Introduce SmtProof (#270)

* add conversion for `SmtLeaf`

* introduce `SmtProof` scaffolding

* implement `verify_membership()`

* SmtLeaf: knows its index

* `SmtLeaf::index`

* `SmtLeaf::get_value()` returns an Option

* fix `verify_membership()`

* impl `SmtProof::get`

* impl `into_parts()`

* `SmtProof::compute_root`

* use `SmtProof` in `Smt::open`

* `SmtLeaf` constructors

* Vec

* impl `Error` for `SmtLeafError`

* fix std Error

* move Word/Digest conversions to LeafIndex

* `SmtProof::new()` returns an error

* `SparseMerkleTree::path_and_leaf_to_opening`

* `SmtLeaf`: serializable/deserializable

* `SmtProof`: serializable/deserializable

* add tests for SmtLeaf serialization

* move `SmtLeaf` to submodule

* use constructors internally

* fix docs

* Add `Vec`

* add `Vec` to tests

* no_std use statements

* fmt

* `Errors`: make heading

* use `SMT_DEPTH`

* SmtLeaf single case: check leaf index

* Multiple case: check consistency with leaf index

* use `pub(super)` instead of `pub(crate)`

* use `pub(super)`

* `SmtLeaf`: add `num_entries()` accessor

* Fix `SmtLeaf` serialization

* improve leaf serialization tests

src/merkle/smt/full/leaf.rs

@@ -0,0 +1,373 @@
+use core::cmp::Ordering;
+
+use crate::utils::{collections::Vec, string::ToString, vec};
+use winter_math::StarkField;
+use winter_utils::{ByteReader, ByteWriter, Deserializable, DeserializationError, Serializable};
+
+use super::{Felt, LeafIndex, Rpo256, RpoDigest, SmtLeafError, Word, EMPTY_WORD, SMT_DEPTH};
+
+#[derive(Clone, Debug, PartialEq, Eq)]
+#[cfg_attr(feature = "serde", derive(serde::Deserialize, serde::Serialize))]
+pub enum SmtLeaf {
+    Empty(LeafIndex<SMT_DEPTH>),
+    Single((RpoDigest, Word)),
+    Multiple(Vec<(RpoDigest, Word)>),
+}
+
+impl SmtLeaf {
+    // CONSTRUCTORS
+    // ---------------------------------------------------------------------------------------------
+
+    /// Returns a new leaf with the specified entries
+    ///
+    /// # Errors
+    ///   - Returns an error if 2 keys in `entries` map to a different leaf index
+    ///   - Returns an error if 1 or more keys in `entries` map to a leaf index
+    ///     different from `leaf_index`
+    pub fn new(
+        entries: Vec<(RpoDigest, Word)>,
+        leaf_index: LeafIndex<SMT_DEPTH>,
+    ) -> Result<Self, SmtLeafError> {
+        match entries.len() {
+            0 => Ok(Self::new_empty(leaf_index)),
+            1 => {
+                let (key, value) = entries[0];
+
+                if LeafIndex::<SMT_DEPTH>::from(key) != leaf_index {
+                    return Err(SmtLeafError::SingleKeyInconsistentWithLeafIndex {
+                        key,
+                        leaf_index,
+                    });
+                }
+
+                Ok(Self::new_single(key, value))
+            }
+            _ => {
+                let leaf = Self::new_multiple(entries)?;
+
+                // `new_multiple()` checked that all keys map to the same leaf index. We still need
+                // to ensure that that leaf index is `leaf_index`.
+                if leaf.index() != leaf_index {
+                    Err(SmtLeafError::MultipleKeysInconsistentWithLeafIndex {
+                        leaf_index_from_keys: leaf.index(),
+                        leaf_index_supplied: leaf_index,
+                    })
+                } else {
+                    Ok(leaf)
+                }
+            }
+        }
+    }
+
+    /// Returns a new empty leaf with the specified leaf index
+    pub fn new_empty(leaf_index: LeafIndex<SMT_DEPTH>) -> Self {
+        Self::Empty(leaf_index)
+    }
+
+    /// Returns a new single leaf with the specified entry. The leaf index is derived from the
+    /// entry's key.
+    pub fn new_single(key: RpoDigest, value: Word) -> Self {
+        Self::Single((key, value))
+    }
+
+    /// Returns a new single leaf with the specified entry. The leaf index is derived from the
+    /// entries' keys.
+    ///
+    /// # Errors
+    ///   - Returns an error if 2 keys in `entries` map to a different leaf index
+    pub fn new_multiple(entries: Vec<(RpoDigest, Word)>) -> Result<Self, SmtLeafError> {
+        if entries.len() < 2 {
+            return Err(SmtLeafError::InvalidNumEntriesForMultiple(entries.len()));
+        }
+
+        // Check that all keys map to the same leaf index
+        {
+            let mut keys = entries.iter().map(|(key, _)| key);
+
+            let first_key = *keys.next().expect("ensured at least 2 entries");
+            let first_leaf_index: LeafIndex<SMT_DEPTH> = first_key.into();
+
+            for &next_key in keys {
+                let next_leaf_index: LeafIndex<SMT_DEPTH> = next_key.into();
+
+                if next_leaf_index != first_leaf_index {
+                    return Err(SmtLeafError::InconsistentKeys {
+                        entries,
+                        key_1: first_key,
+                        key_2: next_key,
