Merkleproof verify circuit (#143)

* merkletree: add keypath circuit

* merkletree-circuit: implement proof of existence verification in-circuit

* parametrize max_depth at the tree circuit

* Constrain selectors in-circuit

* implement merketree nonexistence proof circuit, and add edgecase tests

* add non-existence proofs documentation in the mdbook, mv EMPTY->EMPTY_VALUE & NULL->EMPTY_HASH, dependency clean and public exposure methods

* review comments, some extra polishing and add a test that expects wrong proofs to fail

* Add circuit to check only merkleproofs-of-existence

With this, the merkletree_circuit module offers two different circuits:
- `MerkleProofCircuit`: allows to verify both proofs of existence and proofs
non-existence with the same circuit.
- `MerkleProofExistenceCircuit`: allows to verify proofs of existence only.

In this way, if only proofs of existence are needed,
`MerkleProofExistenceCircuit` should be used, which requires less amount
of constraints than `MerkleProofCircuit`.

* Code review

---------

Co-authored-by: Ahmad <root@ahmadafuni.com>

src/middleware/basetypes.rs

@@ -35,6 +35,6 @@
 /// then the Value, Hash and F types would come from the plonky3 backend.
 #[cfg(feature = "backend_plonky2")]
 pub use crate::backends::plonky2::basetypes::{
-    hash_fields, hash_str, hash_value, Hash, Value, EMPTY, F, HASH_SIZE, NULL, SELF_ID_HASH,
-    VALUE_SIZE,
+    hash_fields, hash_str, hash_value, Hash, Value, EMPTY_HASH, EMPTY_VALUE, F, HASH_SIZE,
+    SELF_ID_HASH, VALUE_SIZE,
 };

src/middleware/containers.rs

@@ -8,7 +8,7 @@ use crate::constants::MAX_DEPTH;
 #[cfg(feature = "backend_plonky2")]
 use crate::backends::plonky2::primitives::merkletree::{Iter as TreeIter, MerkleProof, MerkleTree};
 
-use super::basetypes::{hash_value, Hash, Value, EMPTY};
+use super::basetypes::{hash_value, Hash, Value, EMPTY_VALUE};
 
 /// Dictionary: the user original keys and values are hashed to be used in the leaf.
 ///    leaf.key=hash(original_key)
@@ -78,7 +78,7 @@ impl Set {
             .iter()
             .map(|e| {
                 let h = hash_value(e);
-                (Value::from(h), EMPTY)
+                (Value::from(h), EMPTY_VALUE)
             })
             .collect();
         Ok(Self {
@@ -99,7 +99,7 @@ impl Set {
         self.mt.prove_nonexistence(value)
     }
     pub fn verify(root: Hash, proof: &MerkleProof, value: &Value) -> Result<()> {
-        MerkleTree::verify(MAX_DEPTH, root, proof, value, &EMPTY)
+        MerkleTree::verify(MAX_DEPTH, root, proof, value, &EMPTY_VALUE)
     }
     pub fn verify_nonexistence(root: Hash, proof: &MerkleProof, value: &Value) -> Result<()> {
         MerkleTree::verify_nonexistence(MAX_DEPTH, root, proof, value)

src/middleware/mod.rs

@@ -23,7 +23,7 @@ impl fmt::Display for PodId {
     fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
         if *self == SELF {
             write!(f, "self")
-        } else if self.0 == NULL {
+        } else if self.0 == EMPTY_HASH {
             write!(f, "null")
         } else {
             write!(f, "{}", self.0)
@@ -185,7 +185,7 @@ impl Pod for NonePod {
         true
     }
     fn id(&self) -> PodId {
-        PodId(NULL)
+        PodId(EMPTY_HASH)
     }
     fn pub_statements(&self) -> Vec<Statement> {
         Vec::new()