diff --git a/logproof/benches/linear_relation.rs b/logproof/benches/linear_relation.rs
index fc2bc3301..b11e67b82 100644
--- a/logproof/benches/linear_relation.rs
+++ b/logproof/benches/linear_relation.rs
@@ -76,7 +76,7 @@ where
     // e_1 = q / 2p
     // c_1 = s * a + e_1 + del * m
     // c_2 = a
-    const BIT_SIZE: usize = 2 << 8;
+    const BIT_SIZE: u32 = 2 << 8;
 
     println!("Generating data...");
 
diff --git a/logproof/src/bfv_statement.rs b/logproof/src/bfv_statement.rs
index 490714108..5173da677 100644
--- a/logproof/src/bfv_statement.rs
+++ b/logproof/src/bfv_statement.rs
@@ -26,12 +26,12 @@ use crate::{
 };
 
 /// In SEAL, `u` is sampled from a ternary distribution. The number of bits is 1.
-const U_COEFFICIENT_BOUND: usize = 1;
+const U_COEFFICIENT_BOUND: u32 = 1;
 /// In SEAL, `e` is sampled from a centered binomial distribution with std dev 3.2, and a maximum
 /// width multiplier of 6, so max bound is 19.2. 19.2.ceil_log2() == 5
-const E_COEFFICIENT_BOUND: usize = 5;
+const E_COEFFICIENT_BOUND: u32 = 5;
 /// In SEAL, secret keys are sampled from a ternary distribution. The number of bits is 1.
-const S_COEFFICIENT_BOUND: usize = 1;
+const S_COEFFICIENT_BOUND: u32 = 1;
 
 /// A proof statement verifying that a ciphertext is an encryption of a known plaintext message.
 /// Note that these statements are per SEAL plain/ciphertexts, where Sunscreen encodings are at a
@@ -440,7 +440,7 @@ where
     let degree = params.degree() as usize;
 
     // calculate bounds
-    let m_default_bound = Bounds(vec![params.plain_modulus().ceil_log2() as usize; degree]);
+    let m_default_bound = Bounds(vec![params.plain_modulus().ceil_log2(); degree]);
     let r_bound = m_default_bound.clone();
     let u_bound = Bounds(vec![U_COEFFICIENT_BOUND; degree]);
     let e_bound = Bounds(vec![E_COEFFICIENT_BOUND; degree]);
@@ -449,7 +449,7 @@ where
     let q_div_2_bits = calculate_ciphertext_modulus(params.ciphertext_modulus())
         .div(NonZero::from_uint(Uint::from(2u8)))
         .ceil_log2();
-    let decrypt_e_bound = Bounds(vec![q_div_2_bits as usize; degree]);
+    let decrypt_e_bound = Bounds(vec![q_div_2_bits as u32; degree]);
 
     // insert them
     for i in 0..IdxOffsets::num_messages(statements) {
diff --git a/logproof/src/linear_relation.rs b/logproof/src/linear_relation.rs
index 3e1531277..e12524610 100644
--- a/logproof/src/linear_relation.rs
+++ b/logproof/src/linear_relation.rs
@@ -53,7 +53,7 @@ type MatrixPoly<Q> = Matrix<Polynomial<Q>>;
  * Bounds on the coefficients in the secret S (specified in number of bits).
  */
 #[derive(Clone, Debug, PartialEq)]
-pub struct Bounds(pub Vec<usize>);
+pub struct Bounds(pub Vec<u32>);
 
 impl Zero for Bounds {
     // The empty vector could be seen as no bounds. Also follows the field
@@ -69,7 +69,7 @@ impl Zero for Bounds {
 }
 
 impl std::ops::Deref for Bounds {
-    type Target = [usize];
+    type Target = [u32];
 
     fn deref(&self) -> &Self::Target {
         &self.0
@@ -132,22 +132,22 @@ where
     /**
      * The number of rows in a.
      */
-    pub fn n(&self) -> u64 {
-        self.a.rows as u64
+    pub fn n(&self) -> u32 {
+        self.a.rows as u32
     }
 
     /**
      * The number of cols in a and the number rows in s.
      */
-    pub fn m(&self) -> u64 {
-        self.a.cols as u64
+    pub fn m(&self) -> u32 {
+        self.a.cols as u32
     }
 
