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//! restabilished.
13use super::{
14 super::{InnerNodeInfo, MerklePath, RpoDigest, Vec},
15 bit::TrueBitPositionIterator,
16 MmrPeaks, MmrProof, Rpo256,
17};
18use core::fmt::{Display, Formatter};
19
20#[cfg(feature = "std")]
21use std::error::Error;
22
23// MMR
24// ===============================================================================================
25
26/// A fully materialized Merkle Mountain Range, with every tree in the forest and all their
27/// elements.
28///
29/// Since this is a full representation of the MMR, elements are never removed and the MMR will
30/// grow roughly `O(2n)` in number of leaf elements.
31#[derive(Debug, Clone)]
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
45#[derive(Debug, PartialEq, Eq, Copy, Clone)]
46pub enum MmrError {
47 InvalidPosition(usize),
48}
49
50impl Display for MmrError {
51 fn fmt(&self, fmt: &mut Formatter<'_>) -> Result<(), core::fmt::Error> {
52 match self {
53 MmrError::InvalidPosition(pos) => write!(fmt, "Mmr does not contain position {pos}"),
54 }
55 }
56}
57
58#[cfg(feature = "std")]
59impl Error for MmrError {}
60
61impl Default for Mmr {
62 fn default() -> Self {
63 Self::new()
64 }
65}
66
67impl Mmr {
68 // CONSTRUCTORS
69 // ============================================================================================
70
71 /// Constructor for an empty `Mmr`.
72 pub fn new() -> Mmr {
73 Mmr {
74 forest: 0,
75 nodes: Vec::new(),
76 }
77 }
78
79 // ACCESSORS
80 // ============================================================================================
81
82 /// Returns the MMR forest representation.
83 ///
84 /// The forest value has the following interpretations:
85 /// - its value is the number of elements in the forest
86 /// - bit count corresponds to the number of trees in the forest
87 /// - each true bit position determines the depth of a tree in the forest
88 pub const fn forest(&self) -> usize {
89 self.forest
90 }
91
92 // FUNCTIONALITY
93 // ============================================================================================
94
95 /// Given a leaf position, returns the Merkle path to its corresponding peak. If the position
96 /// is greater-or-equal than the tree size an error is returned.
97 ///
98 /// Note: The leaf position is the 0-indexed number corresponding to the order the leaves were
99 /// added, this corresponds to the MMR size _prior_ to adding the element. So the 1st element
100 /// has position 0, the second position 1, and so on.
101 pub fn open(&self, pos: usize) -> Result<MmrProof, MmrError> {
102 // find the target tree responsible for the MMR position
103 let tree_bit =
104 leaf_to_corresponding_tree(pos, self.forest).ok_or(MmrError::InvalidPosition(pos))?;
105 let forest_target = 1usize << tree_bit;
106
107 // isolate the trees before the target
108 let forest_before = self.forest & high_bitmask(tree_bit + 1);
109 let index_offset = nodes_in_forest(forest_before);
110
111 // find the root
112 let index = nodes_in_forest(forest_target) - 1;
113
114 // update the value position from global to the target tree
115 let relative_pos = pos - forest_before;
116
117 // collect the path and the final index of the target value
118 let (_, path) =
119 self.collect_merkle_path_and_value(tree_bit, relative_pos, index_offset, index);
120
121 Ok(MmrProof {
122 forest: self.forest,
123 position: pos,
124 merkle_path: MerklePath::new(path),
125 })
126 }
127
128 /// Returns the leaf value at position `pos`.
129 ///
130 /// Note: The leaf position is the 0-indexed number corresponding to the order the leaves were
131 /// added, this corresponds to the MMR size _prior_ to adding the element. So the 1st element
132 /// has position 0, the second position 1, and so on.
133 pub fn get(&self, pos: usize) -> Result<RpoDigest, MmrError> {
134 // find the target tree responsible for the MMR position
135 let tree_bit =
136 leaf_to_corresponding_tree(pos, self.forest).ok_or(MmrError::InvalidPosition(pos))?;
137 let forest_target = 1usize << tree_bit;
138
139 // isolate the trees before the target
140 let forest_before = self.forest & high_bitmask(tree_bit + 1);
141 let index_offset = nodes_in_forest(forest_before);
142
143 // find the root
144 let index = nodes_in_forest(forest_target) - 1;
145
146 // update the value position from global to the target tree
147 let relative_pos = pos - forest_before;
148
149 // collect the path and the final index of the target value
150 let (value, _) =
151 self.collect_merkle_path_and_value(tree_bit, relative_pos, index_offset, index);
152
153 Ok(value)
154 }
155
156 /// Adds a new element to the MMR.
