diff --git a/poly-commit/src/constraints.rs b/poly-commit/src/constraints.rs
index 1300509a..a507d80b 100644
--- a/poly-commit/src/constraints.rs
+++ b/poly-commit/src/constraints.rs
@@ -1,6 +1,6 @@
 use crate::{
     data_structures::LabeledCommitment, BatchLCProof, LCTerm, LinearCombination,
-    PCPreparedCommitment, PCPreparedVerifierKey, PolynomialCommitment, String, Vec,
+    PCPreparedCommitment, PCPreparedVerifierKey, PolynomialCommitment,
 };
 use ark_crypto_primitives::sponge::CryptographicSponge;
 use ark_ff::PrimeField;
@@ -8,7 +8,7 @@ use ark_poly::Polynomial;
 use ark_r1cs_std::fields::emulated_fp::EmulatedFpVar;
 use ark_r1cs_std::{fields::fp::FpVar, prelude::*};
 use ark_relations::r1cs::{ConstraintSystemRef, Namespace, Result as R1CSResult, SynthesisError};
-use ark_std::{borrow::Borrow, cmp::Eq, cmp::PartialEq, hash::Hash, marker::Sized};
+use ark_std::{borrow::Borrow, cmp::Eq, cmp::PartialEq, hash::Hash};
 use hashbrown::{HashMap, HashSet};
 
 /// Define the minimal interface of prepared allocated structures.
@@ -94,7 +94,7 @@ pub struct PCCheckRandomDataVar<TargetField: PrimeField, BaseField: PrimeField>
 pub trait PCCheckVar<
     PCF: PrimeField,
     P: Polynomial<PCF>,
-    PC: PolynomialCommitment<PCF, P, S>,
+    PC: PolynomialCommitment<PCF, P>,
     ConstraintF: PrimeField,
     S: CryptographicSponge,
 >: Clone
diff --git a/poly-commit/src/data_structures.rs b/poly-commit/src/data_structures.rs
index 2b942ee1..c9ab92a8 100644
--- a/poly-commit/src/data_structures.rs
+++ b/poly-commit/src/data_structures.rs
@@ -1,4 +1,4 @@
-use crate::{Polynomial, String, Vec};
+use crate::Polynomial;
 use ark_ff::{Field, PrimeField, ToConstraintField};
 use ark_serialize::{CanonicalDeserialize, CanonicalSerialize};
 use ark_std::rand::RngCore;
diff --git a/poly-commit/src/error.rs b/poly-commit/src/error.rs
index de7091eb..dcd755a4 100644
--- a/poly-commit/src/error.rs
+++ b/poly-commit/src/error.rs
@@ -1,5 +1,3 @@
-use crate::String;
-
 /// The error type for `PolynomialCommitment`.
 #[derive(Debug)]
 pub enum Error {
diff --git a/poly-commit/src/ipa_pc/data_structures.rs b/poly-commit/src/ipa_pc/data_structures.rs
index 84fcb7f2..7eb6f1d3 100644
--- a/poly-commit/src/ipa_pc/data_structures.rs
+++ b/poly-commit/src/ipa_pc/data_structures.rs
@@ -1,10 +1,7 @@
 use crate::*;
-use crate::{PCCommitterKey, PCVerifierKey, Vec};
 use ark_ec::AffineRepr;
-use ark_ff::{Field, UniformRand, Zero};
+use ark_ff::{UniformRand, Zero};
 use ark_serialize::{CanonicalDeserialize, CanonicalSerialize};
-use ark_std::rand::RngCore;
-use ark_std::vec;
 