     /**
      * The number of cols in t.
      */
-    pub fn k(&self) -> u64 {
-        self.t.cols as u64
+    pub fn k(&self) -> u32 {
+        self.t.cols as u32
     }
 
     /**
@@ -168,11 +168,11 @@ where
     /**
      * Sum of all the bounds
      */
-    pub fn b_sum(&self) -> u64 {
+    pub fn b_sum(&self) -> u32 {
         self.b()
             .as_slice()
             .iter()
-            .map(|v| v.iter().sum::<usize>() as u64)
+            .map(|v| v.iter().sum::<u32>())
             .sum()
     }
 
@@ -189,7 +189,7 @@ where
         let mut last_end_range = 0;
 
         for (k, b_piece) in b.as_slice().iter().enumerate() {
-            let bits = b_piece.iter().sum::<usize>();
+            let bits = b_piece.iter().sum::<u32>() as usize;
 
             // Get the orginal matrix index
             let i = k / self.bounds.cols;
@@ -210,28 +210,28 @@ where
     /**
      * The degree of `f`.
      */
-    pub fn d(&self) -> u64 {
-        self.f.vartime_degree() as u64
+    pub fn d(&self) -> u32 {
+        self.f.vartime_degree() as u32
     }
 
     /**
      * Number of coefficients in secret vector s
      */
-    pub fn number_coeff_in_s(&self) -> u64 {
+    pub fn number_coeff_in_s(&self) -> u32 {
         self.m() * self.d()
     }
 
     /**
      * Computes the nk(d-1)b_2 term in l.
      */
-    pub fn nk_d_min_1_b_2(&self) -> u64 {
+    pub fn nk_d_min_1_b_2(&self) -> u32 {
         self.n() * self.k() * (self.d() - 1) * self.b_2()
     }
 
     /**
      * Computes the nk(2d-1)b_1 term in l.
      */
-    pub fn nk_2d_min_1_b_1(&self) -> u64 {
+    pub fn nk_2d_min_1_b_1(&self) -> u32 {
         self.n() * self.k() * (2 * self.d() - 1) * self.b_1()
     }
 
@@ -245,7 +245,7 @@ where
                 for r in 0..self.bounds.rows {
                     column_bound_sum += self.bounds[(r, c)]
                         .iter()
-                        .map(|b| if *b > 0 { 2u64.pow(*b as u32) } else { 0 })
+                        .map(|b| if *b > 0 { 2u64.pow(*b) } else { 0 })
                         .sum::<u64>();
                 }
                 column_bound_sum
@@ -256,7 +256,7 @@ where
     /**
      * The number of bits needed to store the elements of R1.
      */
-    pub fn b_1(&self) -> u64 {
+    pub fn b_1(&self) -> u32 {
         let d_big = ZqRistretto::from(self.d());
         let max_bounds_column_sum = ZqRistretto::from(self.max_bounds_column_sum());
 
@@ -270,14 +270,14 @@ where
     /**
      * The number of bits needed to store values in `Fp<Q>`.
      */
-    pub fn b_2(&self) -> u64 {
+    pub fn b_2(&self) -> u32 {
         Log2::ceil_log2(&Q::field_modulus())
     }
 
     /**
      * The length in bits of the binary expansion of the serialized secret * vectors.
      */
-    pub fn l(&self) -> u64 {
+    pub fn l(&self) -> u32 {
         let total_bounds_all_equations = self.b_sum();
         let nk = self.n().checked_mul(self.k()).unwrap();
 
@@ -496,19 +496,19 @@ impl LogProof {
         let r_1_serialized = Self::serialize(&r_1, (2 * d - 1) as usize);
         let r_2_serialized = Self::serialize(&r_2, (d - 1) as usize);
 
-        assert_eq!(s_serialized.len() as u64, m * k * d);
+        assert_eq!(s_serialized.len() as u32, m * k * d);
 
