diff --git a/Cargo.toml b/Cargo.toml
index 21708d41..8c4968ec 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -18,9 +18,11 @@ itertools = "0.10.0"
 num = "0.3"
 rand = "0.7.3"
 rand_chacha = "0.2.2"
-rayon = "1.5.0"
+rayon = "1.5.1"
 unroll = "0.1.5"
 anyhow = "1.0.40"
+serde = { version = "1.0", features = ["derive"] }
+serde_cbor = "0.11.1"
 
 [profile.release]
 opt-level = 3
diff --git a/src/bin/bench_gmimc.rs b/src/bin/bench_gmimc.rs
index 2f81aac0..9611d48e 100644
--- a/src/bin/bench_gmimc.rs
+++ b/src/bin/bench_gmimc.rs
@@ -1,3 +1,4 @@
+use std::convert::TryInto;
 use std::thread;
 use std::time::Instant;
 
@@ -15,15 +16,12 @@ fn main() {
     const THREADS: usize = 12;
     const LDE_BITS: i32 = 3;
     const W: usize = 12;
-    const HASHES_PER_POLY: usize = 1 << (13 + LDE_BITS) / 6;
+    const HASHES_PER_POLY: usize = 1 << ((13 + LDE_BITS) / 6);
 
     let threads = (0..THREADS)
         .map(|_i| {
             thread::spawn(move || {
-                let mut x = [F::ZERO; W];
-                for i in 0..W {
-                    x[i] = F::from_canonical_u64((i as u64) * 123456 + 789);
-                }
+                let mut x: [F; W] = F::rand_vec(W).try_into().unwrap();
 
                 let hashes_per_thread = HASHES_PER_POLY * PROVER_POLYS / THREADS;
                 let start = Instant::now();
diff --git a/src/bin/bench_recursion.rs b/src/bin/bench_recursion.rs
index b75d4bdc..51f93025 100644
--- a/src/bin/bench_recursion.rs
+++ b/src/bin/bench_recursion.rs
@@ -1,4 +1,5 @@
 use env_logger::Env;
+use log::info;
 use plonky2::circuit_builder::CircuitBuilder;
 use plonky2::circuit_data::CircuitConfig;
 use plonky2::field::crandall_field::CrandallField;
@@ -25,10 +26,10 @@ fn bench_prove<F: Field + Extendable<D>, const D: usize>() {
         rate_bits: 3,
         num_challenges: 3,
         fri_config: FriConfig {
-            proof_of_work_bits: 1,
+            proof_of_work_bits: 20,
             rate_bits: 3,
-            reduction_arity_bits: vec![2, 2, 2, 2, 2],
-            num_query_rounds: 1,
+            reduction_arity_bits: vec![2, 2, 2, 2, 2, 2],
+            num_query_rounds: 35,
         },
     };
 
@@ -46,7 +47,10 @@ fn bench_prove<F: Field + Extendable<D>, const D: usize>() {
     builder.add(zero, zero);
     builder.add_extension(zero_ext, zero_ext);
 
-    let prover = builder.build_prover();
+    let circuit = builder.build();
     let inputs = PartialWitness::new();
-    prover.prove(inputs);
+    let proof = circuit.prove(inputs);
+    let proof_bytes = serde_cbor::to_vec(&proof).unwrap();
+    info!("Proof length: {} bytes", proof_bytes.len());
+    circuit.verify(proof).unwrap();
 }
diff --git a/src/bin/bench_rescue.rs b/src/bin/bench_rescue.rs
index 96334689..1b45c31c 100644
--- a/src/bin/bench_rescue.rs
+++ b/src/bin/bench_rescue.rs
@@ -1,3 +1,4 @@
+use std::convert::TryInto;
 use std::thread;
 use std::time::Instant;
 
