Abstract over the vector commitment scheme

air/src/proof/mod.rs

@@ -8,7 +8,7 @@
 use alloc::vec::Vec;
 use core::cmp;
 
-use crypto::Hasher;
+use crypto::{Hasher, MerkleTree};
 use fri::FriProof;
 use math::FieldElement;
 use utils::{ByteReader, Deserializable, DeserializationError, Serializable, SliceReader};
@@ -154,12 +154,8 @@ impl Proof {
             num_unique_queries: 0,
             commitments: Commitments::default(),
             trace_queries: Vec::new(),
-            constraint_queries: Queries::new::<_, DummyField>(
-                BatchMerkleProof::<DummyHasher<DummyField>> {
-                    leaves: Vec::new(),
-                    nodes: Vec::new(),
-                    depth: 0,
-                },
+            constraint_queries: Queries::new::<DummyHasher<DummyField>, DummyField, MerkleTree<_>>(
+                BatchMerkleProof::<DummyHasher<DummyField>> { nodes: Vec::new(), depth: 0 },
                 vec![vec![DummyField::ONE]],
             ),
             ood_frame: OodFrame::default(),

air/src/proof/queries.rs

@@ -5,7 +5,7 @@
 
 use alloc::vec::Vec;
 
-use crypto::{BatchMerkleProof, ElementHasher, Hasher};
+use crypto::{ElementHasher, Hasher, VectorCommitment};
 use math::FieldElement;
 use utils::{
     ByteReader, ByteWriter, Deserializable, DeserializationError, Serializable, SliceReader,
@@ -17,48 +17,45 @@ use super::Table;
 // ================================================================================================
 /// Decommitments to evaluations of a set of functions at multiple points.
 ///
-/// Given a set of functions evaluated over a domain *D*, a commitment is assumed to be a Merkle
-/// tree where a leaf at position *i* contains evaluations of all functions at *x<sub>i</sub>*.
+/// Given a set of functions evaluated over a domain *D*, a commitment is assumed to be a vector
+/// commitment where the *i*-th vector entry contains evaluations of all functions at *x<sub>i</sub>*.
 /// Thus, a query (i.e. a single decommitment) for position *i* includes evaluations of all
-/// functions at *x<sub>i</sub>*, accompanied by a Merkle authentication path from the leaf *i* to
-/// the tree root.
+/// functions at *x<sub>i</sub>*, accompanied by an opening proof of leaf *i* against the vector
+/// commitment string.
 ///
 /// This struct can contain one or more queries. In cases when more than one query is stored,
-/// Merkle authentication paths are compressed to remove redundant nodes.
+/// a batch opening proof is used in order to compress the individual opening proofs.
 ///
-/// Internally, all Merkle paths and query values are stored as a sequence of bytes. Thus, to
-/// retrieve query values and the corresponding Merkle authentication paths,
-/// [parse()](Queries::parse) function should be used.
+/// Internally, all opening proofs and query values are stored as a sequence of bytes. Thus, to
+/// retrieve query values and their corresponding opening proofs, [parse()](Queries::parse)
+/// function should be used.
 #[derive(Debug, Clone, Eq, PartialEq)]
 pub struct Queries {
-    paths: Vec<u8>,
+    opening_proof: Vec<u8>,
     values: Vec<u8>,
 }
 
 impl Queries {
     // CONSTRUCTOR
     // --------------------------------------------------------------------------------------------
     /// Returns queries constructed from evaluations of a set of functions at some number of points
-    /// in a domain and their corresponding Merkle authentication paths.
+    /// in a domain and their corresponding batch opening proof.
     ///
-    /// For each evaluation point, the same number of values must be provided, and a hash of
-    /// these values must be equal to a leaf node in the corresponding Merkle authentication path.
+    /// For each evaluation point, the same number of values must be provided.
     ///
     /// # Panics
     /// Panics if:
     /// * No queries were provided (`query_values` is an empty vector).
     /// * Any of the queries does not contain any evaluations.
     /// * Not all queries contain the same number of evaluations.
-    pub fn new<H: Hasher, E: FieldElement>(
-        merkle_proof: BatchMerkleProof<H>,
+    pub fn new<H: Hasher, E: FieldElement, V: VectorCommitment<H>>(
+        opening_proof: V::MultiProof,
         query_values: Vec<Vec<E>>,
     ) -> Self {
         assert!(!query_values.is_empty(), "query values cannot be empty");
         let elements_per_query = query_values[0].len();
         assert_ne!(elements_per_query, 0, "a query must contain at least one evaluation");
 