-        assert_eq!(r_1_serialized.len() as u64, n * k * (2 * d - 1));
-        assert_eq!(r_2_serialized.len() as u64, n * k * (d - 1));
+        assert_eq!(r_1_serialized.len() as u32, n * k * (2 * d - 1));
+        assert_eq!(r_2_serialized.len() as u32, n * k * (d - 1));
 
         let s_binary: BitVec = Self::to_2s_complement_multibound(&s_serialized, &b_serialized);
-        assert_eq!(s_binary.len() as u64, total_bounds_all_equations);
+        assert_eq!(s_binary.len() as u32, total_bounds_all_equations);
 
         let r_1_binary = Self::to_2s_complement(&r_1_serialized, b_1);
-        assert_eq!(r_1_binary.len() as u64, n * k * (2 * d - 1) * b_1);
+        assert_eq!(r_1_binary.len() as u32, n * k * (2 * d - 1) * b_1);
 
         let r_2_binary = Self::to_2s_complement(&r_2_serialized, b_2);
-        assert_eq!(r_2_binary.len() as u64, n * k * (d - 1) * b_2);
+        assert_eq!(r_2_binary.len() as u32, n * k * (d - 1) * b_2);
 
         let mut s_1 = s_binary.clone();
         s_1.extend(r_1_binary.iter());
@@ -903,7 +903,7 @@ impl LogProof {
             two_b.as_slice(),
         );
 
-        assert_eq!(term_1.len() as u64, b_sum);
+        assert_eq!(term_1.len() as u32, b_sum);
 
         // Compute term 2
         let q = ZqRistretto::try_from(Q::field_modulus()).unwrap();
@@ -919,7 +919,7 @@ impl LogProof {
             .tensor(alpha_2d_minus_1)
             .tensor(two_b_1);
 
-        assert_eq!(term_2.len() as u64, b_1 * (2 * d - 1) * n * k);
+        assert_eq!(term_2.len() as u32, b_1 * (2 * d - 1) * n * k);
 
         // Compute term 3
         let d_min_1 = d as usize - 1;
@@ -935,7 +935,7 @@ impl LogProof {
             .tensor(alpha_d_minus_1)
             .tensor(two_b_2);
 
-        assert_eq!(term_3.len() as u64, b_2 * (d - 1) * n * k);
+        assert_eq!(term_3.len() as u32, b_2 * (d - 1) * n * k);
 
         let mut result = vec![];
 
@@ -1121,7 +1121,7 @@ impl LogProof {
      * panic on any other input.
      *
      */
-    fn to_2s_complement_single<B, const N: usize>(value: &Zq<N, B>, log_b: u64, bitvec: &mut BitVec)
+    fn to_2s_complement_single<B, const N: usize>(value: &Zq<N, B>, log_b: u32, bitvec: &mut BitVec)
     where
         B: ArithmeticBackend<N>,
     {
@@ -1168,7 +1168,7 @@ impl LogProof {
      * `value` is the element in Zq and `b` is the number of bits needed
      * to represent the signed value.
      */
-    fn to_2s_complement<B, const N: usize>(values: &[Zq<N, B>], log_b: u64) -> BitVec
+    fn to_2s_complement<B, const N: usize>(values: &[Zq<N, B>], log_b: u32) -> BitVec
     where
         B: ArithmeticBackend<N>,
     {
@@ -1192,14 +1192,14 @@ impl LogProof {
      * `value` is the element in Zq and `b` is the number of bits needed
      * to represent the signed value.
      */
-    fn to_2s_complement_multibound<B, const N: usize>(values: &[Zq<N, B>], log_b: &[u64]) -> BitVec
+    fn to_2s_complement_multibound<B, const N: usize>(values: &[Zq<N, B>], log_b: &[u32]) -> BitVec
     where
         B: ArithmeticBackend<N>,
     {
         // Make sure we have an equal number of values and bounds to serialize
         assert_eq!(values.len(), log_b.len());
 
-        let mut bitvec = BitVec::with_capacity(log_b.iter().sum::<u64>() as usize);
+        let mut bitvec = BitVec::with_capacity(log_b.iter().sum::<u32>() as usize);
 
         // This code should not feature timing side-channels.
         for (value, bound) in zip(values.iter(), log_b.iter()) {
@@ -1216,11 +1216,11 @@ impl LogProof {
      * The matrix is serialized in row-major order, with bound
      * coefficients being contiguous.
      */
-    pub fn serialize_bounds(bounds: &Matrix<Bounds>) -> Vec<u64> {
+    pub fn serialize_bounds(bounds: &Matrix<Bounds>) -> Vec<u32> {
         bounds
             .as_slice()
             .iter()
-            .flat_map(|x| x.0.iter().map(|x| *x as u64))
+            .flat_map(|x| x.0.iter().copied())
             .collect()
     }
 
