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 /// An iterator over every inner node in the tree. The iterator order is unspecified.
154 pub fn inner_nodes(&self) -> MerkleTreeNodes<'_> {
155 MerkleTreeNodes {
156 nodes: &self.nodes,
157 index: 1, // index 0 is just padding, start at 1
158 }
159 }
160}
161
162// ITERATORS
163// ================================================================================================
164
165/// An iterator over every inner node of the [MerkleTree].
166///
167/// Use this to extract the data of the tree, there is no guarantee on the order of the elements.
168pub struct MerkleTreeNodes<'a> {
169 nodes: &'a Vec<Word>,
170 index: usize,
171}
172
173impl<'a> Iterator for MerkleTreeNodes<'a> {
174 type Item = InnerNodeInfo;
175
176 fn next(&mut self) -> Option<Self::Item> {
177 if self.index < self.nodes.len() / 2 {
178 let value = self.index;
179 let left = self.index * 2;
180 let right = left + 1;
181
182 self.index += 1;
183
184 Some(InnerNodeInfo {
185 value: self.nodes[value],
186 left: self.nodes[left],
187 right: self.nodes[right],
188 })
189 } else {
190 None
191 }
192 }
193}
194
195/// Utility to visualize a [MerkleTree] in text.
196pub fn tree_to_text(tree: &MerkleTree) -> Result<String, fmt::Error> {
197 let indent = " ";
198 let mut s = String::new();
199 s.push_str(&word_to_hex(&tree.root())?);
200 s.push('\n');
201 for d in 1..=tree.depth() {
202 let entries = 2u64.pow(d.into());
203 for i in 0..entries {
204 let index = NodeIndex::new(d, i).expect("The index must always be valid");
205 let node = tree.get_node(index).expect("The node must always be found");
206
207 for _ in 0..d {
208 s.push_str(indent);
209 }
210 s.push_str(&word_to_hex(&node)?);
211 s.push('\n');
212 }
213 }
214
215 Ok(s)
216}
217
218/// Utility to visualize a [MerklePath] in text.
219pub fn path_to_text(path: &MerklePath) -> Result<String, fmt::Error> {
220 let mut s = String::new();
221 s.push('[');
222
223 for el in path.iter() {
224 s.push_str(&word_to_hex(el)?);
225 s.push_str(", ");
226 }
227
228 // remove the last ", "
229 if path.len() != 0 {
230 s.pop();
231 s.pop();
232 }
233 s.push(']');
234
235 Ok(s)
236}
237
238// TESTS
239// ================================================================================================
240
241#[cfg(test)]
242mod tests {
243 use super::*;
244 use crate::merkle::{int_to_node, InnerNodeInfo};
245 use core::mem::size_of;
246 use proptest::prelude::*;
247
248 const LEAVES4: [Word; 4] = [int_to_node(1), int_to_node(2), int_to_node(3), int_to_node(4)];
249
250 const LEAVES8: [Word; 8] = [
251 int_to_node(1),
252 int_to_node(2),
253 int_to_node(3),
254 int_to_node(4),
255 int_to_node(5),
256 int_to_node(6),
257 int_to_node(7),
258 int_to_node(8),
259 ];
260
261 #[test]
262 fn build_merkle_tree() {
263 let tree = super::MerkleTree::new(LEAVES4.to_vec()).unwrap();
264 assert_eq!(8, tree.nodes.len());
265
266 // leaves were copied correctly
267 for (a, b) in tree.nodes.iter().skip(4).zip(LEAVES4.iter()) {
268 assert_eq!(a, b);
269 }
270
271 let (root, node2, node3) = compute_internal_nodes();
272
273 assert_eq!(root, tree.nodes[1]);
274 assert_eq!(node2, tree.nodes[2]);
275 assert_eq!(node3, tree.nodes[3]);
276
277 assert_eq!(root, tree.root());
278 }
279
280 #[test]
281 fn get_leaf() {
282 let tree = super::MerkleTree::new(LEAVES4.to_vec()).unwrap();
283
284 // check depth 2
285 assert_eq!(LEAVES4[0], tree.get_node(NodeIndex::make(2, 0)).unwrap());
286 assert_eq!(LEAVES4[1], tree.get_node(NodeIndex::make(2, 1)).unwrap());
287 assert_eq!(LEAVES4[2], tree.get_node(NodeIndex::make(2, 2)).unwrap());
288 assert_eq!(LEAVES4[3], tree.get_node(NodeIndex::make(2, 3)).unwrap());
289
290 // check depth 1
291 let (_, node2, node3) = compute_internal_nodes();
292
293 assert_eq!(node2, tree.get_node(NodeIndex::make(1, 0)).unwrap());
294 assert_eq!(node3, tree.get_node(NodeIndex::make(1, 1)).unwrap());
