miden-crypto/src/merkle/mmr/full.rs
src/merkle/mmr/full.rsRaw
1//! A fully materialized Merkle mountain range (MMR).
2//!
3//! A MMR is a forest structure, i.e. it is an ordered set of disjoint rooted trees. The trees are
4//! ordered by size, from the most to least number of leaves. Every tree is a perfect binary tree,
5//! meaning a tree has all its leaves at the same depth, and every inner node has a branch-factor
6//! of 2 with both children set.
7//!
8//! Additionally the structure only supports adding leaves to the right-most tree, the one with the
9//! least number of leaves. The structure preserves the invariant that each tree has different
10//! depths, i.e. as part of adding adding a new element to the forest the trees with same depth are
11//! merged, creating a new tree with depth d+1, this process is continued until the property is
12//! reestablished.
13use alloc::vec::Vec;
14
15use super::{
16 super::{InnerNodeInfo, MerklePath},
17 bit::TrueBitPositionIterator,
18 leaf_to_corresponding_tree, nodes_in_forest, MmrDelta, MmrError, MmrPeaks, MmrProof, Rpo256,
19 RpoDigest,
20};
21
22// MMR
23// ===============================================================================================
24
25/// A fully materialized Merkle Mountain Range, with every tree in the forest and all their
26/// elements.
27///
28/// Since this is a full representation of the MMR, elements are never removed and the MMR will
29/// grow roughly `O(2n)` in number of leaf elements.
30#[derive(Debug, Clone)]
31#[cfg_attr(feature = "serde", derive(serde::Deserialize, serde::Serialize))]
32pub struct Mmr {
33 /// Refer to the `forest` method documentation for details of the semantics of this value.
34 pub(super) forest: usize,
35
36 /// Contains every element of the forest.
37 ///
38 /// The trees are in postorder sequential representation. This representation allows for all
39 /// the elements of every tree in the forest to be stored in the same sequential buffer. It
40 /// also means new elements can be added to the forest, and merging of trees is very cheap with
41 /// no need to copy elements.
42 pub(super) nodes: Vec<RpoDigest>,
43}
44
45impl Default for Mmr {
46 fn default() -> Self {
47 Self::new()
48 }
49}
50
51impl Mmr {
52 // CONSTRUCTORS
53 // ============================================================================================
54
55 /// Constructor for an empty `Mmr`.
56 pub fn new() -> Mmr {
57 Mmr { forest: 0, nodes: Vec::new() }
58 }
59
60 // ACCESSORS
61 // ============================================================================================
62
63 /// Returns the MMR forest representation.
64 ///
65 /// The forest value has the following interpretations:
66 /// - its value is the number of elements in the forest
67 /// - bit count corresponds to the number of trees in the forest
68 /// - each true bit position determines the depth of a tree in the forest
69 pub const fn forest(&self) -> usize {
70 self.forest
71 }
72
73 // FUNCTIONALITY
74 // ============================================================================================
75
76 /// Given a leaf position, returns the Merkle path to its corresponding peak. If the position
77 /// is greater-or-equal than the tree size an error is returned.
78 ///
79 /// Note: The leaf position is the 0-indexed number corresponding to the order the leaves were
80 /// added, this corresponds to the MMR size _prior_ to adding the element. So the 1st element
81 /// has position 0, the second position 1, and so on.
82 pub fn open(&self, pos: usize, target_forest: usize) -> Result<MmrProof, MmrError> {
83 // find the target tree responsible for the MMR position
84 let tree_bit =
85 leaf_to_corresponding_tree(pos, target_forest).ok_or(MmrError::InvalidPosition(pos))?;
86
87 // isolate the trees before the target
88 let forest_before = target_forest & high_bitmask(tree_bit + 1);
89 let index_offset = nodes_in_forest(forest_before);
90
91 // update the value position from global to the target tree
92 let relative_pos = pos - forest_before;
93
94 // collect the path and the final index of the target value
95 let (_, path) = self.collect_merkle_path_and_value(tree_bit, relative_pos, index_offset);
96
97 Ok(MmrProof {
98 forest: target_forest,
99 position: pos,
100 merkle_path: MerklePath::new(path),
101 })
102 }
103
104 /// Returns the leaf value at position `pos`.
