diff --git a/src/gates/gate.rs b/src/gates/gate.rs
index e4f81a02..075e2aab 100644
--- a/src/gates/gate.rs
+++ b/src/gates/gate.rs
@@ -1,5 +1,5 @@
 use std::hash::{Hash, Hasher};
-use std::rc::Rc;
+use std::sync::Arc;
 
 use crate::circuit_builder::CircuitBuilder;
 use crate::constraint_polynomial::{EvaluationTargets, EvaluationVars};
@@ -8,7 +8,7 @@ use crate::generator::WitnessGenerator;
 use crate::target::Target;
 
 /// A custom gate.
-pub trait Gate<F: Field>: 'static {
+pub trait Gate<F: Field>: 'static + Send + Sync {
     fn id(&self) -> String;
 
     fn eval_unfiltered(&self, vars: EvaluationVars<F>) -> Vec<F>;
@@ -45,11 +45,11 @@ pub trait Gate<F: Field>: 'static {
 
 /// A wrapper around an `Rc<Gate>` which implements `PartialEq`, `Eq` and `Hash` based on gate IDs.
 #[derive(Clone)]
-pub struct GateRef<F: Field>(pub(crate) Rc<dyn Gate<F>>);
+pub struct GateRef<F: Field>(pub(crate) Arc<dyn Gate<F>>);
 
 impl<F: Field> GateRef<F> {
     pub fn new<G: Gate<F>>(gate: G) -> GateRef<F> {
-        GateRef(Rc::new(gate))
+        GateRef(Arc::new(gate))
     }
 }
 
diff --git a/src/generator.rs b/src/generator.rs
index b2c4ca31..87a9cddd 100644
--- a/src/generator.rs
+++ b/src/generator.rs
@@ -66,7 +66,7 @@ pub(crate) fn generate_partial_witness<F: Field>(
 }
 
 /// A generator participates in the generation of the witness.
-pub trait WitnessGenerator<F: Field>: 'static + Debug {
+pub trait WitnessGenerator<F: Field>: 'static + Debug + Send + Sync {
     /// Targets to be "watched" by this generator. Whenever a target in the watch list is populated,
     /// the generator will be queued to run.
     fn watch_list(&self) -> Vec<Target>;
@@ -80,7 +80,7 @@ pub trait WitnessGenerator<F: Field>: 'static + Debug {
 
 /// A generator which runs once after a list of dependencies is present in the witness.
 // TODO: Remove Debug. Here temporarily to debug generator issues.
-pub trait SimpleGenerator<F: Field>: 'static + Debug {
+pub trait SimpleGenerator<F: Field>: 'static + Debug + Send + Sync {
     fn dependencies(&self) -> Vec<Target>;
 
     fn run_once(&self, witness: &PartialWitness<F>) -> PartialWitness<F>;
diff --git a/src/prover.rs b/src/prover.rs
index 33933a04..96959f28 100644
--- a/src/prover.rs
+++ b/src/prover.rs
@@ -14,7 +14,7 @@ use crate::plonk_common::{eval_l_1, reduce_with_powers_multi};
 use crate::polynomial::division::divide_by_z_h;
 use crate::polynomial::polynomial::{PolynomialCoeffs, PolynomialValues};
 use crate::proof::Proof;
-use crate::util::transpose_poly_values;
+use crate::util::{transpose_poly_values, transpose};
 use crate::wire::Wire;
 use crate::witness::PartialWitness;
 
@@ -146,11 +146,9 @@ fn compute_vanishing_polys<F: Field>(
     let lde_gen = common_data.lde_generator();
     let num_checks = common_data.config.num_checks;
 
-    let mut values = vec![Vec::with_capacity(lde_size); num_checks];
-    let mut point = F::ONE;
-    for i in 0..lde_size {
-        debug_assert!(point != F::ONE);
-
+    // let mut values = vec![Vec::with_capacity(lde_size); num_checks];
+    let points = F::cyclic_subgroup_known_order(lde_gen, lde_size);
+    let values: Vec<Vec<F>> = points.into_par_iter().enumerate().map(|(i, x)| {
         let i_next = (i + 1) % lde_size;
         let local_wires = &wire_ldes_t[i];
         let next_wires = &wire_ldes_t[i_next];
@@ -169,18 +167,12 @@ fn compute_vanishing_polys<F: Field>(
             local_wires,
             next_wires,
         };
-        let values_i = compute_vanishing_poly_entry(
-            common_data, point, vars, local_plonk_zs, next_plonk_zs, s_sigmas, beta, gamma, alphas);
-        for check in 0..num_checks {
-            values[check].push(values_i[check])
-        }
+        compute_vanishing_poly_entry(
+            common_data, x, vars, local_plonk_zs, next_plonk_zs, s_sigmas, beta, gamma, alphas)
+    }).collect();
 
-        point *= lde_gen;
-    }
-
-    debug_assert_eq!(point, F::ONE);
-
-    values.into_iter()
+    transpose(&values)
+        .into_iter()
         .map(PolynomialValues::new)
         .collect()
 }