+                    });
+                }
+            }
+        }
+
+        Ok(Self::Multiple(entries))
+    }
+
+    // PUBLIC ACCESSORS
+    // ---------------------------------------------------------------------------------------------
+
+    /// Returns true if the leaf is empty
+    pub fn is_empty(&self) -> bool {
+        matches!(self, Self::Empty(_))
+    }
+
+    /// Returns the leaf's index in the [`super::Smt`]
+    pub fn index(&self) -> LeafIndex<SMT_DEPTH> {
+        match self {
+            SmtLeaf::Empty(leaf_index) => *leaf_index,
+            SmtLeaf::Single((key, _)) => key.into(),
+            SmtLeaf::Multiple(entries) => {
+                // Note: All keys are guaranteed to have the same leaf index
+                let (first_key, _) = entries[0];
+                first_key.into()
+            }
+        }
+    }
+
+    /// Returns the number of entries stored in the leaf
+    pub fn num_entries(&self) -> u64 {
+        match self {
+            SmtLeaf::Empty(_) => 0,
+            SmtLeaf::Single(_) => 1,
+            SmtLeaf::Multiple(entries) => {
+                entries.len().try_into().expect("shouldn't have more than 2^64 entries")
+            }
+        }
+    }
+
+    /// Computes the hash of the leaf
+    pub fn hash(&self) -> RpoDigest {
+        match self {
+            SmtLeaf::Empty(_) => EMPTY_WORD.into(),
+            SmtLeaf::Single((key, value)) => Rpo256::merge(&[*key, value.into()]),
+            SmtLeaf::Multiple(kvs) => {
+                let elements: Vec<Felt> = kvs.iter().copied().flat_map(kv_to_elements).collect();
+                Rpo256::hash_elements(&elements)
+            }
+        }
+    }
+
+    // ITERATORS
+    // ---------------------------------------------------------------------------------------------
+
+    /// Returns the key-value pairs in the leaf
+    pub fn entries(&self) -> Vec<&(RpoDigest, Word)> {
+        match self {
+            SmtLeaf::Empty(_) => Vec::new(),
+            SmtLeaf::Single(kv_pair) => vec![kv_pair],
+            SmtLeaf::Multiple(kv_pairs) => kv_pairs.iter().collect(),
+        }
+    }
+
+    // CONVERSIONS
+    // ---------------------------------------------------------------------------------------------
+
+    /// Converts a leaf to a list of field elements
+    pub fn to_elements(&self) -> Vec<Felt> {
+        self.clone().into_elements()
+    }
+
+    /// Converts a leaf to a list of field elements
+    pub fn into_elements(self) -> Vec<Felt> {
+        self.into_entries().into_iter().flat_map(kv_to_elements).collect()
+    }
+
+    /// Converts a leaf the key-value pairs in the leaf
+    pub fn into_entries(self) -> Vec<(RpoDigest, Word)> {
+        match self {
+            SmtLeaf::Empty(_) => Vec::new(),
+            SmtLeaf::Single(kv_pair) => vec![kv_pair],
+            SmtLeaf::Multiple(kv_pairs) => kv_pairs,
+        }
+    }
+
+    // HELPERS
+    // ---------------------------------------------------------------------------------------------
+
+    /// Returns the value associated with `key` in the leaf, or `None` if `key` maps to another leaf.
+    pub(super) fn get_value(&self, key: &RpoDigest) -> Option<Word> {
+        // Ensure that `key` maps to this leaf
+        if self.index() != key.into() {
+            return None;
+        }
+
+        match self {
+            SmtLeaf::Empty(_) => Some(EMPTY_WORD),
+            SmtLeaf::Single((key_in_leaf, value_in_leaf)) => {
+                if key == key_in_leaf {
+                    Some(*value_in_leaf)
+                } else {
+                    Some(EMPTY_WORD)
+                }
+            }
+            SmtLeaf::Multiple(kv_pairs) => {
+                for (key_in_leaf, value_in_leaf) in kv_pairs {
+                    if key == key_in_leaf {
+                        return Some(*value_in_leaf);
+                    }
+                }
+
+                Some(EMPTY_WORD)
+            }
+        }
+    }
+
+    /// Inserts key-value pair into the leaf; returns the previous value associated with `key`, if
+    /// any.
+    ///
+    /// The caller needs to ensure that `key` has the same leaf index as all other keys in the leaf
+    pub(super) fn insert(&mut self, key: RpoDigest, value: Word) -> Option<Word> {
+        match self {
+            SmtLeaf::Empty(_) => {
+                *self = SmtLeaf::new_single(key, value);
+                None
+            }
+            SmtLeaf::Single(kv_pair) => {
+                if kv_pair.0 == key {
+                    // the key is already in this leaf. Update the value and return the previous
+                    // value
+                    let old_value = kv_pair.1;
+                    kv_pair.1 = value;
+                    Some(old_value)
+                } else {
+                    // Another entry is present in this leaf. Transform the entry into a list
+                    // entry, and make sure the key-value pairs are sorted by key