105 ///
106 /// Note: The leaf position is the 0-indexed number corresponding to the order the leaves were
107 /// added, this corresponds to the MMR size _prior_ to adding the element. So the 1st element
108 /// has position 0, the second position 1, and so on.
109 pub fn get(&self, pos: usize) -> Result<RpoDigest, MmrError> {
110 // find the target tree responsible for the MMR position
111 let tree_bit =
112 leaf_to_corresponding_tree(pos, self.forest).ok_or(MmrError::InvalidPosition(pos))?;
113
114 // isolate the trees before the target
115 let forest_before = self.forest & high_bitmask(tree_bit + 1);
116 let index_offset = nodes_in_forest(forest_before);
117
118 // update the value position from global to the target tree
119 let relative_pos = pos - forest_before;
120
121 // collect the path and the final index of the target value
122 let (value, _) = self.collect_merkle_path_and_value(tree_bit, relative_pos, index_offset);
123
124 Ok(value)
125 }
126
127 /// Adds a new element to the MMR.
128 pub fn add(&mut self, el: RpoDigest) {
129 // Note: every node is also a tree of size 1, adding an element to the forest creates a new
130 // rooted-tree of size 1. This may temporarily break the invariant that every tree in the
131 // forest has different sizes, the loop below will eagerly merge trees of same size and
132 // restore the invariant.
133 self.nodes.push(el);
134
135 let mut left_offset = self.nodes.len().saturating_sub(2);
136 let mut right = el;
137 let mut left_tree = 1;
138 while self.forest & left_tree != 0 {
139 right = Rpo256::merge(&[self.nodes[left_offset], right]);
140 self.nodes.push(right);
141
142 left_offset = left_offset.saturating_sub(nodes_in_forest(left_tree));
143 left_tree <<= 1;
144 }
145
146 self.forest += 1;
147 }
148
149 /// Returns an peaks of the MMR for the version specified by `forest`.
150 pub fn peaks(&self, forest: usize) -> Result<MmrPeaks, MmrError> {
151 if forest > self.forest {
152 return Err(MmrError::InvalidPeaks);
153 }
154
155 let peaks: Vec<RpoDigest> = TrueBitPositionIterator::new(forest)
156 .rev()
157 .map(|bit| nodes_in_forest(1 << bit))
158 .scan(0, |offset, el| {
159 *offset += el;
160 Some(*offset)
161 })
162 .map(|offset| self.nodes[offset - 1])
163 .collect();
164
165 // Safety: the invariant is maintained by the [Mmr]
166 let peaks = MmrPeaks::new(forest, peaks).unwrap();
167
168 Ok(peaks)
169 }
170
171 /// Compute the required update to `original_forest`.
172 ///
173 /// The result is a packed sequence of the authentication elements required to update the trees
174 /// that have been merged together, followed by the new peaks of the [Mmr].
175 pub fn get_delta(&self, from_forest: usize, to_forest: usize) -> Result<MmrDelta, MmrError> {
176 if to_forest > self.forest || from_forest > to_forest {
177 return Err(MmrError::InvalidPeaks);
178 }
179
180 if from_forest == to_forest {
181 return Ok(MmrDelta { forest: to_forest, data: Vec::new() });
182 }
183
184 let mut result = Vec::new();
185
186 // Find the largest tree in this [Mmr] which is new to `from_forest`.
187 let candidate_trees = to_forest ^ from_forest;
188 let mut new_high = 1 << candidate_trees.ilog2();
189
190 // Collect authentication nodes used for tree merges
191 // ----------------------------------------------------------------------------------------
192
193 // Find the trees from `from_forest` that have been merged into `new_high`.
