Implement Mercury PCS (#38)

* Update rust-toolchain and add type annotation

* Implement Mercury PCS

* Apply parallelization

* Resolve lint errors

* Apply suggestions

Author: DoHoonKim8

plonkish_backend/src/backend/hyperplonk/util.rs

@@ -34,7 +34,7 @@ pub fn vanilla_plonk_circuit_info<F: PrimeField>(
     preprocess_polys: [Vec<F>; 5],
     permutations: Vec<Vec<(usize, usize)>>,
 ) -> PlonkishCircuitInfo<F> {
-    let [pi, q_l, q_r, q_m, q_o, q_c, w_l, w_r, w_o] =
+    let [pi, q_l, q_r, q_m, q_o, q_c, w_l, w_r, w_o]: &[Expression<F>; 9] =
         &array::from_fn(|poly| Query::new(poly, Rotation::cur())).map(Expression::Polynomial);
     PlonkishCircuitInfo {
         k: num_vars,

plonkish_backend/src/pcs/multilinear.rs

@@ -9,6 +9,7 @@ mod gemini;
 mod hyrax;
 mod ipa;
 mod kzg;
+mod mercury;
 mod zeromorph;
 
 pub use brakedown::{
@@ -21,6 +22,7 @@ pub use kzg::{
     MultilinearKzg, MultilinearKzgCommitment, MultilinearKzgParam, MultilinearKzgProverParam,
     MultilinearKzgVerifierParam,
 };
+pub use mercury::Mercury;
 pub use zeromorph::{Zeromorph, ZeromorphKzgProverParam, ZeromorphKzgVerifierParam};
 
 fn validate_input<'a, F: Field>(