@@ -19,10 +20,7 @@ fn main() {
     let threads = (0..THREADS)
         .map(|_i| {
             thread::spawn(move || {
-                let mut x = [F::ZERO; W];
-                for i in 0..W {
-                    x[i] = F::from_canonical_u64((i as u64) * 123456 + 789);
-                }
+                let mut x: [F; W] = F::rand_vec(W).try_into().unwrap();
 
                 let hashes_per_thread = HASHES_PER_POLY * PROVER_POLYS / THREADS;
                 let start = Instant::now();
diff --git a/src/circuit_data.rs b/src/circuit_data.rs
index e389ed27..ac3ede94 100644
--- a/src/circuit_data.rs
+++ b/src/circuit_data.rs
@@ -39,7 +39,7 @@ impl Default for CircuitConfig {
             num_challenges: 3,
             fri_config: FriConfig {
                 proof_of_work_bits: 1,
-                rate_bits: 1,
+                rate_bits: 3,
                 reduction_arity_bits: vec![1, 1, 1, 1],
                 num_query_rounds: 1,
             },
diff --git a/src/field/crandall_field.rs b/src/field/crandall_field.rs
index 7a1d18d6..9d38ff1a 100644
--- a/src/field/crandall_field.rs
+++ b/src/field/crandall_field.rs
@@ -5,6 +5,7 @@ use std::iter::{Product, Sum};
 use std::ops::{Add, AddAssign, Div, DivAssign, Mul, MulAssign, Neg, Sub, SubAssign};
 
 use num::Integer;
+use serde::{Deserialize, Serialize};
 
 use crate::field::extension_field::quadratic::QuadraticCrandallField;
 use crate::field::extension_field::quartic::QuarticCrandallField;
@@ -106,7 +107,7 @@ const CAUCHY_MDS_8: [[CrandallField; 8]; 8] = [
 ///   = 2**64 - 9 * 2**28 + 1
 ///   = 2**28 * (2**36 - 9) + 1
 /// ```
-#[derive(Copy, Clone)]
+#[derive(Copy, Clone, Serialize, Deserialize)]
 pub struct CrandallField(pub u64);
 
 impl PartialEq for CrandallField {
diff --git a/src/field/extension_field/quadratic.rs b/src/field/extension_field/quadratic.rs
index ede2ef26..256803ab 100644
--- a/src/field/extension_field/quadratic.rs
+++ b/src/field/extension_field/quadratic.rs
@@ -4,12 +4,13 @@ use std::iter::{Product, Sum};
 use std::ops::{Add, AddAssign, Div, DivAssign, Mul, MulAssign, Neg, Sub, SubAssign};
 
 use rand::Rng;
+use serde::{Deserialize, Serialize};
 
 use crate::field::crandall_field::CrandallField;
 use crate::field::extension_field::{FieldExtension, Frobenius, OEF};
 use crate::field::field::Field;
 
-#[derive(Copy, Clone, Eq, PartialEq, Hash)]
+#[derive(Copy, Clone, Eq, PartialEq, Hash, Serialize, Deserialize)]
 pub struct QuadraticCrandallField([CrandallField; 2]);
 
 impl OEF<2> for QuadraticCrandallField {
diff --git a/src/field/extension_field/quartic.rs b/src/field/extension_field/quartic.rs
index f609eeb7..22e91353 100644
--- a/src/field/extension_field/quartic.rs
+++ b/src/field/extension_field/quartic.rs
@@ -4,13 +4,14 @@ use std::iter::{Product, Sum};
 use std::ops::{Add, AddAssign, Div, DivAssign, Mul, MulAssign, Neg, Sub, SubAssign};
 
 use rand::Rng;
+use serde::{Deserialize, Serialize};
 
 use crate::field::crandall_field::CrandallField;
 use crate::field::extension_field::{FieldExtension, Frobenius, OEF};
 use crate::field::field::Field;
 