194 let mut merges = from_forest & (new_high - 1);
195
196 // Find the peaks that are common to `from_forest` and this [Mmr]
197 let common_trees = from_forest ^ merges;
198
199 if merges != 0 {
200 // Skip the smallest trees unknown to `from_forest`.
201 let mut target = 1 << merges.trailing_zeros();
202
203 // Collect siblings required to computed the merged tree's peak
204 while target < new_high {
205 // Computes the offset to the smallest know peak
206 // - common_trees: peaks unchanged in the current update, target comes after these.
207 // - merges: peaks that have not been merged so far, target comes after these.
208 // - target: tree from which to load the sibling. On the first iteration this is a
209 // value known by the partial mmr, on subsequent iterations this value is to be
210 // computed from the known peaks and provided authentication nodes.
211 let known = nodes_in_forest(common_trees | merges | target);
212 let sibling = nodes_in_forest(target);
213 result.push(self.nodes[known + sibling - 1]);
214
215 // Update the target and account for tree merges
216 target <<= 1;
217 while merges & target != 0 {
218 target <<= 1;
219 }
220 // Remove the merges done so far
221 merges ^= merges & (target - 1);
222 }
223 } else {
224 // The new high tree may not be the result of any merges, if it is smaller than all the
225 // trees of `from_forest`.
226 new_high = 0;
227 }
228
229 // Collect the new [Mmr] peaks
230 // ----------------------------------------------------------------------------------------
231
232 let mut new_peaks = to_forest ^ common_trees ^ new_high;
233 let old_peaks = to_forest ^ new_peaks;
234 let mut offset = nodes_in_forest(old_peaks);
235 while new_peaks != 0 {
236 let target = 1 << new_peaks.ilog2();
237 offset += nodes_in_forest(target);
238 result.push(self.nodes[offset - 1]);
239 new_peaks ^= target;
240 }
241
242 Ok(MmrDelta { forest: to_forest, data: result })
243 }
244
245 /// An iterator over inner nodes in the MMR. The order of iteration is unspecified.
246 pub fn inner_nodes(&self) -> MmrNodes {
247 MmrNodes {
248 mmr: self,
249 forest: 0,
250 last_right: 0,
251 index: 0,
252 }
253 }
254
255 // UTILITIES
256 // ============================================================================================
257
258 /// Internal function used to collect the Merkle path of a value.
259 ///
260 /// The arguments are relative to the target tree. To compute the opening of the second leaf
261 /// for a tree with depth 2 in the forest `0b110`:
262 ///
263 /// - `tree_bit`: Depth of the target tree, e.g. 2 for the smallest tree.
264 /// - `relative_pos`: 0-indexed leaf position in the target tree, e.g. 1 for the second leaf.
265 /// - `index_offset`: Node count prior to the target tree, e.g. 7 for the tree of depth 3.
266 fn collect_merkle_path_and_value(
267 &self,
268 tree_bit: u32,
269 relative_pos: usize,
270 index_offset: usize,
271 ) -> (RpoDigest, Vec<RpoDigest>) {
272 // see documentation of `leaf_to_corresponding_tree` for details
273 let tree_depth = (tree_bit + 1) as usize;
274 let mut path = Vec::with_capacity(tree_depth);
275
276 // The tree walk below goes from the root to the leaf, compute the root index to start
277 let mut forest_target = 1usize << tree_bit;
278 let mut index = nodes_in_forest(forest_target) - 1;
279
280 // Loop until the leaf is reached
281 while forest_target > 1 {
282 // Update the depth of the tree to correspond to a subtree
283 forest_target >>= 1;
284
285 // compute the indices of the right and left subtrees based on the post-order
286 let right_offset = index - 1;
287 let left_offset = right_offset - nodes_in_forest(forest_target);
288
289 let left_or_right = relative_pos & forest_target;
290 let sibling = if left_or_right != 0 {
291 // going down the right subtree, the right child becomes the new root
292 index = right_offset;
293 // and the left child is the authentication
294 self.nodes[index_offset + left_offset]
295 } else {
296 index = left_offset;
297 self.nodes[index_offset + right_offset]
298 };
299
300 path.push(sibling);
301 }
302
303 debug_assert!(path.len() == tree_depth - 1);
304
305 // the rest of the codebase has the elements going from leaf to root, adjust it here for
306 // easy of use/consistency sake
307 path.reverse();
308
309 let value = self.nodes[index_offset + index];
310 (value, path)
311 }
312}
313
314// CONVERSIONS
315// ================================================================================================
316
317impl<T> From<T> for Mmr
318where
319 T: IntoIterator<Item = RpoDigest>,
320{
321 fn from(values: T) -> Self {
322 let mut mmr = Mmr::new();
323 for v in values {
324 mmr.add(v)
325 }
326 mmr
327 }
328}
329
330// ITERATOR
331// ===============================================================================================
332
333/// Yields inner nodes of the [Mmr].
