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)]
46#[cfg_attr(feature = "serde", derive(serde::Deserialize, serde::Serialize))]
47pub struct TieredSmt {
48 root: RpoDigest,
49 nodes: NodeStore,
50 values: ValueStore,
51}
52
53impl TieredSmt {
54 // CONSTANTS
55 // --------------------------------------------------------------------------------------------
56
57 /// The number of levels between tiers.
58 const TIER_SIZE: u8 = 16;
59
60 /// Depths at which leaves can exist in a tiered SMT.
61 const TIER_DEPTHS: [u8; 4] = [16, 32, 48, 64];
62
63 /// Maximum node depth. This is also the bottom tier of the tree.
64 const MAX_DEPTH: u8 = 64;
65
66 /// Value of an empty leaf.
67 pub const EMPTY_VALUE: Word = super::empty_roots::EMPTY_WORD;
68
69 // CONSTRUCTORS
70 // --------------------------------------------------------------------------------------------
71
72 /// Returns a new [TieredSmt] instantiated with the specified key-value pairs.
73 ///
74 /// # Errors
75 /// Returns an error if the provided entries contain multiple values for the same key.
76 pub fn with_leaves<R, I>(entries: R) -> Result<Self, MerkleError>
77 where
78 R: IntoIterator<IntoIter = I>,
79 I: Iterator<Item = (RpoDigest, Word)> + ExactSizeIterator,
80 {
81 // create an empty tree
82 let mut tree = Self::default();
83
84 // append leaves to the tree returning an error if a duplicate entry for the same key
85 // is found
86 let mut empty_entries = BTreeSet::new();
87 for (key, value) in entries {
88 let old_value = tree.insert(key, value);
89 if old_value != Self::EMPTY_VALUE || empty_entries.contains(&key) {
90 return Err(MerkleError::DuplicateValuesForKey(key));
91 }
92 // if we've processed an empty entry, add the key to the set of empty entry keys, and
93 // if this key was already in the set, return an error
94 if value == Self::EMPTY_VALUE && !empty_entries.insert(key) {
95 return Err(MerkleError::DuplicateValuesForKey(key));
96 }
97 }
98 Ok(tree)
99 }
100
101 // PUBLIC ACCESSORS
102 // --------------------------------------------------------------------------------------------
103
104 /// Returns the root of this Merkle tree.
105 pub const fn root(&self) -> RpoDigest {
106 self.root
107 }
108
109 /// Returns a node at the specified index.
110 ///
111 /// # Errors
112 /// Returns an error if:
113 /// - The specified index depth is 0 or greater than 64.
114 /// - The node with the specified index does not exists in the Merkle tree. This is possible
115 /// when a leaf node with the same index prefix exists at a tier higher than the requested
116 /// node.
117 pub fn get_node(&self, index: NodeIndex) -> Result<RpoDigest, MerkleError> {
118 self.nodes.get_node(index)
119 }
120
121 /// Returns a Merkle path from the node at the specified index to the root.
122 ///
123 /// The node itself is not included in the path.
124 ///
125 /// # Errors
126 /// Returns an error if:
127 /// - The specified index depth is 0 or greater than 64.
128 /// - The node with the specified index does not exists in the Merkle tree. This is possible
129 /// when a leaf node with the same index prefix exists at a tier higher than the node to
130 /// which the path is requested.
131 pub fn get_path(&self, index: NodeIndex) -> Result<MerklePath, MerkleError> {
132 self.nodes.get_path(index)
133 }
134
135 /// Returns the value associated with the specified key.
136 ///
137 /// If nothing was inserted into this tree for the specified key, [ZERO; 4] is returned.
138 pub fn get_value(&self, key: RpoDigest) -> Word {
139 match self.values.get(&key) {
140 Some(value) => *value,
141 None => Self::EMPTY_VALUE,
142 }
143 }
144
145 /// Returns a proof for a key-value pair defined by the specified key.
146 ///
147 /// The proof can be used to attest membership of this key-value pair in a Tiered Sparse Merkle
148 /// Tree defined by the same root as this tree.