295 }
296
297 #[test]
298 fn get_path() {
299 let tree = super::MerkleTree::new(LEAVES4.to_vec()).unwrap();
300
301 let (_, node2, node3) = compute_internal_nodes();
302
303 // check depth 2
304 assert_eq!(vec![LEAVES4[1], node3], *tree.get_path(NodeIndex::make(2, 0)).unwrap());
305 assert_eq!(vec![LEAVES4[0], node3], *tree.get_path(NodeIndex::make(2, 1)).unwrap());
306 assert_eq!(vec![LEAVES4[3], node2], *tree.get_path(NodeIndex::make(2, 2)).unwrap());
307 assert_eq!(vec![LEAVES4[2], node2], *tree.get_path(NodeIndex::make(2, 3)).unwrap());
308
309 // check depth 1
310 assert_eq!(vec![node3], *tree.get_path(NodeIndex::make(1, 0)).unwrap());
311 assert_eq!(vec![node2], *tree.get_path(NodeIndex::make(1, 1)).unwrap());
312 }
313
314 #[test]
315 fn update_leaf() {
316 let mut tree = super::MerkleTree::new(LEAVES8.to_vec()).unwrap();
317
318 // update one leaf
319 let value = 3;
320 let new_node = int_to_node(9);
321 let mut expected_leaves = LEAVES8.to_vec();
322 expected_leaves[value as usize] = new_node;
323 let expected_tree = super::MerkleTree::new(expected_leaves.clone()).unwrap();
324
325 tree.update_leaf(value, new_node).unwrap();
326 assert_eq!(expected_tree.nodes, tree.nodes);
327
328 // update another leaf
329 let value = 6;
330 let new_node = int_to_node(10);
331 expected_leaves[value as usize] = new_node;
332 let expected_tree = super::MerkleTree::new(expected_leaves.clone()).unwrap();
333
334 tree.update_leaf(value, new_node).unwrap();
335 assert_eq!(expected_tree.nodes, tree.nodes);
336 }
337
338 #[test]
339 fn nodes() -> Result<(), MerkleError> {
340 let tree = super::MerkleTree::new(LEAVES4.to_vec()).unwrap();
341 let root = tree.root();
342 let l1n0 = tree.get_node(NodeIndex::make(1, 0))?;
343 let l1n1 = tree.get_node(NodeIndex::make(1, 1))?;
344 let l2n0 = tree.get_node(NodeIndex::make(2, 0))?;
345 let l2n1 = tree.get_node(NodeIndex::make(2, 1))?;
346 let l2n2 = tree.get_node(NodeIndex::make(2, 2))?;
347 let l2n3 = tree.get_node(NodeIndex::make(2, 3))?;
348
349 let nodes: Vec<InnerNodeInfo> = tree.inner_nodes().collect();
350 let expected = vec![
351 InnerNodeInfo {
352 value: root,
353 left: l1n0,
354 right: l1n1,
355 },
356 InnerNodeInfo {
357 value: l1n0,
358 left: l2n0,
359 right: l2n1,
360 },
361 InnerNodeInfo {
362 value: l1n1,
363 left: l2n2,
364 right: l2n3,
365 },
366 ];
367 assert_eq!(nodes, expected);
368
369 Ok(())
370 }
371
372 proptest! {
373 #[test]
374 fn arbitrary_word_can_be_represented_as_digest(
375 a in prop::num::u64::ANY,
376 b in prop::num::u64::ANY,
377 c in prop::num::u64::ANY,
378 d in prop::num::u64::ANY,
379 ) {
380 // this test will assert the memory equivalence between word and digest.
381 // it is used to safeguard the `[MerkleTee::update_leaf]` implementation
382 // that assumes this equivalence.
383
384 // build a word and copy it to another address as digest
385 let word = [Felt::new(a), Felt::new(b), Felt::new(c), Felt::new(d)];
386 let digest = RpoDigest::from(word);
387
388 // assert the addresses are different
389 let word_ptr = (&word).as_ptr() as *const u8;
390 let digest_ptr = (&digest).as_ptr() as *const u8;
391 assert_ne!(word_ptr, digest_ptr);
392
393 // compare the bytes representation
394 let word_bytes = unsafe { slice::from_raw_parts(word_ptr, size_of::<Word>()) };
395 let digest_bytes = unsafe { slice::from_raw_parts(digest_ptr, size_of::<RpoDigest>()) };
396 assert_eq!(word_bytes, digest_bytes);
397 }
398 }
399
400 // HELPER FUNCTIONS
401 // --------------------------------------------------------------------------------------------
402
403 fn compute_internal_nodes() -> (Word, Word, Word) {
404 let node2 = Rpo256::hash_elements(&[LEAVES4[0], LEAVES4[1]].concat());
405 let node3 = Rpo256::hash_elements(&[LEAVES4[2], LEAVES4[3]].concat());
406 let root = Rpo256::merge(&[node2, node3]);
407
408 (root.into(), node2.into(), node3.into())
409 }
410}