 /// `UniversalParams` are the universal parameters for the inner product arg scheme.
 #[derive(Derivative, CanonicalSerialize, CanonicalDeserialize)]
diff --git a/poly-commit/src/ipa_pc/mod.rs b/poly-commit/src/ipa_pc/mod.rs
index 6aab9978..2cb077e4 100644
--- a/poly-commit/src/ipa_pc/mod.rs
+++ b/poly-commit/src/ipa_pc/mod.rs
@@ -1,4 +1,4 @@
-use crate::{BTreeMap, BTreeSet, String, ToString, Vec, CHALLENGE_SIZE};
+use crate::{BTreeMap, BTreeSet, CHALLENGE_SIZE};
 use crate::{BatchLCProof, DenseUVPolynomial, Error, Evaluations, QuerySet};
 use crate::{LabeledCommitment, LabeledPolynomial, LinearCombination};
 use crate::{PCCommitmentState, PCCommitterKey, PCUniversalParams, PolynomialCommitment};
diff --git a/poly-commit/src/kzg10/data_structures.rs b/poly-commit/src/kzg10/data_structures.rs
index d648f19f..f2f970d2 100644
--- a/poly-commit/src/kzg10/data_structures.rs
+++ b/poly-commit/src/kzg10/data_structures.rs
@@ -2,7 +2,7 @@ use crate::*;
 use ark_ec::pairing::Pairing;
 use ark_ec::AdditiveGroup;
 use ark_ec::AffineRepr;
-use ark_ff::{PrimeField, ToConstraintField};
+use ark_ff::ToConstraintField;
 use ark_serialize::{
     CanonicalDeserialize, CanonicalSerialize, Compress, SerializationError, Valid, Validate,
 };
diff --git a/poly-commit/src/kzg10/mod.rs b/poly-commit/src/kzg10/mod.rs
index 508db2cb..1a3fcd66 100644
--- a/poly-commit/src/kzg10/mod.rs
+++ b/poly-commit/src/kzg10/mod.rs
@@ -5,7 +5,7 @@
 //! proposed by Kate, Zaverucha, and Goldberg ([KZG10](http://cacr.uwaterloo.ca/techreports/2010/cacr2010-10.pdf)).
 //! This construction achieves extractability in the algebraic group model (AGM).
 
-use crate::{BTreeMap, Error, LabeledPolynomial, PCCommitmentState, ToString, Vec};
+use crate::{BTreeMap, Error, LabeledPolynomial, PCCommitmentState};
 use ark_ec::AffineRepr;
 use ark_ec::{pairing::Pairing, CurveGroup};
 use ark_ec::{scalar_mul::ScalarMul, VariableBaseMSM};
@@ -479,7 +479,6 @@ mod tests {
     use ark_bls12_377::Bls12_377;
     use ark_bls12_381::Bls12_381;
     use ark_bls12_381::Fr;
-    use ark_ec::pairing::Pairing;
     use ark_poly::univariate::DensePolynomial as DensePoly;
     use ark_std::test_rng;
 
diff --git a/poly-commit/src/lib.rs b/poly-commit/src/lib.rs
index f405ba6f..5ad033fa 100644
--- a/poly-commit/src/lib.rs
+++ b/poly-commit/src/lib.rs
@@ -26,7 +26,6 @@ use ark_std::{
     fmt::Debug,
     hash::Hash,
     iter::FromIterator,
-    string::{String, ToString},
     vec::Vec,
 };
 