157 pub fn add(&mut self, el: RpoDigest) {
158 // Note: every node is also a tree of size 1, adding an element to the forest creates a new
159 // rooted-tree of size 1. This may temporarily break the invariant that every tree in the
160 // forest has different sizes, the loop below will eagerly merge trees of same size and
161 // restore the invariant.
162 self.nodes.push(el);
163
164 let mut left_offset = self.nodes.len().saturating_sub(2);
165 let mut right = el;
166 let mut left_tree = 1;
167 while self.forest & left_tree != 0 {
168 right = Rpo256::merge(&[self.nodes[left_offset], right]);
169 self.nodes.push(right);
170
171 left_offset = left_offset.saturating_sub(nodes_in_forest(left_tree));
172 left_tree <<= 1;
173 }
174
175 self.forest += 1;
176 }
177
178 /// Returns an accumulator representing the current state of the MMR.
179 pub fn accumulator(&self) -> MmrPeaks {
180 let peaks: Vec<RpoDigest> = TrueBitPositionIterator::new(self.forest)
181 .rev()
182 .map(|bit| nodes_in_forest(1 << bit))
183 .scan(0, |offset, el| {
184 *offset += el;
185 Some(*offset)
186 })
187 .map(|offset| self.nodes[offset - 1])
188 .collect();
189
190 MmrPeaks {
191 num_leaves: self.forest,
192 peaks,
193 }
194 }
195
196 /// An iterator over inner nodes in the MMR. The order of iteration is unspecified.
197 pub fn inner_nodes(&self) -> MmrNodes {
198 MmrNodes {
199 mmr: self,
200 forest: 0,
201 last_right: 0,
202 index: 0,
203 }
204 }
205
206 // UTILITIES
207 // ============================================================================================
208
209 /// Internal function used to collect the Merkle path of a value.
210 fn collect_merkle_path_and_value(
211 &self,
212 tree_bit: u32,
213 relative_pos: usize,
214 index_offset: usize,
215 mut index: usize,
216 ) -> (RpoDigest, Vec<RpoDigest>) {
217 // collect the Merkle path
218 let mut tree_depth = tree_bit as usize;
219 let mut path = Vec::with_capacity(tree_depth + 1);
220 while tree_depth > 0 {
221 let bit = relative_pos & tree_depth;
222 let right_offset = index - 1;
223 let left_offset = right_offset - nodes_in_forest(tree_depth);
224
225 // Elements to the right have a higher position because they were
226 // added later. Therefore when the bit is true the node's path is
227 // to the right, and its sibling to the left.
228 let sibling = if bit != 0 {
229 index = right_offset;
230 self.nodes[index_offset + left_offset]
231 } else {
232 index = left_offset;
233 self.nodes[index_offset + right_offset]
234 };
235
236 tree_depth >>= 1;
237 path.push(sibling);
238 }
239
240 // the rest of the codebase has the elements going from leaf to root, adjust it here for
241 // easy of use/consistency sake
242 path.reverse();
243
244 let value = self.nodes[index_offset + index];
245 (value, path)
246 }
247}
248
249impl<T> From<T> for Mmr
250where
251 T: IntoIterator<Item = RpoDigest>,
252{
253 fn from(values: T) -> Self {
254 let mut mmr = Mmr::new();
255 for v in values {
256 mmr.add(v)
257 }
258 mmr
259 }
260}
261
262// ITERATOR
263// ===============================================================================================
264
265/// Yields inner nodes of the [Mmr].
266pub struct MmrNodes<'a> {
267 /// [Mmr] being yielded, when its `forest` value is matched, the iterations is finished.
268 mmr: &'a Mmr,
269 /// Keeps track of the left nodes yielded so far waiting for a right pair, this matches the
270 /// semantics of the [Mmr]'s forest attribute, since that too works as a buffer of left nodes
271 /// waiting for a pair to be hashed together.
272 forest: usize,
273 /// Keeps track of the last right node yielded, after this value is set, the next iteration
274 /// will be its parent with its corresponding left node that has been yield already.
