hyperplonk PolyIOP sketch (#36)

poly-iop/src/hyperplonk/mod.rs

@@ -0,0 +1,128 @@
+//! Main module for the HyperPlonk PolyIOP.
+
+use crate::{
+    errors::PolyIOPErrors, perm_check::PermutationCheck, transcript::IOPTranscript,
+    zero_check::ZeroCheck,
+};
+use ark_ff::PrimeField;
+use ark_poly::DenseMultilinearExtension;
+use std::rc::Rc;
+
+/// A trait for HyperPlonk Poly-IOPs
+pub trait HyperPlonkPIOP<F: PrimeField> {
+    type Parameters;
+    type ProvingKey;
+    type Proof;
+    type SubClaim;
+
+    /// Generate the preprocessed polynomials output by the indexer.
+    ///
+    /// Inputs:
+    /// - `params`: HyperPlonk instance parameters
+    /// - `permutation`: the permutation for the copy constraints
+    /// - `selectors`: the list of selector vectors for custom gates
+    /// Outputs:
+    /// - The HyperPlonk proving key, which includes the preprocessed
+    ///   polynomials.
+    fn preprocess(
+        params: &Self::Parameters,
+        permutation: &[F],
+        selectors: &[&[F]],
+    ) -> Result<Self::ProvingKey, PolyIOPErrors>;
+
+    /// Generate HyperPlonk PIOP proof.
+    ///
+    /// Inputs:
+    /// - `pk`: circuit proving key
+    /// - `pub_input`: online public input
+    /// - `witness`: witness assignement
+    /// - `transcript`: the transcript used for generating pseudorandom
+    ///   challenges
+    /// Outputs:
+    /// - The HyperPlonk PIOP proof.
+    fn prove(
+        pk: &Self::ProvingKey,
+        pub_input: &[F],
+        witness: &[&[F]],
+        transcript: &mut IOPTranscript<F>,
+    ) -> Result<Self::Proof, PolyIOPErrors>;
+
+    /// Verify the HyperPlonk proof and generate the evaluation subclaims to be
+    /// checked later by the SNARK verifier.
+    ///
+    /// Inputs:
+    /// - `params`: instance parameter
+    /// - `pub_input`: online public input
+    /// - `proof`: HyperPlonk PIOP proof
+    /// - `transcript`: the transcript used for generating pseudorandom
+    ///   challenges
+    /// Outputs:
+    /// - Return error if the verification fails, otherwise return the
+    ///   evaluation subclaim
+    fn verify(
+        params: &Self::Parameters,
+        pub_input: &[F],
+        proof: &Self::Proof,
+        transcript: &mut IOPTranscript<F>,
+    ) -> Result<Self::SubClaim, PolyIOPErrors>;
+}
+
+/// The sub-claim for the HyperPlonk PolyIOP, consists of the following:
+///   - the SubClaim for the zero-check PIOP
+///   - the SubClaim for the permutation-check PIOP
+///   - the SubClaim for public input consistency
+#[derive(Clone, Debug, Default, PartialEq)]
+pub struct HyperPlonkSubClaim<F: PrimeField, ZC: ZeroCheck<F>, PC: PermutationCheck<F>> {
+    /// the SubClaim for the custom gate zerocheck
+    pub zero_check_sub_claim: ZC::ZeroCheckSubClaim,
+    /// the SubClaim for the permutation check
+    pub perm_check_sub_claim: PC::PermutationCheckSubClaim,
+    /// the public input consistency check
+    pub pub_input_sub_claim: (Vec<F>, F), // (point, expected_eval)
+}
+
+/// The proof for the HyperPlonk PolyIOP, consists of the following:
+///   - the zero-check proof for checking custom gate-satisfiability
+///   - the permutation-check proof for checking the copy constraints
+#[derive(Clone, Debug, Default, PartialEq)]
+pub struct HyperPlonkProof<F: PrimeField, ZC: ZeroCheck<F>, PC: PermutationCheck<F>> {
+    /// the custom gate zerocheck proof
+    pub zero_check_proof: ZC::Proof,
+    /// the permutation check proof for copy constraints
+    pub perm_check_proof: PC::Proof,
+}
+
+/// The HyperPlonk instance parameters, consists of the following:
+///   - the number of variables in the poly-IOP
+///   - binary log of the number of public input variables
+///   - binary log of the number of selectors
+///   - binary log of the number of witness wires
+///   - the customized gate function
+#[derive(Clone, Debug, Default, PartialEq)]
+pub struct HyperPlonkParams {
+    /// the number of variables in polys
+    pub nv: usize,
+    /// binary log of the public input length
+    pub log_pub_input_len: usize,
+    // binary log of the number of selectors
+    pub log_n_selectors: usize,
+    /// binary log of the number of witness wires
+    pub log_n_wires: usize,
+    /// customized gate function
+    // TODO: define a struct for it.
+    pub gate_func: Vec<Vec<usize>>,
+}
+
+/// The HyperPlonk proving key, consists of the following:
+///   - the hyperplonk instance parameters
+///   - the preprocessed polynomials output by the indexer
+#[derive(Clone, Debug, Default, PartialEq)]
+pub struct HyperPlonkProvingKey<F: PrimeField> {
+    /// hyperplonk instance parameters
+    pub params: HyperPlonkParams,
+    /// the preprocessed index polynomials
+    pub index_oracles: Vec<Rc<DenseMultilinearExtension<F>>>,
+}
+
+#[cfg(test)]
+mod test {}