 /// A quartic extension of `CrandallField`.
-#[derive(Copy, Clone, Eq, PartialEq, Hash)]
+#[derive(Copy, Clone, Eq, PartialEq, Hash, Serialize, Deserialize)]
 pub struct QuarticCrandallField(pub(crate) [CrandallField; 4]);
 
 impl OEF<4> for QuarticCrandallField {
diff --git a/src/field/fft.rs b/src/field/fft.rs
index fa65a5ea..35b11852 100644
--- a/src/field/fft.rs
+++ b/src/field/fft.rs
@@ -250,9 +250,9 @@ fn fft_unrolled<F: Field>(input: Vec<F>, r_orig: usize, root_table: FftRootTable
             // NB: Grouping statements as is done in the main loop below
             // does not seem to help here (worse by a few millis).
             let omega_0 = root_table[0][0];
-            let tmp_0 = omega_0 * values[k + 2 + 0];
-            values[k + 2 + 0] = values[k + 0] - tmp_0;
-            values[k + 0] += tmp_0;
+            let tmp_0 = omega_0 * values[k + 2];
+            values[k + 2] = values[k] - tmp_0;
+            values[k] += tmp_0;
 
             let omega_1 = root_table[0][1];
             let tmp_1 = omega_1 * values[k + 2 + 1];
@@ -281,21 +281,21 @@ fn fft_unrolled<F: Field>(input: Vec<F>, r_orig: usize, root_table: FftRootTable
                 let off1 = k + j;
                 let off2 = k + m + j;
 
-                let omega_0 = root_table[lg_m - 1][j + 0];
+                let omega_0 = root_table[lg_m - 1][j];
                 let omega_1 = root_table[lg_m - 1][j + 1];
                 let omega_2 = root_table[lg_m - 1][j + 2];
                 let omega_3 = root_table[lg_m - 1][j + 3];
 
-                let tmp_0 = omega_0 * values[off2 + 0];
+                let tmp_0 = omega_0 * values[off2];
                 let tmp_1 = omega_1 * values[off2 + 1];
                 let tmp_2 = omega_2 * values[off2 + 2];
                 let tmp_3 = omega_3 * values[off2 + 3];
 
-                values[off2 + 0] = values[off1 + 0] - tmp_0;
+                values[off2] = values[off1] - tmp_0;
                 values[off2 + 1] = values[off1 + 1] - tmp_1;
                 values[off2 + 2] = values[off1 + 2] - tmp_2;
                 values[off2 + 3] = values[off1 + 3] - tmp_3;
-                values[off1 + 0] += tmp_0;
+                values[off1] += tmp_0;
                 values[off1 + 1] += tmp_1;
                 values[off1 + 2] += tmp_2;
                 values[off1 + 3] += tmp_3;
diff --git a/src/field/field.rs b/src/field/field.rs
index f4ef5990..28a52202 100644
--- a/src/field/field.rs
+++ b/src/field/field.rs
@@ -6,6 +6,8 @@ use std::ops::{Add, AddAssign, Div, DivAssign, Mul, MulAssign, Neg, Sub, SubAssi
 
 use num::Integer;
 use rand::Rng;
+use serde::de::DeserializeOwned;
+use serde::Serialize;
 
 use crate::field::extension_field::Frobenius;
 use crate::util::bits_u64;
@@ -31,6 +33,8 @@ pub trait Field:
     + Display
     + Send
     + Sync
+    + Serialize
+    + DeserializeOwned
 {
     type PrimeField: Field;
 
