feat(nullifier_tree): make empty nullifier tree leaves hash be 0 (#360)

* feat(nullifier_tree): make empty nullifier tree leaves be 0

* fix: add append zero behaviour and test

* fix: explicit type name

* clean: update class semantics

---------

Co-authored-by: cheethas <[email protected]>
Co-authored-by: cheethas <[email protected]>

cpp/src/barretenberg/stdlib/merkle_tree/nullifier_tree/nullifier_leaf.hpp

@@ -40,14 +40,79 @@ struct nullifier_leaf {
     barretenberg::fr hash() const { return stdlib::merkle_tree::hash_multiple_native({ value, nextIndex, nextValue }); }
 };
 
-inline std::pair<size_t, bool> find_closest_leaf(std::vector<nullifier_leaf> const& leaves_, fr const& new_value)
+/**
+ * @brief Wrapper for the Nullifier leaf class that allows for 0 values
+ *
+ */
+class WrappedNullifierLeaf {
+
+  public:
+    // Initialise with a nullifier leaf
+    WrappedNullifierLeaf(nullifier_leaf value)
+        : data(value)
+    {}
+    // Initialise an empty leaf
+    WrappedNullifierLeaf()
+        : data(std::nullopt)
+    {}
+
+    bool operator==(WrappedNullifierLeaf const&) const = default;
+
+    /**
+     * @brief Pass through the underlying std::optional method
+     *
+     * @return true
+     * @return false
+     */
+    bool has_value() const { return data.has_value(); }
+
+    /**
+     * @brief Return the wrapped nullifier_leaf object
+     *
+     * @return nullifier_leaf
+     */
+    nullifier_leaf unwrap() const { return data.value(); }
+
+    /**
+     * @brief Set the wrapped nullifier_leaf object value
+     *
+     * @param value
+     */
+    void set(nullifier_leaf value) { data.emplace(value); }
+
+    /**
+     * @brief Return the hash of the wrapped object, other return the zero hash of 0
+     *
+     * @return barretenberg::fr
+     */
+    barretenberg::fr hash() const { return data.has_value() ? data.value().hash() : barretenberg::fr::zero(); }
+
+    /**
+     * @brief Generate a zero leaf (call the constructor with no arguments)
+     *
+     * @return NullifierLeaf
+     */
+    static WrappedNullifierLeaf zero() { return WrappedNullifierLeaf(); }
+
+  private:
+    // Underlying data
+    std::optional<nullifier_leaf> data;
+};
+
+inline std::pair<size_t, bool> find_closest_leaf(std::vector<WrappedNullifierLeaf> const& leaves_, fr const& new_value)
 {
     std::vector<uint256_t> diff;
     bool repeated = false;
     auto new_value_ = uint256_t(new_value);
 
     for (size_t i = 0; i < leaves_.size(); i++) {
-        auto leaf_value_ = uint256_t(leaves_[i].value);
+
+        if (!leaves_[i].has_value()) {
+            diff.push_back(new_value_);
+            continue;
+        }
+
+        auto leaf_value_ = uint256_t(leaves_[i].unwrap().value);
         if (leaf_value_ > new_value_) {
             diff.push_back(leaf_value_);
         } else if (leaf_value_ == new_value_) {

cpp/src/barretenberg/stdlib/merkle_tree/nullifier_tree/nullifier_memory_tree.cpp

@@ -12,11 +12,8 @@ NullifierMemoryTree::NullifierMemoryTree(size_t depth)
     total_size_ = 1UL << depth_;
     hashes_.resize(total_size_ * 2 - 2);
 
-    // Build the entire tree.
-    nullifier_leaf zero_leaf = { 0, 0, 0 };
-    leaves_.push_back(zero_leaf);
-    auto current = zero_leaf.hash();
-    update_element(0, current);
+    // Build the entire tree and fill with 0 hashes.
+    auto current = WrappedNullifierLeaf::zero().hash();
     size_t layer_size = total_size_;
     for (size_t offset = 0; offset < hashes_.size(); offset += layer_size, layer_size /= 2) {
         for (size_t i = 0; i < layer_size; ++i) {
@@ -25,30 +22,45 @@ NullifierMemoryTree::NullifierMemoryTree(size_t depth)
         current = hash_pair_native(current, current);
     }
 
-    root_ = current;
+    // Insert the initial leaf at index 0
+    auto initial_leaf = WrappedNullifierLeaf(nullifier_leaf{ .value = 0, .nextIndex = 0, .nextValue = 0 });
+    leaves_.push_back(initial_leaf);
+    root_ = update_element(0, initial_leaf.hash());
 }
 
 fr NullifierMemoryTree::update_element(fr const& value)
 {
     // Find the leaf with the value closest and less than `value`
+
+    // If value is 0 we simply append 0 a null NullifierLeaf to the tree
+    if (value == 0) {
+        auto zero_leaf = WrappedNullifierLeaf::zero();
+        leaves_.push_back(zero_leaf);
+        return update_element(leaves_.size() - 1, zero_leaf.hash());
+    }
+
     size_t current;
     bool is_already_present;
     std::tie(current, is_already_present) = find_closest_leaf(leaves_, value);
 
+    nullifier_leaf current_leaf = leaves_[current].unwrap();
     nullifier_leaf new_leaf = { .value = value,
-                                .nextIndex = leaves_[current].nextIndex,
-                                .nextValue = leaves_[current].nextValue };
+                                .nextIndex = current_leaf.nextIndex,
+                                .nextValue = current_leaf.nextValue };
+
     if (!is_already_present) {
         // Update the current leaf to point it to the new leaf
-        leaves_[current].nextIndex = leaves_.size();
-        leaves_[current].nextValue = value;
+        current_leaf.nextIndex = leaves_.size();
+        current_leaf.nextValue = value;
+
+        leaves_[current].set(current_leaf);
 
         // Insert the new leaf with (nextIndex, nextValue) of the current leaf
         leaves_.push_back(new_leaf);
     }
 
     // Update the old leaf in the tree
-    auto old_leaf_hash = leaves_[current].hash();
+    auto old_leaf_hash = current_leaf.hash();
     size_t old_leaf_index = current;
     auto root = update_element(old_leaf_index, old_leaf_hash);
 

cpp/src/barretenberg/stdlib/merkle_tree/nullifier_tree/nullifier_memory_tree.hpp

@@ -68,6 +68,7 @@ using namespace barretenberg;
  *  nextVal   10      50      20      30       0       0       0       0
  */
 class NullifierMemoryTree : public MemoryTree {
+
   public:
     NullifierMemoryTree(size_t depth);
 
@@ -78,15 +79,18 @@ class NullifierMemoryTree : public MemoryTree {
     fr update_element(fr const& value);
 
     const std::vector<barretenberg::fr>& get_hashes() { return hashes_; }
-    const std::vector<nullifier_leaf>& get_leaves() { return leaves_; }
-    const nullifier_leaf& get_leaf(size_t index) { return leaves_[index]; }
+    const WrappedNullifierLeaf get_leaf(size_t index)
+    {
+        return (index < leaves_.size()) ? leaves_[index] : WrappedNullifierLeaf::zero();
+    }
+    const std::vector<WrappedNullifierLeaf>& get_leaves() { return leaves_; }
 
   protected:
     using MemoryTree::depth_;
     using MemoryTree::hashes_;
     using MemoryTree::root_;
     using MemoryTree::total_size_;
-    std::vector<nullifier_leaf> leaves_;
+    std::vector<WrappedNullifierLeaf> leaves_;
 };
 
 } // namespace merkle_tree