf value for this tree.
121 pub fn update_leaf<'a>(&'a mut self, index_value: u64, value: Word) -> Result<(), MerkleError> {
122 let mut index = NodeIndex::new(self.depth(), index_value)?;
123
124 // we don't need to copy the pairs into a new address as we are logically guaranteed to not
125 // overlap write instructions. however, it's important to bind the lifetime of pairs to
126 // `self.nodes` so the compiler will never move one without moving the other.
127 debug_assert_eq!(self.nodes.len() & 1, 0);
128 let n = self.nodes.len() / 2;
129
130 // Safety: the length of nodes is guaranteed to contain pairs of words; hence, pairs of
131 // digests. we explicitly bind the lifetime here so we add an extra layer of guarantee that
132 // `self.nodes` will be moved only if `pairs` is moved as well. also, the algorithm is
133 // logically guaranteed to not overlap write positions as the write index is always half
134 // the index from which we read the digest input.
135 let ptr = self.nodes.as_ptr() as *const [RpoDigest; 2];
136 let pairs: &'a [[RpoDigest; 2]] = unsafe { slice::from_raw_parts(ptr, n) };
137
138 // update the current node
139 let pos = index.to_scalar_index() as usize;
140 self.nodes[pos] = value;
141
142 // traverse to the root, updating each node with the merged values of its parents
143 for _ in 0..index.depth() {
144 index.move_up();
145 let pos = index.to_scalar_index() as usize;
146 let value = Rpo256::merge(&pairs[pos]).into();
147 self.nodes[pos] = value;
148 }
149
150 Ok(())
151 }
152
153 /// Returns n iterator over every inner node of this [MerkleTree].
154 ///
155 /// The iterator order is unspecified.
156 pub fn inner_nodes(&self) -> InnerNodeIterator<'_> {
157 InnerNodeIterator {
158 nodes: &self.nodes,
159 index: 1, // index 0 is just padding, start at 1
160 }
161 }
162}
163
164// ITERATORS
165// ================================================================================================
166
167/// An iterator over every inner node of the [MerkleTree].
168///
169/// Use this to extract the data of the tree, there is no guarantee on the order of the elements.
170pub struct InnerNodeIterator<'a> {
171 nodes: &'a Vec<Word>,
172 index: usize,
173}
174
175impl<'a> Iterator for InnerNodeIterator<'a> {
176 type Item = InnerNodeInfo;
177
178 fn next(&mut self) -> Option<Self::Item> {
179 if self.index < self.nodes.len() / 2 {
180 let value = self.index;
181 let left = self.index * 2;
182 let right = left + 1;
183
184 self.index += 1;
185
186 Some(InnerNodeInfo {
187 value: self.nodes[value],
188 left: self.nodes[left],
189 right: self.nodes[right],
190 })
191 } else {
192 None
193 }
194 }
195}
196
197// UTILITY FUNCTIONS
198// ================================================================================================
199
200/// Utility to visualize a [MerkleTree] in text.
201pub fn tree_to_text(tree: &MerkleTree) -> Result<String, fmt::Error> {
202 let indent = " ";
203 let mut s = String::new();
204 s.push_str(&word_to_hex(&tree.root())?);
205 s.push('\n');
206 for d in 1..=tree.depth() {
207 let entries = 2u64.pow(d.into());
208 for i in 0..entries {
209 let index = NodeIndex::new(d, i).expect("The index must always be valid");
210 let node = tree.get_node(index).expect("The node must always be found");
211
212 for _ in 0..d {
213 s.push_str(indent);
214 }
215 s.push_str(&word_to_hex(&node)?);
216 s.push('\n');
217 }
218 }
219
220 Ok(s)
221}
222
223/// Utility to visualize a [MerklePath] in text.
224pub fn path_to_text(path: &MerklePath) -> Result<String, fmt::Error> {
225 let mut s = String::new();
226 s.push('[');
227
228 for el in path.iter() {
229 s.push_str(&word_to_hex(el)?);
230 s.push_str(", ");
231 }
232
233 // remove the last ", "
234 if path.len() != 0 {
235 s.pop();
236 s.pop();
237 }
238 s.push(']');
239
240 Ok(s)
241}
242
243// TESTS
244// ================================================================================================
245
246#[cfg(test)]
247mod tests {
248 use super::*;
249 use crate::merkle::{int_to_node, InnerNodeInfo};
250 use core::mem::size_of;
251 use proptest::prelude::*;
252
253 const LEAVES4: [Word; 4] = [int_to_node(1), int_to_node(2), int_to_node(3), int_to_node(4)];
254
255 const LEAVES8: [Word; 8] = [
256 int_to_node(1),
257 int_to_node(2),
258 int_to_node(3),
259 int_to_node(4),
260 int_to_node(5),
261 int_to_node(6),
262 int_to_node(7),
263 int_to_node(8),
264 ];
265
266 #[test]
267 fn build_merkle_tree() {
268 let tree = super::MerkleTree::new(LEAVES4.to_vec()).unwrap();
269 assert_eq!(8, tree.nodes.len());
270
271 // leaves were copied correctly
272 for (a, b) in tree.nodes.iter().skip(4).zip(LEAVES4.iter()) {
273 assert_eq!(a, b);
274 }
275