149 pub fn prove(&self, key: RpoDigest) -> TieredSmtProof {
150 let (path, index, leaf_exists) = self.nodes.get_proof(&key);
151
152 let entries = if index.depth() == Self::MAX_DEPTH {
153 match self.values.get_all(index.value()) {
154 Some(entries) => entries,
155 None => vec![(key, Self::EMPTY_VALUE)],
156 }
157 } else if leaf_exists {
158 let entry =
159 self.values.get_first(index_to_prefix(&index)).expect("leaf entry not found");
160 debug_assert_eq!(entry.0, key);
161 vec![*entry]
162 } else {
163 vec![(key, Self::EMPTY_VALUE)]
164 };
165
166 TieredSmtProof::new(path, entries).expect("Bug detected, TSMT produced invalid proof")
167 }
168
169 // STATE MUTATORS
170 // --------------------------------------------------------------------------------------------
171
172 /// Inserts the provided value into the tree under the specified key and returns the value
173 /// previously stored under this key.
174 ///
175 /// If the value for the specified key was not previously set, [ZERO; 4] is returned.
176 pub fn insert(&mut self, key: RpoDigest, value: Word) -> Word {
177 // if an empty value is being inserted, remove the leaf node to make it look as if the
178 // value was never inserted
179 if value == Self::EMPTY_VALUE {
180 return self.remove_leaf_node(key);
181 }
182
183 // insert the value into the value store, and if the key was already in the store, update
184 // it with the new value
185 if let Some(old_value) = self.values.insert(key, value) {
186 if old_value != value {
187 // if the new value is different from the old value, determine the location of
188 // the leaf node for this key, build the node, and update the root
189 let (index, leaf_exists) = self.nodes.get_leaf_index(&key);
190 debug_assert!(leaf_exists);
191 let node = self.build_leaf_node(index, key, value);
192 self.root = self.nodes.update_leaf_node(index, node);
193 }
194 return old_value;
195 };
196
197 // determine the location for the leaf node; this index could have 3 different meanings:
198 // - it points to a root of an empty subtree or an empty node at depth 64; in this case,
199 // we can replace the node with the value node immediately.
200 // - it points to an existing leaf at the bottom tier (i.e., depth = 64); in this case,
201 // we need to process update the bottom leaf.
202 // - it points to an existing leaf node for a different key with the same prefix (same
203 // key case was handled above); in this case, we need to move the leaf to a lower tier
204 let (index, leaf_exists) = self.nodes.get_leaf_index(&key);
205
206 self.root = if leaf_exists && index.depth() == Self::MAX_DEPTH {
207 // returned index points to a leaf at the bottom tier
208 let node = self.build_leaf_node(index, key, value);
209 self.nodes.update_leaf_node(index, node)
210 } else if leaf_exists {
211 // returned index pointes to a leaf for a different key with the same prefix
212
213 // get the key-value pair for the key with the same prefix; since the key-value
214 // pair has already been inserted into the value store, we need to filter it out
215 // when looking for the other key-value pair
216 let (other_key, other_value) = self
217 .values
218 .get_first_filtered(index_to_prefix(&index), &key)
219 .expect("other key-value pair not found");
220
221 // determine how far down the tree should we move the leaves
222 let common_prefix_len = get_common_prefix_tier_depth(&key, other_key);
223 let depth = cmp::min(common_prefix_len + Self::TIER_SIZE, Self::MAX_DEPTH);
224
225 // compute node locations for new and existing key-value paris
226 let new_index = LeafNodeIndex::from_key(&key, depth);
227 let other_index = LeafNodeIndex::from_key(other_key, depth);
228
229 // compute node values for the new and existing key-value pairs
230 let new_node = self.build_leaf_node(new_index, key, value);
231 let other_node = self.build_leaf_node(other_index, *other_key, *other_value);
232
233 // replace the leaf located at index with a subtree containing nodes for new and
234 // existing key-value paris
235 self.nodes.replace_leaf_with_subtree(
236 index,
237 [(new_index, new_node), (other_index, other_node)],
238 )
239 } else {
240 // returned index points to an empty subtree or an empty leaf at the bottom tier
241 let node = self.build_leaf_node(index, key, value);
242 self.nodes.insert_leaf_node(index, node)
243 };
244
245 Self::EMPTY_VALUE
246 }
247
248 // ITERATORS
249 // --------------------------------------------------------------------------------------------
250
251 /// Returns an iterator over all key-value pairs in this [TieredSmt].