@@ -263,7 +262,7 @@ pub trait PolynomialCommitment<F: PrimeField, P: Polynomial<F>>: Sized {
         // order to gather (i.e. batch) all polynomials that should be queried at
         // the same point, then opening their commitments simultaneously with a
         // single call to `open` (per point)
-        let rng = &mut crate::optional_rng::OptionalRng(rng);
+        let rng = &mut optional_rng::OptionalRng(rng);
         let poly_st_comm: BTreeMap<_, _> = labeled_polynomials
             .into_iter()
             .zip(states)
@@ -622,7 +621,6 @@ fn lc_query_set_to_poly_query_set<'a, F: Field, T: Clone + Ord>(
 pub mod tests {
     use crate::*;
     use ark_crypto_primitives::sponge::poseidon::{PoseidonConfig, PoseidonSponge};
-    use ark_poly::Polynomial;
     use ark_std::rand::{
         distributions::{Distribution, Uniform},
         Rng, SeedableRng,
diff --git a/poly-commit/src/marlin/marlin_pc/data_structures.rs b/poly-commit/src/marlin/marlin_pc/data_structures.rs
index 203e3201..4bb761f8 100644
--- a/poly-commit/src/marlin/marlin_pc/data_structures.rs
+++ b/poly-commit/src/marlin/marlin_pc/data_structures.rs
@@ -1,6 +1,6 @@
 use crate::{
     DenseUVPolynomial, PCCommitment, PCCommitmentState, PCCommitterKey, PCPreparedCommitment,
-    PCPreparedVerifierKey, PCVerifierKey, Vec,
+    PCPreparedVerifierKey, PCVerifierKey,
 };
 use ark_ec::pairing::Pairing;
 use ark_ec::AdditiveGroup;
diff --git a/poly-commit/src/marlin/marlin_pc/mod.rs b/poly-commit/src/marlin/marlin_pc/mod.rs
index 2549db61..673aca44 100644
--- a/poly-commit/src/marlin/marlin_pc/mod.rs
+++ b/poly-commit/src/marlin/marlin_pc/mod.rs
@@ -1,5 +1,5 @@
 use crate::{kzg10, marlin::Marlin, PCCommitterKey, CHALLENGE_SIZE};
-use crate::{BTreeMap, BTreeSet, ToString, Vec};
+use crate::{BTreeMap, BTreeSet};
 use crate::{BatchLCProof, Error, Evaluations, QuerySet};
 use crate::{LabeledCommitment, LabeledPolynomial, LinearCombination};
 use crate::{PCCommitmentState, PCUniversalParams, PolynomialCommitment};
diff --git a/poly-commit/src/marlin/marlin_pst13_pc/combinations.rs b/poly-commit/src/marlin/marlin_pst13_pc/combinations.rs
index dd1aaf14..808038cf 100644
--- a/poly-commit/src/marlin/marlin_pst13_pc/combinations.rs
+++ b/poly-commit/src/marlin/marlin_pst13_pc/combinations.rs
@@ -1,6 +1,5 @@
 //! Compute all combinations of values in a given list
 //! Credit: https://github.com/meltinglava/uniquecombinations/
-use crate::Vec;
 
 /// Compute all combinations of values in a given list.
 pub(crate) struct Combinations<T>
diff --git a/poly-commit/src/marlin/marlin_pst13_pc/data_structures.rs b/poly-commit/src/marlin/marlin_pst13_pc/data_structures.rs
index 9cc8d73b..3b606702 100644
--- a/poly-commit/src/marlin/marlin_pst13_pc/data_structures.rs
+++ b/poly-commit/src/marlin/marlin_pst13_pc/data_structures.rs
@@ -1,4 +1,4 @@
-use crate::{BTreeMap, Vec};
+use crate::BTreeMap;
 use crate::{
     PCCommitmentState, PCCommitterKey, PCPreparedVerifierKey, PCUniversalParams, PCVerifierKey,
 };
diff --git a/poly-commit/src/marlin/marlin_pst13_pc/mod.rs b/poly-commit/src/marlin/marlin_pst13_pc/mod.rs
index 57c0a56b..4752f7d4 100644
--- a/poly-commit/src/marlin/marlin_pst13_pc/mod.rs
+++ b/poly-commit/src/marlin/marlin_pst13_pc/mod.rs
@@ -6,7 +6,6 @@ use crate::{
 use crate::{BatchLCProof, Error, Evaluations, QuerySet};
 use crate::{LabeledCommitment, LabeledPolynomial, LinearCombination};
 use crate::{PCCommitmentState, PCUniversalParams, PolynomialCommitment};
-use crate::{ToString, Vec};
 use ark_ec::AffineRepr;
 use ark_ec::{
     pairing::Pairing,
@@ -706,7 +705,6 @@ mod tests {
         multivariate::{SparsePolynomial as SparsePoly, SparseTerm},
         DenseMVPolynomial,
     };
-    use ark_std::vec::Vec;
     use rand_chacha::ChaCha20Rng;
 
