miden-crypto/src/merkle/tiered_smt/mod.rs
src/merkle/tiered_smt/mod.rsRaw
1use super::{
2 BTreeMap, BTreeSet, EmptySubtreeRoots, InnerNodeInfo, MerkleError, MerklePath, NodeIndex,
3 Rpo256, RpoDigest, StarkField, Vec, Word,
4};
5use crate::utils::vec;
6use core::{cmp, ops::Deref};
7
8mod nodes;
9use nodes::NodeStore;
10
11mod values;
12use values::ValueStore;
13
14mod proof;
15pub use proof::TieredSmtProof;
16
17mod error;
18pub use error::TieredSmtProofError;
19
20#[cfg(test)]
21mod tests;
22
23// TIERED SPARSE MERKLE TREE
24// ================================================================================================
25
26/// Tiered (compacted) Sparse Merkle tree mapping 256-bit keys to 256-bit values. Both keys and
27/// values are represented by 4 field elements.
28///
29/// Leaves in the tree can exist only on specific depths called "tiers". These depths are: 16, 32,
30/// 48, and 64. Initially, when a tree is empty, it is equivalent to an empty Sparse Merkle tree
31/// of depth 64 (i.e., leaves at depth 64 are set to [ZERO; 4]). As non-empty values are inserted
32/// into the tree they are added to the first available tier.
33///
34/// For example, when the first key-value pair is inserted, it will be stored in a node at depth
35/// 16 such that the 16 most significant bits of the key determine the position of the node at
36/// depth 16. If another value with a key sharing the same 16-bit prefix is inserted, both values
37/// move into the next tier (depth 32). This process is repeated until values end up at the bottom
38/// tier (depth 64). If multiple values have keys with a common 64-bit prefix, such key-value pairs
39/// are stored in a sorted list at the bottom tier.
40///
41/// To differentiate between internal and leaf nodes, node values are computed as follows:
42/// - Internal nodes: hash(left_child, right_child).
43/// - Leaf node at depths 16, 32, or 64: hash(key, value, domain=depth).
44/// - Leaf node at depth 64: hash([key_0, value_0, ..., key_n, value_n], domain=64).
45#[derive(Debug, Clone, PartialEq, Eq)]
46pub struct TieredSmt {
47 root: RpoDigest,
48 nodes: NodeStore,
49 values: ValueStore,
50}
51
52impl TieredSmt {
53 // CONSTANTS
54 // --------------------------------------------------------------------------------------------
55
56 /// The number of levels between tiers.
57 const TIER_SIZE: u8 = 16;
58
59 /// Depths at which leaves can exist in a tiered SMT.
60 const TIER_DEPTHS: [u8; 4] = [16, 32, 48, 64];
61
62 /// Maximum node depth. This is also the bottom tier of the tree.
63 const MAX_DEPTH: u8 = 64;
64
65 /// Value of an empty leaf.
66 pub const EMPTY_VALUE: Word = super::empty_roots::EMPTY_WORD;
67
68 // CONSTRUCTORS
69 // --------------------------------------------------------------------------------------------
70
71 /// Returns a new [TieredSmt] instantiated with the specified key-value pairs.
72 ///
73 /// # Errors
74 /// Returns an error if the provided entries contain multiple values for the same key.
75 pub fn with_leaves<R, I>(entries: R) -> Result<Self, MerkleError>
76 where
77 R: IntoIterator<IntoIter = I>,
78 I: Iterator<Item = (RpoDigest, Word)> + ExactSizeIterator,
79 {
80 // create an empty tree
81 let mut tree = Self::default();
82
83 // append leaves to the tree returning an error if a duplicate entry for the same key
84 // is found
85 let mut empty_entries = BTreeSet::new();
86 for (key, value) in entries {
87 let old_value = tree.insert(key, value);
88 if old_value != Self::EMPTY_VALUE || empty_entries.contains(&key) {
89 return Err(MerkleError::DuplicateValuesForKey(key));
90 }
91 // if we've processed an empty entry, add the key to the set of empty entry keys, and
92 // if this key was already in the set, return an error
93 if value == Self::EMPTY_VALUE && !empty_entries.insert(key) {
94 return Err(MerkleError::DuplicateValuesForKey(key));
95 }
96 }
97 Ok(tree)
98 }
99
100 // PUBLIC ACCESSORS
101 // --------------------------------------------------------------------------------------------
102
103 /// Returns the root of this Merkle tree.