252 pub fn iter(&self) -> impl Iterator<Item = &(RpoDigest, Word)> {
253 self.values.iter()
254 }
255
256 /// Returns an iterator over all inner nodes of this [TieredSmt] (i.e., nodes not at depths 16
257 /// 32, 48, or 64).
258 ///
259 /// The iterator order is unspecified.
260 pub fn inner_nodes(&self) -> impl Iterator<Item = InnerNodeInfo> + '_ {
261 self.nodes.inner_nodes()
262 }
263
264 /// Returns an iterator over upper leaves (i.e., depth = 16, 32, or 48) for this [TieredSmt]
265 /// where each yielded item is a (node, key, value) tuple.
266 ///
267 /// The iterator order is unspecified.
268 pub fn upper_leaves(&self) -> impl Iterator<Item = (RpoDigest, RpoDigest, Word)> + '_ {
269 self.nodes.upper_leaves().map(|(index, node)| {
270 let key_prefix = index_to_prefix(index);
271 let (key, value) = self.values.get_first(key_prefix).expect("upper leaf not found");
272 debug_assert_eq!(*index, LeafNodeIndex::from_key(key, index.depth()).into());
273 (*node, *key, *value)
274 })
275 }
276
277 /// Returns an iterator over bottom leaves (i.e., depth = 64) of this [TieredSmt].
278 ///
279 /// Each yielded item consists of the hash of the leaf and its contents, where contents is
280 /// a vector containing key-value pairs of entries storied in this leaf.
281 ///
282 /// The iterator order is unspecified.
283 pub fn bottom_leaves(&self) -> impl Iterator<Item = (RpoDigest, Vec<(RpoDigest, Word)>)> + '_ {
284 self.nodes.bottom_leaves().map(|(&prefix, node)| {
285 let values = self.values.get_all(prefix).expect("bottom leaf not found");
286 (*node, values)
287 })
288 }
289
290 // HELPER METHODS
291 // --------------------------------------------------------------------------------------------
292
293 /// Removes the node holding the key-value pair for the specified key from this tree, and
294 /// returns the value associated with the specified key.
295 ///
296 /// If no value was associated with the specified key, [ZERO; 4] is returned.
297 fn remove_leaf_node(&mut self, key: RpoDigest) -> Word {
298 // remove the key-value pair from the value store; if no value was associated with the
299 // specified key, return.