334pub struct MmrNodes<'a> {
335 /// [Mmr] being yielded, when its `forest` value is matched, the iterations is finished.
336 mmr: &'a Mmr,
337 /// Keeps track of the left nodes yielded so far waiting for a right pair, this matches the
338 /// semantics of the [Mmr]'s forest attribute, since that too works as a buffer of left nodes
339 /// waiting for a pair to be hashed together.
340 forest: usize,
341 /// Keeps track of the last right node yielded, after this value is set, the next iteration
342 /// will be its parent with its corresponding left node that has been yield already.
343 last_right: usize,
344 /// The current index in the `nodes` vector.
345 index: usize,
346}
347
348impl<'a> Iterator for MmrNodes<'a> {
349 type Item = InnerNodeInfo;
350
351 fn next(&mut self) -> Option<Self::Item> {
352 debug_assert!(self.last_right.count_ones() <= 1, "last_right tracks zero or one element");
353
354 // only parent nodes are emitted, remove the single node tree from the forest
355 let target = self.mmr.forest & (usize::MAX << 1);
356
357 if self.forest < target {
358 if self.last_right == 0 {
359 // yield the left leaf
360 debug_assert!(self.last_right == 0, "left must be before right");
361 self.forest |= 1;
362 self.index += 1;
363
364 // yield the right leaf
365 debug_assert!((self.forest & 1) == 1, "right must be after left");
366 self.last_right |= 1;
367 self.index += 1;
368 };
369
370 debug_assert!(
371 self.forest & self.last_right != 0,
372 "parent requires both a left and right",
373 );
374
375 // compute the number of nodes in the right tree, this is the offset to the
376 // previous left parent
377 let right_nodes = nodes_in_forest(self.last_right);
378 // the next parent position is one above the position of the pair
379 let parent = self.last_right << 1;
380
381 // the left node has been paired and the current parent yielded, removed it from the
382 // forest
383 self.forest ^= self.last_right;
384 if self.forest & parent == 0 {
385 // this iteration yielded the left parent node
386 debug_assert!(self.forest & 1 == 0, "next iteration yields a left leaf");
387 self.last_right = 0;
388 self.forest ^= parent;
389 } else {
390 // the left node of the parent level has been yielded already, this iteration
391 // was the right parent. Next iteration yields their parent.
392 self.last_right = parent;
393 }
394
395 // yields a parent
396 let value = self.mmr.nodes[self.index];
397 let right = self.mmr.nodes[self.index - 1];
398 let left = self.mmr.nodes[self.index - 1 - right_nodes];
399 self.index += 1;
400 let node = InnerNodeInfo { value, left, right };
401
402 Some(node)
403 } else {
404 None
405 }
406 }
407}
408
409// UTILITIES
410// ===============================================================================================
411
412/// Return a bitmask for the bits including and above the given position.
413pub(crate) const fn high_bitmask(bit: u32) -> usize {
414 if bit > usize::BITS - 1 {
415 0
416 } else {
417 usize::MAX << bit
418 }
419}