initial implemetation of Sumcheck protocol (#7)

Cargo.toml

@@ -1,4 +1,6 @@
 [workspace]
 members = [
-  "hyperplonk"
+  "hyperplonk",
+  "pcs",
+  "poly-iop"
 ]

pcs/Cargo.toml

@@ -0,0 +1,8 @@
+[package]
+name = "pcs"
+version = "0.1.0"
+edition = "2021"
+
+# See more keys and their definitions at https://doc.rust-lang.org/cargo/reference/manifest.html
+
+[dependencies]

pcs/readme.md

@@ -0,0 +1,3 @@
+KZG based multilinear polynomial commitment
+-----
+

pcs/src/lib.rs

@@ -0,0 +1,8 @@
+#[cfg(test)]
+mod tests {
+    #[test]
+    fn it_works() {
+        let result = 2 + 2;
+        assert_eq!(result, 4);
+    }
+}

poly-iop/Cargo.toml

@@ -0,0 +1,32 @@
+[package]
+name = "poly-iop"
+version = "0.1.0"
+edition = "2021"
+
+# See more keys and their definitions at https://doc.rust-lang.org/cargo/reference/manifest.html
+
+[dependencies]
+
+ark-ff = { version = "^0.3.0", default-features = false }
+ark-std = { version = "^0.3.0", default-features = false }
+ark-poly = { version = "^0.3.0", default-features = false }
+ark-serialize =  { version = "^0.3.0", default-features = false }
+ark-bls12-381 = { version = "0.3.0", default-features = false, features = [ "curve" ] }
+
+rand_chacha = { version = "0.3.0", default-features = false }
+merlin = { version = "3.0.0", default-features = false }
+displaydoc = { version = "0.2.3", default-features = false }
+
+rayon = { version = "1.5.2", default-features = false, optional = true }
+
+[features]
+default = [ "parallel" ]
+parallel = [ 
+    "rayon",
+    "ark-std/parallel", 
+    "ark-ff/parallel",  
+    "ark-poly/parallel" 
+    ]
+print-trace = [ 
+    "ark-std/print-trace" 
+    ] 

poly-iop/readme.md

@@ -0,0 +1,7 @@
+Poly IOP
+-----
+
+Implements the following protocols
+
+- [ ] sum checks
+- [ ] zero checks

poly-iop/src/errors.rs

@@ -0,0 +1,27 @@
+//! Error module.
+
+use ark_std::string::String;
+use displaydoc::Display;
+
+/// A `enum` specifying the possible failure modes of the PolyIOP.
+#[derive(Display, Debug)]
+pub enum PolyIOPErrors {
+    /// Invalid Prover
+    InvalidProver(String),
+    /// Invalid Verifier
+    InvalidVerifier(String),
+    /// Invalid Proof
+    InvalidProof(String),
+    /// Invalid parameters
+    InvalidParameters(String),
+    /// Invalid Transcript
+    InvalidTranscript(String),
+    /// An error during (de)serialization
+    SerializationError(ark_serialize::SerializationError),
+}
+
+impl From<ark_serialize::SerializationError> for PolyIOPErrors {
+    fn from(e: ark_serialize::SerializationError) -> Self {
+        Self::SerializationError(e)
+    }
+}

poly-iop/src/lib.rs

@@ -0,0 +1,23 @@
+#![allow(dead_code)]
+
+use std::marker::PhantomData;
+
+use ark_ff::PrimeField;
+
+mod errors;
+mod structs;
+mod sum_check;
+mod transcript;
+mod utils;
+mod virtual_poly;
+// mod zero_check;
+
+pub use virtual_poly::VirtualPolynomial;
+
+/// Struct for PolyIOP protocol.
+/// It is instantiated with
+/// - SumCheck protocol.
+/// - ZeroCheck protocol. (WIP)
+pub struct PolyIOP<F: PrimeField> {
+    phantom: PhantomData<F>,
+}

poly-iop/src/structs.rs

@@ -0,0 +1,40 @@
+//! Structs for polynomials and extensions.
+
+use ark_ff::PrimeField;
+use std::marker::PhantomData;
+
+#[derive(Clone, Debug, Default, PartialEq)]
+/// Auxiliary information about the multilinear polynomial
+pub struct DomainInfo<F: PrimeField> {
+    /// max number of multiplicands in each product
+    pub max_degree: usize,
+    /// number of variables of the polynomial
+    pub num_variables: usize,
+    /// Associated field
+    #[doc(hidden)]
+    pub(crate) phantom: PhantomData<F>,
+}
+
+/// Subclaim when verifier is convinced
+pub struct SubClaim<F: PrimeField> {
+    /// the multi-dimensional point that this multilinear extension is evaluated
+    /// to
+    pub point: Vec<F>,
+    /// the expected evaluation
+    pub expected_evaluation: F,
+}
+
+/// An IOP proof is a list of messages from prover to verifier
+/// through the interactive protocol.
+/// It is a shared struct for both sumcheck and zerocheck protocols.
+#[derive(Clone, Debug, Default, PartialEq)]
+pub struct IOPProof<F: PrimeField> {
+    pub proofs: Vec<IOPProverMessage<F>>,
+}
+
+/// A message from the prover to the verifier at a given round
+/// is a list of evaluations.
+#[derive(Clone, Debug, Default, PartialEq)]
+pub struct IOPProverMessage<F: PrimeField> {
+    pub(crate) evaluations: Vec<F>,
+}