300 let old_value = match self.values.remove(&key) {
301 Some(old_value) => old_value,
302 None => return Self::EMPTY_VALUE,
303 };
304
305 // determine the location of the leaf holding the key-value pair to be removed
306 let (index, leaf_exists) = self.nodes.get_leaf_index(&key);
307 debug_assert!(leaf_exists);
308
309 // if the leaf is at the bottom tier and after removing the key-value pair from it, the
310 // leaf is still not empty, we either just update it, or move it up to a higher tier (if
311 // the leaf doesn't have siblings at lower tiers)
312 if index.depth() == Self::MAX_DEPTH {
313 if let Some(entries) = self.values.get_all(index.value()) {
314 // if there is only one key-value pair left at the bottom leaf, and it can be
315 // moved up to a higher tier, truncate the branch and return
316 if entries.len() == 1 {
317 let new_depth = self.nodes.get_last_single_child_parent_depth(index.value());
318 if new_depth != Self::MAX_DEPTH {
319 let node = hash_upper_leaf(entries[0].0, entries[0].1, new_depth);
320 self.root = self.nodes.truncate_branch(index.value(), new_depth, node);
321 return old_value;
322 }
323 }
324
325 // otherwise just recompute the leaf hash and update the leaf node
326 let node = hash_bottom_leaf(&entries);
327 self.root = self.nodes.update_leaf_node(index, node);
328 return old_value;
329 };
330 }
331
332 // if the removed key-value pair has a lone sibling at the current tier with a root at
333 // higher tier, we need to move the sibling to a higher tier
334 if let Some((sib_key, sib_val, new_sib_index)) = self.values.get_lone_sibling(index) {
335 // determine the current index of the sibling node
336 let sib_index = LeafNodeIndex::from_key(sib_key, index.depth());
337 debug_assert!(sib_index.depth() > new_sib_index.depth());
338
339 // compute node value for the new location of the sibling leaf and replace the subtree
340 // with this leaf node
341 let node = self.build_leaf_node(new_sib_index, *sib_key, *sib_val);
342 let new_sib_depth = new_sib_index.depth();
343 self.root = self.nodes.replace_subtree_with_leaf(index, sib_index, new_sib_depth, node);
344 } else {
345 // if the removed key-value pair did not have a sibling at the current tier with a
346 // root at higher tiers, just clear the leaf node
347 self.root = self.nodes.clear_leaf_node(index);
348 }
349
350 old_value
351 }
352
353 /// Builds and returns a leaf node value for the node located as the specified index.
354 ///
355 /// This method assumes that the key-value pair for the node has already been inserted into
356 /// the value store, however, for depths 16, 32, and 48, the node is computed directly from
357 /// the passed-in values (for depth 64, the value store is queried to get all the key-value
358 /// pairs located at the specified index).
359 fn build_leaf_node(&self, index: LeafNodeIndex, key: RpoDigest, value: Word) -> RpoDigest {
360 let depth = index.depth();
361
362 // insert the key into index-key map and compute the new value of the node
363 if index.depth() == Self::MAX_DEPTH {
364 // for the bottom tier, we add the key-value pair to the existing leaf, or create a
365 // new leaf with this key-value pair
366 let values = self.values.get_all(index.value()).unwrap();
367 hash_bottom_leaf(&values)
368 } else {
369 debug_assert_eq!(self.values.get_first(index_to_prefix(&index)), Some(&(key, value)));
370 hash_upper_leaf(key, value, depth)
371 }
372 }
373}
374
375impl Default for TieredSmt {
376 fn default() -> Self {
377 let root = EmptySubtreeRoots::empty_hashes(Self::MAX_DEPTH)[0];
378 Self {
379 root,
380 nodes: NodeStore::new(root),
381 values: ValueStore::default(),
382 }
383 }
384}
385
386// LEAF NODE INDEX
387// ================================================================================================
388/// A wrapper around [NodeIndex] to provide type-safe references to nodes at depths 16, 32, 48, and
389/// 64.
390#[derive(Debug, Default, Copy, Clone, Eq, PartialEq, PartialOrd, Ord, Hash)]
391pub struct LeafNodeIndex(NodeIndex);
392
393impl LeafNodeIndex {
394 /// Returns a new [LeafNodeIndex] instantiated from the provided [NodeIndex].
395 ///
396 /// In debug mode, panics if index depth is not 16, 32, 48, or 64.
397 pub fn new(index: NodeIndex) -> Self {
398 // check if the depth is 16, 32, 48, or 64; this works because for a valid depth,
399 // depth - 16, can be 0, 16, 32, or 48 - i.e., the value is either 0 or any of the 4th
400 // or 5th bits are set. We can test for this by computing a bitwise AND with a value
401 // which has all but the 4th and 5th bits set (which is !48).
402 debug_assert_eq!(((index.depth() - 16) & !48), 0, "invalid tier depth {}", index.depth());
403 Self(index)
404 }
405
406 /// Returns a new [LeafNodeIndex] instantiated from the specified key inserted at the specified
407 /// depth.
408 ///
409 /// The value for the key is computed by taking n most significant bits from the most significant
410 /// element of the key, where n is the specified depth.
