benchmark commit step and ark counterparts

this MR adds a benchmark for

• the KZG10 trusted setup creating of ark-poly-commit
• the KZG10 commit of ark-poly-commit
• our own implement of the commit in zk::commit

there is also a slight improvement to the previous benchmarking of our zk::setup: the degree of the trusted setup is now computed once and for all before the benchmarking loop starts, because it's not what is of interest, let's not benchmark it.

benches/commit.rs

+use ark_bls12_381::{Bls12_381, Fr, G1Projective};
+use ark_ec::{pairing::Pairing, CurveGroup};
+use ark_ff::PrimeField;
+use ark_poly::{univariate::DensePolynomial, DenseUVPolynomial};
+use ark_std::{ops::Div, test_rng};
+
+use ark_poly_commit::kzg10::{Powers, KZG10};
+
+use criterion::{black_box, criterion_group, criterion_main, Criterion};
+
+use komodo::zk;
+
+fn commit_template<F, G, P>(c: &mut Criterion, nb_bytes: usize)
+where
+    F: PrimeField,
+    G: CurveGroup<ScalarField = F>,
+    P: DenseUVPolynomial<F>,
+    for<'a, 'b> &'a P: Div<&'b P, Output = P>,
+{
+    let rng = &mut test_rng();
+
+    let degree = zk::nb_elements_in_setup::<F>(nb_bytes);
+
+    let setup = zk::setup::<_, F, G>(degree, rng).unwrap();
+    let polynomial = P::rand(degree, rng);
+
+    c.bench_function(
+        &format!(
+            "commit {} bytes on {}",
+            nb_bytes,
+            std::any::type_name::<F>()
+        ),
+        |b| b.iter(|| zk::commit(&setup, &polynomial)),
+    );
+}
+
+fn ark_commit_template<E, P>(c: &mut Criterion, nb_bytes: usize)
+where
+    E: Pairing,
+    P: DenseUVPolynomial<E::ScalarField>,
+    for<'a, 'b> &'a P: Div<&'b P, Output = P>,
+{
+    let rng = &mut test_rng();
+
+    let degree = zk::nb_elements_in_setup::<E::ScalarField>(nb_bytes);
+
+    let setup = KZG10::<E, P>::setup(degree, false, rng).unwrap();
+    let powers_of_g = setup.powers_of_g[..=degree].to_vec();
+    let powers_of_gamma_g = (0..=degree).map(|i| setup.powers_of_gamma_g[&i]).collect();
+    let powers = Powers::<E> {
+        powers_of_g: ark_std::borrow::Cow::Owned(powers_of_g),
+        powers_of_gamma_g: ark_std::borrow::Cow::Owned(powers_of_gamma_g),
+    };
+    let polynomial = P::rand(degree, rng);
+
+    c.bench_function(
+        &format!(
+            "commit (arkworks) {} bytes on {}",
+            nb_bytes,
+            std::any::type_name::<E>()
+        ),
+        |b| b.iter(|| KZG10::commit(&powers, &polynomial, None, None)),
+    );
+}
+
+fn commit(c: &mut Criterion) {
+    for n in [1, 2, 4, 8, 16] {
+        commit_template::<Fr, G1Projective, DensePolynomial<Fr>>(c, black_box(n * 1024));
+    }
+}
+
+fn ark_commit(c: &mut Criterion) {
+    for n in [1, 2, 4, 8, 16] {
+        ark_commit_template::<Bls12_381, DensePolynomial<<Bls12_381 as Pairing>::ScalarField>>(
+            c,
+            black_box(n * 1024),
+        );
+    }
+}
+
+criterion_group!(benches, commit, ark_commit);
+criterion_main!(benches);