104 pub const fn root(&self) -> RpoDigest {
105 self.root
106 }
107
108 /// Returns a node at the specified index.
109 ///
110 /// # Errors
111 /// Returns an error if:
112 /// - The specified index depth is 0 or greater than 64.
113 /// - The node with the specified index does not exists in the Merkle tree. This is possible
114 /// when a leaf node with the same index prefix exists at a tier higher than the requested
115 /// node.
116 pub fn get_node(&self, index: NodeIndex) -> Result<RpoDigest, MerkleError> {
117 self.nodes.get_node(index)
118 }
119
120 /// Returns a Merkle path from the node at the specified index to the root.
121 ///
122 /// The node itself is not included in the path.
123 ///
124 /// # Errors
125 /// Returns an error if:
126 /// - The specified index depth is 0 or greater than 64.
127 /// - The node with the specified index does not exists in the Merkle tree. This is possible
128 /// when a leaf node with the same index prefix exists at a tier higher than the node to
129 /// which the path is requested.
130 pub fn get_path(&self, index: NodeIndex) -> Result<MerklePath, MerkleError> {
131 self.nodes.get_path(index)
132 }
133
134 /// Returns the value associated with the specified key.
135 ///
136 /// If nothing was inserted into this tree for the specified key, [ZERO; 4] is returned.
137 pub fn get_value(&self, key: RpoDigest) -> Word {
138 match self.values.get(&key) {
139 Some(value) => *value,
140 None => Self::EMPTY_VALUE,
141 }
142 }
143
144 /// Returns a proof for a key-value pair defined by the specified key.
145 ///
146 /// The proof can be used to attest membership of this key-value pair in a Tiered Sparse Merkle
147 /// Tree defined by the same root as this tree.
148 pub fn prove(&self, key: RpoDigest) -> TieredSmtProof {
149 let (path, index, leaf_exists) = self.nodes.get_proof(&key);
150
151 let entries = if index.depth() == Self::MAX_DEPTH {
152 match self.values.get_all(index.value()) {
153 Some(entries) => entries,
154 None => vec![(key, Self::EMPTY_VALUE)],
155 }
156 } else if leaf_exists {
157 let entry =
158 self.values.get_first(index_to_prefix(&index)).expect("leaf entry not found");
159 debug_assert_eq!(entry.0, key);
160 vec![*entry]
161 } else {
162 vec![(key, Self::EMPTY_VALUE)]
163 };
164
165 TieredSmtProof::new(path, entries).expect("Bug detected, TSMT produced invalid proof")
166 }
167
168 // STATE MUTATORS
169 // --------------------------------------------------------------------------------------------
170
171 /// Inserts the provided value into the tree under the specified key and returns the value
172 /// previously stored under this key.
173 ///
174 /// If the value for the specified key was not previously set, [ZERO; 4] is returned.
175 pub fn insert(&mut self, key: RpoDigest, value: Word) -> Word {
176 // if an empty value is being inserted, remove the leaf node to make it look as if the
177 // value was never inserted
178 if value == Self::EMPTY_VALUE {
179 return self.remove_leaf_node(key);
180 }
181
182 // insert the value into the value store, and if the key was already in the store, update
183 // it with the new value
184 if let Some(old_value) = self.values.insert(key, value) {
185 if old_value != value {
186 // if the new value is different from the old value, determine the location of
187 // the leaf node for this key, build the node, and update the root
188 let (index, leaf_exists) = self.nodes.get_leaf_index(&key);
189 debug_assert!(leaf_exists);
190 let node = self.build_leaf_node(index, key, value);
191 self.root = self.nodes.update_leaf_node(index, node);
192 }
193 return old_value;
194 };
195
196 // determine the location for the leaf node; this index could have 3 different meanings:
197 // - it points to a root of an empty subtree or an empty node at depth 64; in this case,
198 // we can replace the node with the value node immediately.
199 // - it points to an existing leaf at the bottom tier (i.e., depth = 64); in this case,
200 // we need to process update the bottom leaf.