@@ -131,7 +135,7 @@ pub trait Field:
 
     fn primitive_root_of_unity(n_log: usize) -> Self {
         assert!(n_log <= Self::TWO_ADICITY);
-        let mut base = Self::POWER_OF_TWO_GENERATOR;
+        let base = Self::POWER_OF_TWO_GENERATOR;
         base.exp_power_of_2(Self::TWO_ADICITY - n_log)
     }
 
diff --git a/src/fri/prover.rs b/src/fri/prover.rs
index f937ee55..12968c06 100644
--- a/src/fri/prover.rs
+++ b/src/fri/prover.rs
@@ -1,3 +1,5 @@
+use rayon::prelude::*;
+
 use crate::field::extension_field::{flatten, unflatten, Extendable};
 use crate::field::field::Field;
 use crate::fri::FriConfig;
@@ -7,6 +9,7 @@ use crate::plonk_challenger::Challenger;
 use crate::plonk_common::reduce_with_powers;
 use crate::polynomial::polynomial::{PolynomialCoeffs, PolynomialValues};
 use crate::proof::{FriInitialTreeProof, FriProof, FriQueryRound, FriQueryStep, Hash};
+use crate::timed;
 use crate::util::reverse_index_bits_in_place;
 
 /// Builds a FRI proof.
@@ -32,7 +35,10 @@ pub fn fri_proof<F: Field + Extendable<D>, const D: usize>(
 
     // PoW phase
     let current_hash = challenger.get_hash();
-    let pow_witness = fri_proof_of_work(current_hash, config);
+    let pow_witness = timed!(
+        fri_proof_of_work(current_hash, config),
+        "to find for proof-of-work witness"
+    );
 
     // Query phase
     let query_round_proofs =
@@ -94,8 +100,9 @@ fn fri_committed_trees<F: Field + Extendable<D>, const D: usize>(
 }
 
 fn fri_proof_of_work<F: Field>(current_hash: Hash<F>, config: &FriConfig) -> F {
-    (0u64..)
-        .find(|&i| {
+    (0..u64::MAX)
+        .into_par_iter()
+        .find_any(|&i| {
             hash_n_to_1(
                 current_hash
                     .elements
@@ -110,7 +117,7 @@ fn fri_proof_of_work<F: Field>(current_hash: Hash<F>, config: &FriConfig) -> F {
                 >= config.proof_of_work_bits + F::ORDER.leading_zeros()
         })
         .map(F::from_canonical_u64)
-        .expect("Proof of work failed.")
+        .expect("Proof of work failed. This is highly unlikely!")
 }
 
 fn fri_prover_query_rounds<F: Field + Extendable<D>, const D: usize>(
diff --git a/src/gates/mod.rs b/src/gates/mod.rs
index fa23b273..298c9138 100644
--- a/src/gates/mod.rs
+++ b/src/gates/mod.rs
@@ -1,3 +1,6 @@
+// Gates have `new` methods that return `GateRef`s.
+#![allow(clippy::new_ret_no_self)]
+
 pub mod arithmetic;
 pub mod base_sum;
 pub mod constant;
diff --git a/src/gmimc.rs b/src/gmimc.rs
index 9a65d49d..db80f19a 100644
--- a/src/gmimc.rs
+++ b/src/gmimc.rs
@@ -56,8 +56,8 @@ pub fn gmimc_permute_array<F: Field, const W: usize, const R: usize>(
         xs[active] -= f;
     }
 
-    for i in 0..W {
-        xs[i] += addition_buffer;
+    for x_i in xs.iter_mut() {
+        *x_i += addition_buffer;
     }
 
     xs
diff --git a/src/hash.rs b/src/hash.rs
index fd551a6c..2c7bad64 100644
--- a/src/hash.rs
+++ b/src/hash.rs
@@ -117,12 +117,6 @@ pub const GMIMC_CONSTANTS: [u64; GMIMC_ROUNDS] = [
     8651171085167737860,
 ];
 