+                    let mut pairs = vec![*kv_pair, (key, value)];
+                    pairs.sort_by(|(key_1, _), (key_2, _)| cmp_keys(*key_1, *key_2));
+
+                    *self = SmtLeaf::Multiple(pairs);
+
+                    None
+                }
+            }
+            SmtLeaf::Multiple(kv_pairs) => {
+                match kv_pairs.binary_search_by(|kv_pair| cmp_keys(kv_pair.0, key)) {
+                    Ok(pos) => {
+                        let old_value = kv_pairs[pos].1;
+                        kv_pairs[pos].1 = value;
+
+                        Some(old_value)
+                    }
+                    Err(pos) => {
+                        kv_pairs.insert(pos, (key, value));
+
+                        None
+                    }
+                }
+            }
+        }
+    }
+
+    /// Removes key-value pair from the leaf stored at key; returns the previous value associated
+    /// with `key`, if any. Also returns an `is_empty` flag, indicating whether the leaf became
+    /// empty, and must be removed from the data structure it is contained in.
+    pub(super) fn remove(&mut self, key: RpoDigest) -> (Option<Word>, bool) {
+        match self {
+            SmtLeaf::Empty(_) => (None, false),
+            SmtLeaf::Single((key_at_leaf, value_at_leaf)) => {
+                if *key_at_leaf == key {
+                    // our key was indeed stored in the leaf, so we return the value that was stored
+                    // in it, and indicate that the leaf should be removed
+                    let old_value = *value_at_leaf;
+
+                    // Note: this is not strictly needed, since the caller is expected to drop this
+                    // `SmtLeaf` object.
+                    *self = SmtLeaf::new_empty(key.into());
+
+                    (Some(old_value), true)
+                } else {
+                    // another key is stored at leaf; nothing to update
+                    (None, false)
+                }
+            }
+            SmtLeaf::Multiple(kv_pairs) => {
+                match kv_pairs.binary_search_by(|kv_pair| cmp_keys(kv_pair.0, key)) {
+                    Ok(pos) => {
+                        let old_value = kv_pairs[pos].1;
+
+                        kv_pairs.remove(pos);
+                        debug_assert!(!kv_pairs.is_empty());
+
+                        if kv_pairs.len() == 1 {
+                            // convert the leaf into `Single`
+                            *self = SmtLeaf::Single(kv_pairs[0]);
+                        }
+
+                        (Some(old_value), false)
+                    }
+                    Err(_) => {
+                        // other keys are stored at leaf; nothing to update
+                        (None, false)
+                    }
+                }
+            }
+        }
+    }
+}
+
+impl Serializable for SmtLeaf {
+    fn write_into<W: ByteWriter>(&self, target: &mut W) {
+        // Write: num entries
+        self.num_entries().write_into(target);
+
+        // Write: leaf index
+        let leaf_index: u64 = self.index().value();
+        leaf_index.write_into(target);
+
+        // Write: entries
+        for (key, value) in self.entries() {
+            key.write_into(target);
+            value.write_into(target);
+        }
+    }
+}
+
+impl Deserializable for SmtLeaf {
+    fn read_from<R: ByteReader>(source: &mut R) -> Result<Self, DeserializationError> {
+        // Read: num entries
+        let num_entries = source.read_u64()?;
+
+        // Read: leaf index
+        let leaf_index: LeafIndex<SMT_DEPTH> = {
+            let value = source.read_u64()?;
+            LeafIndex::new_max_depth(value)
+        };
+
+        // Read: entries
+        let mut entries: Vec<(RpoDigest, Word)> = Vec::new();
+        for _ in 0..num_entries {
+            let key: RpoDigest = source.read()?;
+            let value: Word = source.read()?;
+
+            entries.push((key, value));
+        }
+
+        Self::new(entries, leaf_index)
+            .map_err(|err| DeserializationError::InvalidValue(err.to_string()))
+    }
+}
+
+// HELPER FUNCTIONS
+// ================================================================================================
+
+/// Converts a key-value tuple to an iterator of `Felt`s
+fn kv_to_elements((key, value): (RpoDigest, Word)) -> impl Iterator<Item = Felt> {
+    let key_elements = key.into_iter();
+    let value_elements = value.into_iter();
+
+    key_elements.chain(value_elements)
+}
+
+/// Compares two keys, compared element-by-element using their integer representations starting with
+/// the most significant element.
+fn cmp_keys(key_1: RpoDigest, key_2: RpoDigest) -> Ordering {
+    for (v1, v2) in key_1.iter().zip(key_2.iter()).rev() {
+        let v1 = v1.as_int();
+        let v2 = v2.as_int();
+        if v1 != v2 {
+            return v1.cmp(&v2);
+        }
+    }
+
+    Ordering::Equal
+}