@@ -1403,7 +1403,7 @@ mod test {
                                             0
                                         } else {
                                             next_higher_power_of_two(x.unsigned_abs()).ilog2()
-                                                as usize
+                                                as u32
                                         }
                                     })
                                     .collect::<Vec<_>>(),
diff --git a/logproof/src/math.rs b/logproof/src/math.rs
index c8dcec561..0bf1b780d 100644
--- a/logproof/src/math.rs
+++ b/logproof/src/math.rs
@@ -1,6 +1,6 @@
 use std::{borrow::Borrow, ops::Mul};
 
-use crypto_bigint::Uint;
+use crypto_bigint::{Limb, Uint};
 use curve25519_dalek::{ristretto::RistrettoPoint, scalar::Scalar, traits::VartimeMultiscalarMul};
 use rand::Rng;
 use rayon::prelude::{IndexedParallelIterator, IntoParallelRefIterator, ParallelIterator};
@@ -139,7 +139,7 @@ pub trait Log2 {
      * # Panics
      * When the given value is zero.
      */
-    fn log2(&self) -> u64;
+    fn log2(&self) -> u32;
 
     /**
      * Compute the ceiling of the log2 of the given value.
@@ -147,14 +147,14 @@ pub trait Log2 {
      * # Panics
      * When the given value is zero.
      */
-    fn ceil_log2(&self) -> u64;
+    fn ceil_log2(&self) -> u32;
 }
 
 impl Log2 for u64 {
     /**
      * An implementation of log2 that works on stable.
      */
-    fn log2(&self) -> u64 {
+    fn log2(&self) -> u32 {
         let mut mask = 0x8000_0000_0000_0000;
 
         for i in 0..64 {
@@ -168,7 +168,7 @@ impl Log2 for u64 {
         panic!("Value was zero.");
     }
 
-    fn ceil_log2(&self) -> u64 {
+    fn ceil_log2(&self) -> u32 {
         let ceil_factor = if self.is_power_of_two() { 0 } else { 1 };
         self.log2() + ceil_factor
     }
@@ -179,7 +179,9 @@ fn is_power_of_two_bigint<const N: usize>(b: &Uint<N>) -> bool {
 }
 
 impl<const N: usize> Log2 for Uint<N> {
-    fn log2(&self) -> u64 {
+    fn log2(&self) -> u32 {
+        let limb_bits = Limb::BITS as u32;
+
         for i in 0..self.as_limbs().len() {
             let i = self.as_limbs().len() - i - 1;
             let limb = self.as_limbs()[i];
@@ -188,13 +190,13 @@ impl<const N: usize> Log2 for Uint<N> {
                 continue;
             }
 
-            return Log2::log2(&limb.0) + (i as u64) * 64;
+            return Log2::log2(&limb.0) + (i as u32) * limb_bits;
         }
 
         panic!("Value was zero.");
     }
 
-    fn ceil_log2(&self) -> u64 {
+    fn ceil_log2(&self) -> u32 {
         let ceil_factor = if is_power_of_two_bigint(self) { 0 } else { 1 };
 
         self.log2() + ceil_factor
@@ -202,11 +204,11 @@ impl<const N: usize> Log2 for Uint<N> {
 }
 
 impl<const N: usize, B: ArithmeticBackend<N>> Log2 for Zq<N, B> {
-    fn log2(&self) -> u64 {
+    fn log2(&self) -> u32 {
         Uint::<N>::log2(&self.val)
     }
 
-    fn ceil_log2(&self) -> u64 {
+    fn ceil_log2(&self) -> u32 {
         Uint::<N>::ceil_log2(&self.val)
     }
 }
@@ -663,7 +665,7 @@ mod test {
 
         for value in options {
             let f = value as f64;
-            let expected = f.log2().ceil() as u64;
+            let expected = f.log2().ceil() as u32;
 
             let calculated = Log2::ceil_log2(&value);
 