201 // - it points to an existing leaf node for a different key with the same prefix (same
202 // key case was handled above); in this case, we need to move the leaf to a lower tier
203 let (index, leaf_exists) = self.nodes.get_leaf_index(&key);
204
205 self.root = if leaf_exists && index.depth() == Self::MAX_DEPTH {
206 // returned index points to a leaf at the bottom tier
207 let node = self.build_leaf_node(index, key, value);
208 self.nodes.update_leaf_node(index, node)
209 } else if leaf_exists {
210 // returned index pointes to a leaf for a different key with the same prefix
211
212 // get the key-value pair for the key with the same prefix; since the key-value
213 // pair has already been inserted into the value store, we need to filter it out
214 // when looking for the other key-value pair
215 let (other_key, other_value) = self
216 .values
217 .get_first_filtered(index_to_prefix(&index), &key)
218 .expect("other key-value pair not found");
219
220 // determine how far down the tree should we move the leaves
221 let common_prefix_len = get_common_prefix_tier_depth(&key, other_key);
222 let depth = cmp::min(common_prefix_len + Self::TIER_SIZE, Self::MAX_DEPTH);
223
224 // compute node locations for new and existing key-value paris
225 let new_index = LeafNodeIndex::from_key(&key, depth);
226 let other_index = LeafNodeIndex::from_key(other_key, depth);
227
228 // compute node values for the new and existing key-value pairs
229 let new_node = self.build_leaf_node(new_index, key, value);
230 let other_node = self.build_leaf_node(other_index, *other_key, *other_value);
231
232 // replace the leaf located at index with a subtree containing nodes for new and
233 // existing key-value paris
234 self.nodes.replace_leaf_with_subtree(
235 index,
236 [(new_index, new_node), (other_index, other_node)],
237 )
238 } else {
239 // returned index points to an empty subtree or an empty leaf at the bottom tier
240 let node = self.build_leaf_node(index, key, value);
241 self.nodes.insert_leaf_node(index, node)
242 };
243
244 Self::EMPTY_VALUE
245 }
246
247 // ITERATORS
248 // --------------------------------------------------------------------------------------------
249
250 /// Returns an iterator over all key-value pairs in this [TieredSmt].
251 pub fn iter(&self) -> impl Iterator<Item = &(RpoDigest, Word)> {
252 self.values.iter()
253 }
254
255 /// Returns an iterator over all inner nodes of this [TieredSmt] (i.e., nodes not at depths 16
256 /// 32, 48, or 64).
257 ///
258 /// The iterator order is unspecified.
259 pub fn inner_nodes(&self) -> impl Iterator<Item = InnerNodeInfo> + '_ {
260 self.nodes.inner_nodes()
261 }
262
263 /// Returns an iterator over upper leaves (i.e., depth = 16, 32, or 48) for this [TieredSmt]
264 /// where each yielded item is a (node, key, value) tuple.
265 ///
266 /// The iterator order is unspecified.
267 pub fn upper_leaves(&self) -> impl Iterator<Item = (RpoDigest, RpoDigest, Word)> + '_ {
268 self.nodes.upper_leaves().map(|(index, node)| {
269 let key_prefix = index_to_prefix(index);
270 let (key, value) = self.values.get_first(key_prefix).expect("upper leaf not found");
271 debug_assert_eq!(*index, LeafNodeIndex::from_key(key, index.depth()).into());
272 (*node, *key, *value)
273 })
274 }
275
276 /// Returns an iterator over bottom leaves (i.e., depth = 64) of this [TieredSmt].
277 ///
278 /// Each yielded item consists of the hash of the leaf and its contents, where contents is
279 /// a vector containing key-value pairs of entries storied in this leaf.
280 ///
281 /// The iterator order is unspecified.
282 pub fn bottom_leaves(&self) -> impl Iterator<Item = (RpoDigest, Vec<(RpoDigest, Word)>)> + '_ {
283 self.nodes.bottom_leaves().map(|(&prefix, node)| {
284 let values = self.values.get_all(prefix).expect("bottom leaf not found");
285 (*node, values)
286 })
287 }
288
289 // HELPER METHODS
290 // --------------------------------------------------------------------------------------------
291
292 /// Removes the node holding the key-value pair for the specified key from this tree, and
293 /// returns the value associated with the specified key.
294 ///
295 /// If no value was associated with the specified key, [ZERO; 4] is returned.
296 fn remove_leaf_node(&mut self, key: RpoDigest) -> Word {
297 // remove the key-value pair from the value store; if no value was associated with the
298 // specified key, return.