poly-iop/src/lib.rs

@@ -2,6 +2,7 @@ use ark_ff::PrimeField;
 use std::marker::PhantomData;
 
 mod errors;
+mod hyperplonk;
 mod perm_check;
 mod structs;
 mod sum_check;
@@ -11,6 +12,7 @@ mod virtual_poly;
 mod zero_check;
 
 pub use errors::PolyIOPErrors;
+pub use hyperplonk::HyperPlonkPIOP;
 pub use perm_check::{
     util::{identity_permutation_mle, random_permutation_mle},
     PermutationCheck,

poly-iop/src/perm_check/mod.rs

@@ -31,6 +31,18 @@ pub trait PermutationCheck: ZeroCheck {
     type PermutationCheckSubClaim;
     type PermutationChallenge;
 
+    /// Generate the preprocessed polynomial for the permutation check.
+    ///
+    /// The algorithm takes as input a permutation and outputs a merged
+    /// multilinear polynomial s(X0, X1, ..., Xn) such that
+    /// - s(0, X1, ..., Xn) = s_id(X1, ..., Xn) (identity permutation
+    ///   polynomial)
+    /// - s(1, X1, ..., Xn) = s_perm(X1, ..., Xn) (permutation polynomial)
+    fn preprocess(
+        permutation: &[F],
+        aux_info: &Self::VPAuxInfo,
+    ) -> Result<DenseMultilinearExtension<F>, PolyIOPErrors>;
+
     /// Initialize the system with a transcript
     ///
     /// This function is optional -- in the case where a PermutationCheck is
@@ -81,6 +93,8 @@ pub trait PermutationCheck: ZeroCheck {
     ///
     /// The caller needs to check num_vars matches in f/g/s_id/s_perm
     /// Cost: linear in N.
+    ///
+    /// TODO: replace argument `s_perm` with the merged polynomial `s`.
     fn compute_products(
         challenge: &Self::PermutationChallenge,
         fx: &DenseMultilinearExtension<F>,
@@ -162,6 +176,20 @@ impl PermutationCheck for PolyIOP {
 
     type PermutationChallenge = PermutationChallenge<F>;
 
+    /// Generate the preprocessed polynomial for the permutation check.
+    ///
+    /// The algorithm takes as input a permutation and outputs a merged
+    /// multilinear polynomial s(X0, X1, ..., Xn) such that
+    /// - s(0, X1, ..., Xn) = s_id(X1, ..., Xn) (identity permutation
+    ///   polynomial)
+    /// - s(1, X1, ..., Xn) = s_perm(X1, ..., Xn) (permutation polynomial)
+    fn preprocess(
+        _permutation: &[F],
+        _aux_info: &Self::VPAuxInfo,
+    ) -> Result<DenseMultilinearExtension<F>, PolyIOPErrors> {
+        unimplemented!();
+    }
+
     /// Initialize the system with a transcript
     ///
     /// This function is optional -- in the case where a PermutationCheck is
@@ -229,6 +257,8 @@ impl PermutationCheck for PolyIOP {
     ///
     /// The caller needs to check num_vars matches in f/g/s_id/s_perm
     /// Cost: linear in N.
+    ///
+    /// TODO: replace argument `s_perm` with the merged polynomial `s`.
     fn compute_products(
         challenge: &Self::PermutationChallenge,
         fx: &DenseMultilinearExtension<F>,

poly-iop/src/perm_check/util.rs

@@ -25,6 +25,8 @@ use ark_std::{end_timer, rand::RngCore, start_timer};
 ///
 /// The caller needs to check num_vars matches in f/g/s_id/s_perm
 /// Cost: linear in N.
+///
+/// TODO: replace `s_perm` with the merged poly `s`.
 #[allow(clippy::type_complexity)]
 pub(super) fn compute_prod_0<F: PrimeField>(
     beta: &F,
@@ -47,6 +49,7 @@ pub(super) fn compute_prod_0(
     let mut numerator_evals = vec![];
     let mut denominator_evals = vec![];
 
+    // TODO: remove this line after replacing `s_perm` with `s`.
     let s_id = identity_permutation_mle::<F>(num_vars);
 
     for (&fi, (&gi, (&s_id_i, &s_perm_i))) in