-        // TODO: add debug check that values actually hash into the leaf nodes of the batch proof
-
         // concatenate all elements together into a single vector of bytes
         let num_queries = query_values.len();
         let mut values = Vec::with_capacity(num_queries * elements_per_query * E::ELEMENT_BYTES);
@@ -70,33 +67,31 @@ impl Queries {
             );
             values.write_many(elements);
         }
+        let opening_proof = opening_proof.to_bytes();
 
-        // serialize internal nodes of the batch Merkle proof; we care about internal nodes only
-        // because leaf nodes can be reconstructed from hashes of query values
-        let paths = merkle_proof.serialize_nodes();
-
-        Queries { paths, values }
+        Queries { opening_proof, values }
     }
 
     // PARSER
     // --------------------------------------------------------------------------------------------
-    /// Convert internally stored bytes into a set of query values and the corresponding Merkle
-    /// authentication paths.
+    /// Convert internally stored bytes into a set of query values and the corresponding batch
+    /// opening proof.
     ///
     /// # Panics
     /// Panics if:
     /// * `domain_size` is not a power of two.
     /// * `num_queries` is zero.
     /// * `values_per_query` is zero.
-    pub fn parse<H, E>(
+    pub fn parse<E, H, V>(
         self,
         domain_size: usize,
         num_queries: usize,
         values_per_query: usize,
-    ) -> Result<(BatchMerkleProof<H>, Table<E>), DeserializationError>
+    ) -> Result<(V::MultiProof, Table<E>), DeserializationError>
     where
         E: FieldElement,
         H: ElementHasher<BaseField = E::BaseField>,
+        V: VectorCommitment<H>,
     {
         assert!(domain_size.is_power_of_two(), "domain size must be a power of two");
         assert!(num_queries > 0, "there must be at least one query");
@@ -113,20 +108,27 @@ impl Queries {
             )));
         }
 
-        // read bytes corresponding to each query, convert them into field elements,
-        // and also hash them to build leaf nodes of the batch Merkle proof
+        // read bytes corresponding to each query and convert them into field elements.
         let query_values = Table::<E>::from_bytes(&self.values, num_queries, values_per_query)?;
-        let hashed_queries = query_values.rows().map(|row| H::hash_elements(row)).collect();
 
-        // build batch Merkle proof
-        let mut reader = SliceReader::new(&self.paths);
-        let tree_depth = domain_size.ilog2() as u8;
-        let merkle_proof = BatchMerkleProof::deserialize(&mut reader, hashed_queries, tree_depth)?;
+        // build batch opening proof
+        let mut reader = SliceReader::new(&self.opening_proof);
+        let opening_proof = <V::MultiProof as Deserializable>::read_from(&mut reader)?;
+
+        // check that the opening proof matches the domain length
+        if <V as VectorCommitment<H>>::get_multiproof_domain_len(&opening_proof) != domain_size {
+            return Err(DeserializationError::InvalidValue(format!(
+                "expected a domain of size {} but was {}",
+                domain_size,
+                <V as VectorCommitment<H>>::get_multiproof_domain_len(&opening_proof),
+            )));
+        }
+
         if reader.has_more_bytes() {
             return Err(DeserializationError::UnconsumedBytes);
         }
 
-        Ok((merkle_proof, query_values))
+        Ok((opening_proof, query_values))
     }
 }
 
@@ -137,17 +139,15 @@ impl Serializable for Queries {
     /// Serializes `self` and writes the resulting bytes into the `target`.
     fn write_into<W: ByteWriter>(&self, target: &mut W) {
         // write value bytes
-        target.write_u32(self.values.len() as u32);
-        target.write_bytes(&self.values);
+        self.values.write_into(target);
 
         // write path bytes
-        target.write_u32(self.paths.len() as u32);
-        target.write_bytes(&self.paths);
+        self.opening_proof.write_into(target);
     }
 
     /// Returns an estimate of how many bytes are needed to represent self.
     fn get_size_hint(&self) -> usize {
-        self.paths.len() + self.values.len() + 8
+        self.opening_proof.len() + self.values.len() + 8
     }
 }
 
@@ -158,13 +158,11 @@ impl Deserializable for Queries {
     /// Returns an error of a valid query struct could not be read from the specified source.
     fn read_from<R: ByteReader>(source: &mut R) -> Result<Self, DeserializationError> {
         // read values
-        let num_value_bytes = source.read_u32()?;
-        let values = source.read_vec(num_value_bytes as usize)?;
+        let values = Vec::<_>::read_from(source)?;
 