     type MVPoly_381 = SparsePoly<<Bls12_381 as Pairing>::ScalarField, SparseTerm>;
diff --git a/poly-commit/src/marlin/mod.rs b/poly-commit/src/marlin/mod.rs
index 8a1e3976..1507ae06 100644
--- a/poly-commit/src/marlin/mod.rs
+++ b/poly-commit/src/marlin/mod.rs
@@ -1,6 +1,6 @@
 use crate::CHALLENGE_SIZE;
 use crate::{kzg10, Error};
-use crate::{BTreeMap, BTreeSet, Debug, RngCore, String, ToString, Vec};
+use crate::{BTreeMap, BTreeSet, Debug, RngCore};
 use crate::{BatchLCProof, LabeledPolynomial, LinearCombination};
 use crate::{Evaluations, LabeledCommitment, QuerySet};
 use crate::{PCCommitmentState, Polynomial, PolynomialCommitment};
diff --git a/poly-commit/src/multilinear_pc/data_structures.rs b/poly-commit/src/multilinear_pc/data_structures.rs
index 6920ece7..760c2869 100644
--- a/poly-commit/src/multilinear_pc/data_structures.rs
+++ b/poly-commit/src/multilinear_pc/data_structures.rs
@@ -1,6 +1,5 @@
 use ark_ec::pairing::Pairing;
 use ark_serialize::{CanonicalDeserialize, CanonicalSerialize};
-use ark_std::vec::Vec;
 #[allow(type_alias_bounds)]
 /// Evaluations over {0,1}^n for G1
 pub type EvaluationHyperCubeOnG1<E: Pairing> = Vec<E::G1Affine>;
diff --git a/poly-commit/src/multilinear_pc/mod.rs b/poly-commit/src/multilinear_pc/mod.rs
index cff20eb5..4822d248 100644
--- a/poly-commit/src/multilinear_pc/mod.rs
+++ b/poly-commit/src/multilinear_pc/mod.rs
@@ -13,7 +13,6 @@ use ark_std::iter::FromIterator;
 use ark_std::marker::PhantomData;
 use ark_std::ops::Mul;
 use ark_std::rand::RngCore;
-use ark_std::vec::Vec;
 use ark_std::UniformRand;
 
 /// data structures used by multilinear extension commitment scheme
@@ -244,7 +243,6 @@ mod tests {
     use ark_poly::{DenseMultilinearExtension, MultilinearExtension, SparseMultilinearExtension};
     use ark_std::rand::RngCore;
     use ark_std::test_rng;
-    use ark_std::vec::Vec;
     type E = Bls12_381;
     type Fr = <E as Pairing>::ScalarField;
 
diff --git a/poly-commit/src/sonic_pc/data_structures.rs b/poly-commit/src/sonic_pc/data_structures.rs
index 4e1cd309..3f2267c9 100644
--- a/poly-commit/src/sonic_pc/data_structures.rs
+++ b/poly-commit/src/sonic_pc/data_structures.rs
@@ -1,6 +1,6 @@
 use crate::kzg10;
 use crate::{
-    BTreeMap, PCCommitterKey, PCPreparedCommitment, PCPreparedVerifierKey, PCVerifierKey, Vec,
+    BTreeMap, PCCommitterKey, PCPreparedCommitment, PCPreparedVerifierKey, PCVerifierKey,
 };
 use ark_ec::pairing::Pairing;
 use ark_ec::AdditiveGroup;
diff --git a/poly-commit/src/sonic_pc/mod.rs b/poly-commit/src/sonic_pc/mod.rs
index 95d67272..61ed8362 100644
--- a/poly-commit/src/sonic_pc/mod.rs
+++ b/poly-commit/src/sonic_pc/mod.rs
@@ -1,5 +1,5 @@
 use crate::{kzg10, PCCommitterKey, CHALLENGE_SIZE};
-use crate::{BTreeMap, BTreeSet, String, ToString, Vec};
+use crate::{BTreeMap, BTreeSet};
 use crate::{BatchLCProof, DenseUVPolynomial, Error, Evaluations, QuerySet};
 use crate::{LabeledCommitment, LabeledPolynomial, LinearCombination};
 use crate::{PCCommitmentState, PCUniversalParams, PolynomialCommitment};
diff --git a/poly-commit/src/streaming_kzg/data_structures.rs b/poly-commit/src/streaming_kzg/data_structures.rs
index 0dc68e87..43a9ec29 100644
--- a/poly-commit/src/streaming_kzg/data_structures.rs
+++ b/poly-commit/src/streaming_kzg/data_structures.rs
@@ -1,6 +1,5 @@
 use ark_ff::Field;
 use ark_std::borrow::Borrow;
-use ark_std::vec::Vec;
 