299 let old_value = match self.values.remove(&key) {
300 Some(old_value) => old_value,
301 None => return Self::EMPTY_VALUE,
302 };
303
304 // determine the location of the leaf holding the key-value pair to be removed
305 let (index, leaf_exists) = self.nodes.get_leaf_index(&key);
306 debug_assert!(leaf_exists);
307
308 // if the leaf is at the bottom tier and after removing the key-value pair from it, the
309 // leaf is still not empty, we either just update it, or move it up to a higher tier (if
310 // the leaf doesn't have siblings at lower tiers)
311 if index.depth() == Self::MAX_DEPTH {
312 if let Some(entries) = self.values.get_all(index.value()) {
313 // if there is only one key-value pair left at the bottom leaf, and it can be
314 // moved up to a higher tier, truncate the branch and return
315 if entries.len() == 1 {
316 let new_depth = self.nodes.get_last_single_child_parent_depth(index.value());
317 if new_depth != Self::MAX_DEPTH {
318 let node = hash_upper_leaf(entries[0].0, entries[0].1, new_depth);
319 self.root = self.nodes.truncate_branch(index.value(), new_depth, node);
320 return old_value;
321 }
322 }
323
324 // otherwise just recompute the leaf hash and update the leaf node
325 let node = hash_bottom_leaf(&entries);
326 self.root = self.nodes.update_leaf_node(index, node);
327 return old_value;
328 };
329 }
330
331 // if the removed key-value pair has a lone sibling at the current tier with a root at
332 // higher tier, we need to move the sibling to a higher tier
333 if let Some((sib_key, sib_val, new_sib_index)) = self.values.get_lone_sibling(index) {
334 // determine the current index of the sibling node
335 let sib_index = LeafNodeIndex::from_key(sib_key, index.depth());
336 debug_assert!(sib_index.depth() > new_sib_index.depth());
337
338 // compute node value for the new location of the sibling leaf and replace the subtree
339 // with this leaf node
340 let node = self.build_leaf_node(new_sib_index, *sib_key, *sib_val);
341 let new_sib_depth = new_sib_index.depth();
342 self.root = self.nodes.replace_subtree_with_leaf(index, sib_index, new_sib_depth, node);
343 } else {
344 // if the removed key-value pair did not have a sibling at the current tier with a
345 // root at higher tiers, just clear the leaf node
346 self.root = self.nodes.clear_leaf_node(index);
347 }
348
349 old_value
350 }
351
352 /// Builds and returns a leaf node value for the node located as the specified index.
353 ///
354 /// This method assumes that the key-value pair for the node has already been inserted into
355 /// the value store, however, for depths 16, 32, and 48, the node is computed directly from
356 /// the passed-in values (for depth 64, the value store is queried to get all the key-value
357 /// pairs located at the specified index).
358 fn build_leaf_node(&self, index: LeafNodeIndex, key: RpoDigest, value: Word) -> RpoDigest {
359 let depth = index.depth();
360
361 // insert the key into index-key map and compute the new value of the node
362 if index.depth() == Self::MAX_DEPTH {
363 // for the bottom tier, we add the key-value pair to the existing leaf, or create a
364 // new leaf with this key-value pair
365 let values = self.values.get_all(index.value()).unwrap();
366 hash_bottom_leaf(&values)
367 } else {
368 debug_assert_eq!(self.values.get_first(index_to_prefix(&index)), Some(&(key, value)));
369 hash_upper_leaf(key, value, depth)
370 }
371 }
372}
373
374impl Default for TieredSmt {
375 fn default() -> Self {
376 let root = EmptySubtreeRoots::empty_hashes(Self::MAX_DEPTH)[0];
377 Self {
378 root,
379 nodes: NodeStore::new(root),
380 values: ValueStore::default(),
381 }
382 }
383}
384
385// LEAF NODE INDEX
386// ================================================================================================
387/// A wrapper around [NodeIndex] to provide type-safe references to nodes at depths 16, 32, 48, and
388/// 64.
389#[derive(Debug, Default, Copy, Clone, Eq, PartialEq, PartialOrd, Ord, Hash)]
390pub struct LeafNodeIndex(NodeIndex);
391
392impl LeafNodeIndex {
393 /// Returns a new [LeafNodeIndex] instantiated from the provided [NodeIndex].
394 ///
395 /// In debug mode, panics if index depth is not 16, 32, 48, or 64.
396 pub fn new(index: NodeIndex) -> Self {
397 // check if the depth is 16, 32, 48, or 64; this works because for a valid depth,
398 // depth - 16, can be 0, 16, 32, or 48 - i.e., the value is either 0 or any of the 4th
399 // or 5th bits are set. We can test for this by computing a bitwise AND with a value
400 // which has all but the 4th and 5th bits set (which is !48).