         // read paths
-        let num_paths_bytes = source.read_u32()?;
-        let paths = source.read_vec(num_paths_bytes as usize)?;
+        let paths = Vec::<_>::read_from(source)?;
 
-        Ok(Queries { paths, values })
+        Ok(Queries { opening_proof: paths, values })
     }
 }

crypto/src/commitment.rs

@@ -0,0 +1,86 @@
+// Copyright (c) Facebook, Inc. and its affiliates.
+//
+// This source code is licensed under the MIT license found in the
+// LICENSE file in the root directory of this source tree.
+
+use alloc::vec::Vec;
+use core::fmt::Debug;
+
+use utils::{Deserializable, Serializable};
+
+use crate::Hasher;
+
+/// A vector commitment (VC) scheme.
+///
+/// This is a cryptographic primitive allowing one to commit, using a commitment string `com`, to
+/// a vector of values (v_0, ..., v_{n-1}) such that one can later reveal the value at the i-th
+/// position.
+///
+/// This is achieved by providing the value `v_i` together with a proof `proof_i` such that anyone
+/// posessing `com` can be convinced, with high confidence, that the claim is true.
+///
+/// Vector commitment schemes usually have some batching properties in the sense that opening
+/// proofs for a number of `(i, v_i)` can be batched together into one batch opening proof in order
+/// to optimize both the proof size as well as the verification time.
+///
+/// The current implementation restricts both of the commitment string as well as the leaf values
+/// to be `H::Digest` where `H` is a type parameter such that `H: Hasher`.
+pub trait VectorCommitment<H: Hasher>: Sized {
+    /// Options defining the VC i.e., public parameters.
+    type Options: Default;
+    /// Opening proof of some value at some position index.
+    type Proof: Clone + Serializable + Deserializable;
+    /// Batch opening proof of a number of {(i, v_i)}_{i ∈ S} for an index set.
+    type MultiProof: Serializable + Deserializable;
+    /// Error returned by the scheme.
+    type Error: Debug;
+
+    /// Creates a commitment to a vector of values (v_0, ..., v_{n-1}) using the default
+    /// options.
+    fn new(items: Vec<H::Digest>) -> Result<Self, Self::Error> {
+        Self::with_options(items, Self::Options::default())
+    }
+
+    /// Creates a commitment to a vector of values (v_0, ..., v_{n-1}) given a set of
+    /// options.
+    fn with_options(items: Vec<H::Digest>, options: Self::Options) -> Result<Self, Self::Error>;
+
+    /// Returns the commitment string to the committed values.
+    fn commitment(&self) -> H::Digest;
+
+    /// Returns the length of the vector committed to for `Self`.
+    fn domain_len(&self) -> usize;
+
+    /// Returns the length of the vector committed to for `Self::Proof`.
+    fn get_proof_domain_len(proof: &Self::Proof) -> usize;
+
+    /// Returns the length of the vector committed to for `Self::MultiProof`.
+    fn get_multiproof_domain_len(proof: &Self::MultiProof) -> usize;
+
+    /// Opens the value at a given index and provides a proof for the correctness of claimed value.
+    fn open(&self, index: usize) -> Result<(H::Digest, Self::Proof), Self::Error>;
+
+    /// Opens the values at a given index set and provides a proof for the correctness of claimed
+    /// values.
+    #[allow(clippy::type_complexity)]
+    fn open_many(
+        &self,
+        indexes: &[usize],
+    ) -> Result<(Vec<H::Digest>, Self::MultiProof), Self::Error>;
+
+    /// Verifies that the claimed value is at the given index using a proof.
+    fn verify(
+        commitment: H::Digest,
+        index: usize,
+        item: H::Digest,
+        proof: &Self::Proof,
+    ) -> Result<(), Self::Error>;
+
+    /// Verifies that the claimed values are at the given set of indices using a batch proof.
+    fn verify_many(
+        commitment: H::Digest,
+        indexes: &[usize],
+        items: &[H::Digest],
+        proof: &Self::MultiProof,
+    ) -> Result<(), Self::Error>;
+}

crypto/src/lib.rs

@@ -39,3 +39,6 @@ pub use random::{DefaultRandomCoin, RandomCoin};
 
 mod errors;
 pub use errors::{MerkleTreeError, RandomCoinError};
+
+mod commitment;
+pub use commitment::VectorCommitment;