-/// Controls the granularity of parallelization when building Merkle trees. I.e., we will try to
-/// split up the task into units of work, such that each unit involves hashing roughly this many
-/// elements. If this is too small, there may be too much synchronization overhead; if it's too
-/// large, some threads may spend significant time idle.
-const ELEMS_PER_CHUNK: usize = 1 << 8;
-
 /// Hash the vector if necessary to reduce its length to ~256 bits. If it already fits, this is a
 /// no-op.
 pub fn hash_or_noop<F: Field>(inputs: Vec<F>) -> Hash<F> {
@@ -226,8 +220,8 @@ pub fn hash_n_to_m<F: Field>(mut inputs: Vec<F>, num_outputs: usize, pad: bool)
     // Squeeze until we have the desired number of outputs.
     let mut outputs = Vec::new();
     loop {
-        for i in 0..SPONGE_RATE {
-            outputs.push(state[i]);
+        for &item in state.iter().take(SPONGE_RATE) {
+            outputs.push(item);
             if outputs.len() == num_outputs {
                 return outputs;
             }
diff --git a/src/merkle_proofs.rs b/src/merkle_proofs.rs
index a9aeeb27..b7625f63 100644
--- a/src/merkle_proofs.rs
+++ b/src/merkle_proofs.rs
@@ -1,4 +1,5 @@
 use anyhow::{ensure, Result};
+use serde::{Deserialize, Serialize};
 
 use crate::circuit_builder::CircuitBuilder;
 use crate::field::extension_field::Extendable;
@@ -10,7 +11,8 @@ use crate::proof::{Hash, HashTarget};
 use crate::target::Target;
 use crate::wire::Wire;
 
-#[derive(Clone, Debug)]
+#[derive(Clone, Debug, Serialize, Deserialize)]
+#[serde(bound = "")]
 pub struct MerkleProof<F: Field> {
     /// The Merkle digest of each sibling subtree, staying from the bottommost layer.
     pub siblings: Vec<Hash<F>>,
diff --git a/src/permutation_argument.rs b/src/permutation_argument.rs
index 5c1ead6a..9a692cd3 100644
--- a/src/permutation_argument.rs
+++ b/src/permutation_argument.rs
@@ -46,7 +46,7 @@ impl<T: Debug + Copy + Eq + PartialEq + Hash, F: Fn(T) -> usize> TargetPartition
     }
 
     /// Path compression method, see https://en.wikipedia.org/wiki/Disjoint-set_data_structure#Finding_set_representatives.
-    pub fn find(&mut self, mut x: ForestNode<T>) -> ForestNode<T> {
+    pub fn find(&mut self, x: ForestNode<T>) -> ForestNode<T> {
         if x.parent != x.index {
             let root = self.find(self.forest[x.parent]);
             self.forest[x.index].parent = root.index;
diff --git a/src/polynomial/commitment.rs b/src/polynomial/commitment.rs
index 7c580ad9..4436a454 100644
--- a/src/polynomial/commitment.rs
+++ b/src/polynomial/commitment.rs
@@ -1,5 +1,6 @@
 use anyhow::Result;
 use rayon::prelude::*;
+use serde::{Deserialize, Serialize};
 
 use crate::circuit_builder::CircuitBuilder;
 use crate::circuit_data::CommonCircuitData;
@@ -247,9 +248,10 @@ impl<F: Field> ListPolynomialCommitment<F> {
     }
 }
 
-#[derive(Clone)]
+#[derive(Serialize, Deserialize, Debug)]
+#[serde(bound = "")]
 pub struct OpeningProof<F: Extendable<D>, const D: usize> {
-    pub fri_proof: FriProof<F, D>,
+    fri_proof: FriProof<F, D>,
     // TODO: Get the degree from `CommonCircuitData` instead.
     quotient_degree: usize,
 }
@@ -281,7 +283,7 @@ impl<F: Extendable<D>, const D: usize> OpeningProof<F, D> {
 }
 
 pub struct OpeningProofTarget<const D: usize> {
-    pub fri_proof: FriProofTarget<D>,
+    fri_proof: FriProofTarget<D>,
 }
 
 impl<const D: usize> OpeningProofTarget<D> {
diff --git a/src/polynomial/polynomial.rs b/src/polynomial/polynomial.rs
index 81d07b8f..5f9bccd9 100644
--- a/src/polynomial/polynomial.rs
+++ b/src/polynomial/polynomial.rs
@@ -3,6 +3,7 @@ use std::iter::Sum;
 use std::ops::{Add, AddAssign, Mul, MulAssign, Sub, SubAssign};
 
 use anyhow::{ensure, Result};
+use serde::{Deserialize, Serialize};
 
 use crate::field::extension_field::Extendable;
 use crate::field::fft::{fft, fft_with_options, ifft};
@@ -76,7 +77,8 @@ impl<F: Field> From<Vec<F>> for PolynomialValues<F> {
 }
 