411 pub fn from_key(key: &RpoDigest, depth: u8) -> Self {
412 let mse = get_key_prefix(key);
413 Self::new(NodeIndex::new_unchecked(depth, mse >> (TieredSmt::MAX_DEPTH - depth)))
414 }
415
416 /// Returns a new [LeafNodeIndex] instantiated for testing purposes.
417 #[cfg(test)]
418 pub fn make(depth: u8, value: u64) -> Self {
419 Self::new(NodeIndex::make(depth, value))
420 }
421
422 /// Traverses towards the root until the specified depth is reached.
423 ///
424 /// The new depth must be a valid tier depth - i.e., 16, 32, 48, or 64.
425 pub fn move_up_to(&mut self, depth: u8) {
426 debug_assert_eq!(((depth - 16) & !48), 0, "invalid tier depth: {depth}");
427 self.0.move_up_to(depth);
428 }
429}
430
431impl Deref for LeafNodeIndex {
432 type Target = NodeIndex;
433
434 fn deref(&self) -> &Self::Target {
435 &self.0
436 }
437}
438
439impl From<NodeIndex> for LeafNodeIndex {
440 fn from(value: NodeIndex) -> Self {
441 Self::new(value)
442 }
443}
444
445impl From<LeafNodeIndex> for NodeIndex {
446 fn from(value: LeafNodeIndex) -> Self {
447 value.0
448 }
449}
450
451// HELPER FUNCTIONS
452// ================================================================================================
453
454/// Returns the value representing the 64 most significant bits of the specified key.
455fn get_key_prefix(key: &RpoDigest) -> u64 {
456 Word::from(key)[3].as_int()
457}
458
459/// Returns the index value shifted to be in the most significant bit positions of the returned
460/// u64 value.
461fn index_to_prefix(index: &NodeIndex) -> u64 {
462 index.value() << (TieredSmt::MAX_DEPTH - index.depth())
463}
464
465/// Returns tiered common prefix length between the most significant elements of the provided keys.
466///
467/// Specifically:
468/// - returns 64 if the most significant elements are equal.
469/// - returns 48 if the common prefix is between 48 and 63 bits.
470/// - returns 32 if the common prefix is between 32 and 47 bits.
471/// - returns 16 if the common prefix is between 16 and 31 bits.
472/// - returns 0 if the common prefix is fewer than 16 bits.
473fn get_common_prefix_tier_depth(key1: &RpoDigest, key2: &RpoDigest) -> u8 {
474 let e1 = get_key_prefix(key1);
475 let e2 = get_key_prefix(key2);
476 let ex = (e1 ^ e2).leading_zeros() as u8;
477 (ex / 16) * 16
478}
479
480/// Computes node value for leaves at tiers 16, 32, or 48.
481///
482/// Node value is computed as: hash(key || value, domain = depth).
483pub fn hash_upper_leaf(key: RpoDigest, value: Word, depth: u8) -> RpoDigest {
484 const NUM_UPPER_TIERS: usize = TieredSmt::TIER_DEPTHS.len() - 1;
485 debug_assert!(TieredSmt::TIER_DEPTHS[..NUM_UPPER_TIERS].contains(&depth));
486 Rpo256::merge_in_domain(&[key, value.into()], depth.into())
487}
488
489/// Computes node value for leaves at the bottom tier (depth 64).
490///
491/// Node value is computed as: hash([key_0, value_0, ..., key_n, value_n], domain=64).
492///
493/// TODO: when hashing in domain is implemented for `hash_elements()`, combine this function with
494/// `hash_upper_leaf()` function.
495pub fn hash_bottom_leaf(values: &[(RpoDigest, Word)]) -> RpoDigest {
496 let mut elements = Vec::with_capacity(values.len() * 8);
497 for (key, val) in values.iter() {
498 elements.extend_from_slice(key.as_elements());
499 elements.extend_from_slice(val.as_slice());
500 }
501 // TODO: hash in domain
502 Rpo256::hash_elements(&elements)
503}