 use crate::streaming_kzg::ceil_div;
 use ark_std::iterable::Iterable;
diff --git a/poly-commit/src/streaming_kzg/mod.rs b/poly-commit/src/streaming_kzg/mod.rs
index e3bdb2af..ff0ee6e1 100644
--- a/poly-commit/src/streaming_kzg/mod.rs
+++ b/poly-commit/src/streaming_kzg/mod.rs
@@ -88,7 +88,6 @@ mod time;
 
 use ark_ec::CurveGroup;
 use ark_serialize::{CanonicalSerialize, Compress};
-use ark_std::vec::Vec;
 pub use data_structures::*;
 pub use space::CommitterKeyStream;
 pub use time::CommitterKey;
diff --git a/poly-commit/src/streaming_kzg/space.rs b/poly-commit/src/streaming_kzg/space.rs
index ab50adfd..e8ac3d21 100644
--- a/poly-commit/src/streaming_kzg/space.rs
+++ b/poly-commit/src/streaming_kzg/space.rs
@@ -4,7 +4,6 @@ use ark_ff::{PrimeField, Zero};
 use ark_poly::Polynomial;
 use ark_std::borrow::Borrow;
 use ark_std::collections::VecDeque;
-use ark_std::vec::Vec;
 
 use crate::streaming_kzg::{ceil_div, vanishing_polynomial, FoldedPolynomialTree};
 use ark_ec::scalar_mul::variable_base::{ChunkedPippenger, HashMapPippenger, VariableBaseMSM};
diff --git a/poly-commit/src/streaming_kzg/tests.rs b/poly-commit/src/streaming_kzg/tests.rs
index bb2aa34e..c399cef7 100644
--- a/poly-commit/src/streaming_kzg/tests.rs
+++ b/poly-commit/src/streaming_kzg/tests.rs
@@ -1,7 +1,6 @@
 use ark_bls12_381::{Bls12_381, Fr};
 use ark_poly::univariate::DensePolynomial;
 use ark_poly::DenseUVPolynomial;
-use ark_std::vec::Vec;
 use ark_std::{UniformRand, Zero};
 
 use crate::streaming_kzg::space::CommitterKeyStream;
diff --git a/poly-commit/src/streaming_kzg/time.rs b/poly-commit/src/streaming_kzg/time.rs
index b8d52093..b6aa3d14 100644
--- a/poly-commit/src/streaming_kzg/time.rs
+++ b/poly-commit/src/streaming_kzg/time.rs
@@ -5,7 +5,7 @@ use ark_ec::scalar_mul::ScalarMul;
 use ark_ec::CurveGroup;
 use ark_ff::Zero;
 use ark_poly::{univariate::DensePolynomial, DenseUVPolynomial};
-use ark_std::{borrow::Borrow, ops::Div, ops::Mul, rand::RngCore, vec::Vec, UniformRand};
+use ark_std::{borrow::Borrow, ops::Div, ops::Mul, rand::RngCore, UniformRand};
 
 use crate::streaming_kzg::{
     linear_combination, msm, powers, Commitment, EvaluationProof, VerifierKey,