 /// A polynomial in coefficient form.
-#[derive(Clone, Debug)]
+#[derive(Clone, Debug, Serialize, Deserialize)]
+#[serde(bound = "")]
 pub struct PolynomialCoeffs<F: Field> {
     pub(crate) coeffs: Vec<F>,
 }
diff --git a/src/proof.rs b/src/proof.rs
index b5875927..85ef44b5 100644
--- a/src/proof.rs
+++ b/src/proof.rs
@@ -1,5 +1,7 @@
 use std::convert::TryInto;
 
+use serde::{Deserialize, Serialize};
+
 use crate::circuit_data::CommonCircuitData;
 use crate::field::extension_field::target::ExtensionTarget;
 use crate::field::extension_field::Extendable;
@@ -12,7 +14,8 @@ use crate::polynomial::polynomial::PolynomialCoeffs;
 use crate::target::Target;
 
 /// Represents a ~256 bit hash output.
-#[derive(Copy, Clone, Debug, Eq, PartialEq)]
+#[derive(Copy, Clone, Debug, Eq, PartialEq, Serialize, Deserialize)]
+#[serde(bound = "")]
 pub struct Hash<F: Field> {
     pub(crate) elements: [F; 4],
 }
@@ -61,7 +64,8 @@ impl HashTarget {
     }
 }
 
-#[derive(Clone)]
+#[derive(Serialize, Deserialize, Clone, Debug)]
+#[serde(bound = "")]
 pub struct Proof<F: Extendable<D>, const D: usize> {
     /// Merkle root of LDEs of wire values.
     pub wires_root: Hash<F>,
@@ -84,8 +88,9 @@ pub struct ProofTarget<const D: usize> {
 }
 
 /// Evaluations and Merkle proof produced by the prover in a FRI query step.
-#[derive(Clone)]
-pub struct FriQueryStep<F: Field + Extendable<D>, const D: usize> {
+#[derive(Serialize, Deserialize, Clone, Debug)]
+#[serde(bound = "")]
+pub struct FriQueryStep<F: Extendable<D>, const D: usize> {
     pub evals: Vec<F::Extension>,
     pub merkle_proof: MerkleProof<F>,
 }
@@ -98,7 +103,8 @@ pub struct FriQueryStepTarget<const D: usize> {
 
 /// Evaluations and Merkle proofs of the original set of polynomials,
 /// before they are combined into a composition polynomial.
-#[derive(Clone)]
+#[derive(Serialize, Deserialize, Clone, Debug)]
+#[serde(bound = "")]
 pub struct FriInitialTreeProof<F: Field> {
     pub evals_proofs: Vec<(Vec<F>, MerkleProof<F>)>,
 }
@@ -123,8 +129,9 @@ impl FriInitialTreeProofTarget {
 }
 
 /// Proof for a FRI query round.
-#[derive(Clone)]
-pub struct FriQueryRound<F: Field + Extendable<D>, const D: usize> {
+#[derive(Serialize, Deserialize, Clone, Debug)]
+#[serde(bound = "")]
+pub struct FriQueryRound<F: Extendable<D>, const D: usize> {
     pub initial_trees_proof: FriInitialTreeProof<F>,
     pub steps: Vec<FriQueryStep<F, D>>,
 }
@@ -135,8 +142,9 @@ pub struct FriQueryRoundTarget<const D: usize> {
     pub steps: Vec<FriQueryStepTarget<D>>,
 }
 