401 debug_assert_eq!(((index.depth() - 16) & !48), 0, "invalid tier depth {}", index.depth());
402 Self(index)
403 }
404
405 /// Returns a new [LeafNodeIndex] instantiated from the specified key inserted at the specified
406 /// depth.
407 ///
408 /// The value for the key is computed by taking n most significant bits from the most significant
409 /// element of the key, where n is the specified depth.
410 pub fn from_key(key: &RpoDigest, depth: u8) -> Self {
411 let mse = get_key_prefix(key);
412 Self::new(NodeIndex::new_unchecked(depth, mse >> (TieredSmt::MAX_DEPTH - depth)))
413 }
414
415 /// Returns a new [LeafNodeIndex] instantiated for testing purposes.
416 #[cfg(test)]
417 pub fn make(depth: u8, value: u64) -> Self {
418 Self::new(NodeIndex::make(depth, value))
419 }
420
421 /// Traverses towards the root until the specified depth is reached.
422 ///
423 /// The new depth must be a valid tier depth - i.e., 16, 32, 48, or 64.
424 pub fn move_up_to(&mut self, depth: u8) {
425 debug_assert_eq!(((depth - 16) & !48), 0, "invalid tier depth: {depth}");
426 self.0.move_up_to(depth);
427 }
428}
429
430impl Deref for LeafNodeIndex {
431 type Target = NodeIndex;
432
433 fn deref(&self) -> &Self::Target {
434 &self.0
435 }
436}
437
438impl From<NodeIndex> for LeafNodeIndex {
439 fn from(value: NodeIndex) -> Self {
440 Self::new(value)
441 }
442}
443
444impl From<LeafNodeIndex> for NodeIndex {
445 fn from(value: LeafNodeIndex) -> Self {
446 value.0
447 }
448}
449
450// HELPER FUNCTIONS
451// ================================================================================================
452
453/// Returns the value representing the 64 most significant bits of the specified key.
454fn get_key_prefix(key: &RpoDigest) -> u64 {
455 Word::from(key)[3].as_int()
456}
457
458/// Returns the index value shifted to be in the most significant bit positions of the returned
459/// u64 value.
460fn index_to_prefix(index: &NodeIndex) -> u64 {
461 index.value() << (TieredSmt::MAX_DEPTH - index.depth())
462}
463
464/// Returns tiered common prefix length between the most significant elements of the provided keys.
465///
466/// Specifically:
467/// - returns 64 if the most significant elements are equal.
468/// - returns 48 if the common prefix is between 48 and 63 bits.
469/// - returns 32 if the common prefix is between 32 and 47 bits.
470/// - returns 16 if the common prefix is between 16 and 31 bits.
471/// - returns 0 if the common prefix is fewer than 16 bits.
472fn get_common_prefix_tier_depth(key1: &RpoDigest, key2: &RpoDigest) -> u8 {
473 let e1 = get_key_prefix(key1);
474 let e2 = get_key_prefix(key2);
475 let ex = (e1 ^ e2).leading_zeros() as u8;
476 (ex / 16) * 16
477}
478
479/// Computes node value for leaves at tiers 16, 32, or 48.
480///
481/// Node value is computed as: hash(key || value, domain = depth).
482pub fn hash_upper_leaf(key: RpoDigest, value: Word, depth: u8) -> RpoDigest {
483 const NUM_UPPER_TIERS: usize = TieredSmt::TIER_DEPTHS.len() - 1;
484 debug_assert!(TieredSmt::TIER_DEPTHS[..NUM_UPPER_TIERS].contains(&depth));
485 Rpo256::merge_in_domain(&[key, value.into()], depth.into())
486}
487
488/// Computes node value for leaves at the bottom tier (depth 64).
489///
490/// Node value is computed as: hash([key_0, value_0, ..., key_n, value_n], domain=64).
491///
492/// TODO: when hashing in domain is implemented for `hash_elements()`, combine this function with
493/// `hash_upper_leaf()` function.
494pub fn hash_bottom_leaf(values: &[(RpoDigest, Word)]) -> RpoDigest {
495 let mut elements = Vec::with_capacity(values.len() * 8);
496 for (key, val) in values.iter() {
497 elements.extend_from_slice(key.as_elements());
498 elements.extend_from_slice(val.as_slice());
499 }
500 // TODO: hash in domain
501 Rpo256::hash_elements(&elements)
502}