@@ -677,7 +679,7 @@ mod test {
 
         for value in options {
             let f = value as f64;
-            let expected = f.log2().ceil() as u64;
+            let expected = f.log2().ceil() as u32;
 
             let b: Uint<1> = Uint::from(value);
             let calculated = Log2::ceil_log2(&b);
diff --git a/sunscreen_runtime/src/builder.rs b/sunscreen_runtime/src/builder.rs
index 77b16ce04..755a50db0 100644
--- a/sunscreen_runtime/src/builder.rs
+++ b/sunscreen_runtime/src/builder.rs
@@ -742,7 +742,7 @@ mod linked {
 
         fn mk_bounds<P: LinkWithZkp>(&self) -> Bounds {
             let params = self.runtime.params();
-            let mut bounds = vec![params.plain_modulus.ceil_log2() as usize; P::DEGREE_BOUND];
+            let mut bounds = vec![params.plain_modulus.ceil_log2(); P::DEGREE_BOUND];
             bounds.resize(params.lattice_dimension as usize, 0);
             Bounds(bounds)
         }
diff --git a/sunscreen_runtime/src/linked.rs b/sunscreen_runtime/src/linked.rs
index a9dff3bd7..3da8315e6 100644
--- a/sunscreen_runtime/src/linked.rs
+++ b/sunscreen_runtime/src/linked.rs
@@ -453,7 +453,7 @@ impl SealSdlpVerifierKnowledge {
     /// Get the length in bits of the binary expansion of the serialized secret * vectors.
     ///
     /// Delegate to [`LogProofVerifierKnowledge::l`].
-    pub fn l(&self) -> u64 {
+    pub fn l(&self) -> u32 {
         seq_zq!({
             match &self.0 {
                 #(
diff --git a/sunscreen_tfhe/src/zkp.rs b/sunscreen_tfhe/src/zkp.rs
index 3fdd49b53..97073af83 100644
--- a/sunscreen_tfhe/src/zkp.rs
+++ b/sunscreen_tfhe/src/zkp.rs
@@ -221,7 +221,7 @@ fn compute_bounds<S: TorusOps + TorusZq>(
     // Bounds for messages
     for i in 0..num_messages {
         let mut b = Bounds(vec![0; num_coeffs]);
-        b.0[0] = 0x1u64 << plaintext_bits.0;
+        b.0[0] = 0x1_u32 << plaintext_bits.0;
         debug_assert_eq!(bounds[(i, 0)].0, &[]);
         bounds[(i, 0)] = b;
     }
@@ -232,7 +232,7 @@ fn compute_bounds<S: TorusOps + TorusZq>(
             let mut b = Bounds(vec![0; num_coeffs]);
 
             // Values of r are binary
-            b.0[0] = 0x1u64 << plaintext_bits.0;
+            b.0[0] = 0x1_u32 << plaintext_bits.0;
             debug_assert_eq!(
                 bounds[(offsets.public_keys + i * lwe_dimension + j, 0)].0,
                 &[]
@@ -242,7 +242,7 @@ fn compute_bounds<S: TorusOps + TorusZq>(
 
         // e is normal distributed over the torus.
         // TODO: This bound is too high. Get a tighter bound.
-        let b = Bounds(vec![0x1u64 << (60 - plaintext_bits.0); num_coeffs]);
+        let b = Bounds(vec![0x1_u32 << (60 - plaintext_bits.0); num_coeffs]);
 
         debug_assert_eq!(bounds[(offsets.public_e + i, 0)].0, &[]);
         bounds[(offsets.public_e + i, 0)] = b;
@@ -254,7 +254,7 @@ fn compute_bounds<S: TorusOps + TorusZq>(
             let mut b = Bounds(vec![0; num_coeffs]);
 
             // Values of s are binary
-            b.0[0] = 0x1u64 << plaintext_bits.0;
+            b.0[0] = 0x1_u32 << plaintext_bits.0;
             debug_assert_eq!(
                 bounds[(offsets.private_a + j + i * lwe_dimension, 0)].0,
                 &[]
@@ -266,7 +266,7 @@ fn compute_bounds<S: TorusOps + TorusZq>(
 
         // e is normal distributed over the torus.
         // TODO: This bound is too high. Get a tighter bound.
-        b.0[0] = 0x1u64 << (62 - plaintext_bits.0);
+        b.0[0] = 0x1_u32 << (62 - plaintext_bits.0);
         debug_assert_eq!(bounds[(offsets.private_e + i, 0)].0, &[]);
         bounds[(offsets.private_e + i, 0)] = b;
     }