-#[derive(Clone)]
-pub struct FriProof<F: Field + Extendable<D>, const D: usize> {
+#[derive(Serialize, Deserialize, Clone, Debug)]
+#[serde(bound = "")]
+pub struct FriProof<F: Extendable<D>, const D: usize> {
     /// A Merkle root for each reduced polynomial in the commit phase.
     pub commit_phase_merkle_roots: Vec<Hash<F>>,
     /// Query rounds proofs
@@ -154,9 +162,9 @@ pub struct FriProofTarget<const D: usize> {
     pub pow_witness: Target,
 }
 
-#[derive(Clone, Debug)]
+#[derive(Clone, Debug, Serialize, Deserialize)]
 /// The purported values of each polynomial at a single point.
-pub struct OpeningSet<F: Field + Extendable<D>, const D: usize> {
+pub struct OpeningSet<F: Extendable<D>, const D: usize> {
     pub constants: Vec<F::Extension>,
     pub plonk_sigmas: Vec<F::Extension>,
     pub wires: Vec<F::Extension>,
@@ -166,7 +174,7 @@ pub struct OpeningSet<F: Field + Extendable<D>, const D: usize> {
     pub quotient_polys: Vec<F::Extension>,
 }
 
-impl<F: Field + Extendable<D>, const D: usize> OpeningSet<F, D> {
+impl<F: Extendable<D>, const D: usize> OpeningSet<F, D> {
     pub fn new(
         z: F::Extension,
         g: F::Extension,
diff --git a/src/prover.rs b/src/prover.rs
index 0411ce09..ce83f0a5 100644
--- a/src/prover.rs
+++ b/src/prover.rs
@@ -86,7 +86,7 @@ pub(crate) fn prove<F: Extendable<D>, const D: usize>(
     let gammas = challenger.get_n_challenges(num_challenges);
 
     assert!(
-        common_data.quotient_degree_factor + 1 <=common_data.config.num_routed_wires,
+        common_data.quotient_degree_factor < common_data.config.num_routed_wires,
         "When the number of routed wires is smaller that the degree, we should change the logic to avoid computing partial products."
     );
     let mut partial_products = timed!(
diff --git a/src/rescue.rs b/src/rescue.rs
index f088fdb7..9aa12bc5 100644
--- a/src/rescue.rs
+++ b/src/rescue.rs
@@ -179,7 +179,7 @@ const MDS: [[u64; W]; W] = [
     ],
 ];
 
-const RESCUE_CONSTANTS: [[u64; W]; 16] = [
+const RESCUE_CONSTANTS: [[u64; W]; ROUNDS * 2] = [
     [
         12050887499329086906,
         1748247961703512657,
@@ -442,7 +442,7 @@ fn mds_layer<F: Field>(x: [F; W]) -> [F; W] {
     let mut result = [F::ZERO; W];
     for r in 0..W {
         for c in 0..W {
-            result[r] = result[r] + F::from_canonical_u64(MDS[r][c]) * x[c];
+            result[r] += F::from_canonical_u64(MDS[r][c]) * x[c];
         }
     }
     result
diff --git a/src/util/mod.rs b/src/util/mod.rs
index 6fd0e562..bfebe058 100644
--- a/src/util/mod.rs
+++ b/src/util/mod.rs
@@ -43,8 +43,8 @@ pub(crate) fn transpose<T: Clone>(matrix: &[Vec<T>]) -> Vec<Vec<T>> {
     let old_cols = matrix[0].len();
     let mut transposed = vec![Vec::with_capacity(old_rows); old_cols];
     for new_r in 0..old_cols {
-        for new_c in 0..old_rows {
-            transposed[new_r].push(matrix[new_c][new_r].clone());
+        for old_row in matrix.iter() {
+            transposed[new_r].push(old_row[new_r].clone());
         }
     }
     transposed