275 last_right: usize,
276 /// The current index in the `nodes` vector.
277 index: usize,
278}
279
280impl<'a> Iterator for MmrNodes<'a> {
281 type Item = InnerNodeInfo;
282
283 fn next(&mut self) -> Option<Self::Item> {
284 debug_assert!(self.last_right.count_ones() <= 1, "last_right tracks zero or one element");
285
286 // only parent nodes are emitted, remove the single node tree from the forest
287 let target = self.mmr.forest & (usize::MAX << 1);
288
289 if self.forest < target {
290 if self.last_right == 0 {
291 // yield the left leaf
292 debug_assert!(self.last_right == 0, "left must be before right");
293 self.forest |= 1;
294 self.index += 1;
295
296 // yield the right leaf
297 debug_assert!((self.forest & 1) == 1, "right must be after left");
298 self.last_right |= 1;
299 self.index += 1;
300 };
301
302 debug_assert!(
303 self.forest & self.last_right != 0,
304 "parent requires both a left and right",
305 );
306
307 // compute the number of nodes in the right tree, this is the offset to the
308 // previous left parent
309 let right_nodes = nodes_in_forest(self.last_right);
310 // the next parent position is one above the position of the pair
311 let parent = self.last_right << 1;
312
313 // the left node has been paired and the current parent yielded, removed it from the forest
314 self.forest ^= self.last_right;
315 if self.forest & parent == 0 {
316 // this iteration yielded the left parent node
317 debug_assert!(self.forest & 1 == 0, "next iteration yields a left leaf");
318 self.last_right = 0;
319 self.forest ^= parent;
320 } else {
321 // the left node of the parent level has been yielded already, this iteration
322 // was the right parent. Next iteration yields their parent.
323 self.last_right = parent;
324 }
325
326 // yields a parent
327 let value = self.mmr.nodes[self.index];
328 let right = self.mmr.nodes[self.index - 1];
329 let left = self.mmr.nodes[self.index - 1 - right_nodes];
330 self.index += 1;
331 let node = InnerNodeInfo { value, left, right };
332
333 Some(node)
334 } else {
335 None
336 }
337 }
338}
339
340// UTILITIES
341// ===============================================================================================
342
343/// Given a 0-indexed leaf position and the current forest, return the tree number responsible for
344/// the position.
345///
346/// Note:
347/// The result is a tree position `p`, it has the following interpretations. $p+1$ is the depth of
348/// the tree, which corresponds to the size of a Merkle proof for that tree. $2^p$ is equal to the
349/// number of leaves in this particular tree. and $2^(p+1)-1$ corresponds to size of the tree.
350pub(crate) const fn leaf_to_corresponding_tree(pos: usize, forest: usize) -> Option<u32> {
351 if pos >= forest {
352 None
353 } else {
354 // - each bit in the forest is a unique tree and the bit position its power-of-two size
355 // - each tree owns a consecutive range of positions equal to its size from left-to-right
356 // - this means the first tree owns from `0` up to the `2^k_0` first positions, where `k_0`
357 // is the highest true bit position, the second tree from `2^k_0 + 1` up to `2^k_1` where
358 // `k_1` is the second higest bit, so on.
359 // - this means the highest bits work as a category marker, and the position is owned by
360 // the first tree which doesn't share a high bit with the position
361 let before = forest & pos;
362 let after = forest ^ before;
363 let tree = after.ilog2();
364
365 Some(tree)
366 }
367}
368
369/// Return a bitmask for the bits including and above the given position.
370pub(crate) const fn high_bitmask(bit: u32) -> usize {
371 if bit > usize::BITS - 1 {
372 0
373 } else {
374 usize::MAX << bit
375 }
376}
377
378/// Return the total number of nodes of a given forest
379///
380/// Panics:
381///
382/// This will panic if the forest has size greater than `usize::MAX / 2`
383pub(crate) const fn nodes_in_forest(forest: usize) -> usize {
384 // - the size of a perfect binary tree is $2^{k+1}-1$ or $2*2^k-1$
385 // - the forest represents the sum of $2^k$ so a single multiplication is necessary
386 // - the number of `-1` is the same as the number of trees, which is the same as the number
387 // bits set
388 let tree_count = forest.count_ones() as usize;
389 forest * 2 - tree_count
390}