276 let (root, node2, node3) = compute_internal_nodes();
277
278 assert_eq!(root, tree.nodes[1]);
279 assert_eq!(node2, tree.nodes[2]);
280 assert_eq!(node3, tree.nodes[3]);
281
282 assert_eq!(root, tree.root());
283 }
284
285 #[test]
286 fn get_leaf() {
287 let tree = super::MerkleTree::new(LEAVES4.to_vec()).unwrap();
288
289 // check depth 2
290 assert_eq!(LEAVES4[0], tree.get_node(NodeIndex::make(2, 0)).unwrap());
291 assert_eq!(LEAVES4[1], tree.get_node(NodeIndex::make(2, 1)).unwrap());
292 assert_eq!(LEAVES4[2], tree.get_node(NodeIndex::make(2, 2)).unwrap());
293 assert_eq!(LEAVES4[3], tree.get_node(NodeIndex::make(2, 3)).unwrap());
294
295 // check depth 1
296 let (_, node2, node3) = compute_internal_nodes();
297
298 assert_eq!(node2, tree.get_node(NodeIndex::make(1, 0)).unwrap());
299 assert_eq!(node3, tree.get_node(NodeIndex::make(1, 1)).unwrap());
300 }
301
302 #[test]
303 fn get_path() {
304 let tree = super::MerkleTree::new(LEAVES4.to_vec()).unwrap();
305
306 let (_, node2, node3) = compute_internal_nodes();
307
308 // check depth 2
309 assert_eq!(vec![LEAVES4[1], node3], *tree.get_path(NodeIndex::make(2, 0)).unwrap());
310 assert_eq!(vec![LEAVES4[0], node3], *tree.get_path(NodeIndex::make(2, 1)).unwrap());
311 assert_eq!(vec![LEAVES4[3], node2], *tree.get_path(NodeIndex::make(2, 2)).unwrap());
312 assert_eq!(vec![LEAVES4[2], node2], *tree.get_path(NodeIndex::make(2, 3)).unwrap());
313
314 // check depth 1
315 assert_eq!(vec![node3], *tree.get_path(NodeIndex::make(1, 0)).unwrap());
316 assert_eq!(vec![node2], *tree.get_path(NodeIndex::make(1, 1)).unwrap());
317 }
318
319 #[test]
320 fn update_leaf() {
321 let mut tree = super::MerkleTree::new(LEAVES8.to_vec()).unwrap();
322
323 // update one leaf
324 let value = 3;
325 let new_node = int_to_node(9);
326 let mut expected_leaves = LEAVES8.to_vec();
327 expected_leaves[value as usize] = new_node;
328 let expected_tree = super::MerkleTree::new(expected_leaves.clone()).unwrap();
329
330 tree.update_leaf(value, new_node).unwrap();
331 assert_eq!(expected_tree.nodes, tree.nodes);
332
333 // update another leaf
334 let value = 6;
335 let new_node = int_to_node(10);
336 expected_leaves[value as usize] = new_node;
337 let expected_tree = super::MerkleTree::new(expected_leaves.clone()).unwrap();
338
339 tree.update_leaf(value, new_node).unwrap();
340 assert_eq!(expected_tree.nodes, tree.nodes);
341 }
342
343 #[test]
344 fn nodes() -> Result<(), MerkleError> {
345 let tree = super::MerkleTree::new(LEAVES4.to_vec()).unwrap();
346 let root = tree.root();
347 let l1n0 = tree.get_node(NodeIndex::make(1, 0))?;
348 let l1n1 = tree.get_node(NodeIndex::make(1, 1))?;
349 let l2n0 = tree.get_node(NodeIndex::make(2, 0))?;
350 let l2n1 = tree.get_node(NodeIndex::make(2, 1))?;
351 let l2n2 = tree.get_node(NodeIndex::make(2, 2))?;
352 let l2n3 = tree.get_node(NodeIndex::make(2, 3))?;
353
354 let nodes: Vec<InnerNodeInfo> = tree.inner_nodes().collect();
355 let expected = vec![
356 InnerNodeInfo {
357 value: root,
358 left: l1n0,
359 right: l1n1,
360 },
361 InnerNodeInfo {
362 value: l1n0,
363 left: l2n0,
364 right: l2n1,
365 },
366 InnerNodeInfo {
367 value: l1n1,
368 left: l2n2,
369 right: l2n3,
370 },
371 ];
372 assert_eq!(nodes, expected);
373
374 Ok(())
375 }
376
377 proptest! {
378 #[test]
379 fn arbitrary_word_can_be_represented_as_digest(
380 a in prop::num::u64::ANY,
381 b in prop::num::u64::ANY,
382 c in prop::num::u64::ANY,
383 d in prop::num::u64::ANY,
384 ) {
385 // this test will assert the memory equivalence between word and digest.
386 // it is used to safeguard the `[MerkleTee::update_leaf]` implementation
387 // that assumes this equivalence.
388
389 // build a word and copy it to another address as digest
390 let word = [Felt::new(a), Felt::new(b), Felt::new(c), Felt::new(d)];
391 let digest = RpoDigest::from(word);
392
393 // assert the addresses are different
394 let word_ptr = (&word).as_ptr() as *const u8;
395 let digest_ptr = (&digest).as_ptr() as *const u8;
396 assert_ne!(word_ptr, digest_ptr);
397
398 // compare the bytes representation
399 let word_bytes = unsafe { slice::from_raw_parts(word_ptr, size_of::<Word>()) };
400 let digest_bytes = unsafe { slice::from_raw_parts(digest_ptr, size_of::<RpoDigest>()) };
401 assert_eq!(word_bytes, digest_bytes);
402 }
403 }
404
405 // HELPER FUNCTIONS
406 // --------------------------------------------------------------------------------------------
407
408 fn compute_internal_nodes() -> (Word, Word, Word) {
409 let node2 = Rpo256::hash_elements(&[LEAVES4[0], LEAVES4[1]].concat());
410 let node3 = Rpo256::hash_elements(&[LEAVES4[2], LEAVES4[3]].concat());
411 let root = Rpo256::merge(&[node2, node3]);
412
413 (root.into(), node2.into(), node3.into())
414 }
415}