diff --git a/Cargo.lock b/Cargo.lock
index e82d47d690a..6e367788c7c 100644
--- a/Cargo.lock
+++ b/Cargo.lock
@@ -31,6 +31,7 @@ dependencies = [
  "ark-bls12-381",
  "ark-bn254 0.5.0",
  "ark-ff 0.5.0",
+ "ark-std 0.5.0",
  "cfg-if",
  "hex",
  "num-bigint",
diff --git a/acvm-repo/acir_field/Cargo.toml b/acvm-repo/acir_field/Cargo.toml
index f9ae3a4ea3f..fea0775e10c 100644
--- a/acvm-repo/acir_field/Cargo.toml
+++ b/acvm-repo/acir_field/Cargo.toml
@@ -23,6 +23,7 @@ serde.workspace = true
 ark-bn254.workspace = true
 ark-bls12-381 = { workspace = true, optional = true }
 ark-ff.workspace = true
+ark-std.workspace = true
 
 cfg-if.workspace = true
 
diff --git a/acvm-repo/acir_field/src/field_element.rs b/acvm-repo/acir_field/src/field_element.rs
index 0249b410aa7..e53fb760476 100644
--- a/acvm-repo/acir_field/src/field_element.rs
+++ b/acvm-repo/acir_field/src/field_element.rs
@@ -1,5 +1,6 @@
 use ark_ff::PrimeField;
 use ark_ff::Zero;
+use ark_std::io::Write;
 use num_bigint::BigUint;
 use serde::{Deserialize, Serialize};
 use std::borrow::Cow;
@@ -195,26 +196,9 @@ impl<F: PrimeField> AcirField for FieldElement<F> {
 
     /// This is the number of bits required to represent this specific field element
     fn num_bits(&self) -> u32 {
-        let bytes = self.to_be_bytes();
-
-        // Iterate through the byte decomposition and pop off all leading zeroes
-        let mut iter = bytes.iter().skip_while(|x| (**x) == 0);
-
-        // The first non-zero byte in the decomposition may have some leading zero-bits.
-        let Some(head_byte) = iter.next() else {
-            // If we don't have a non-zero byte then the field element is zero,
-            // which we consider to require a single bit to represent.
-            return 1;
-        };
-        let num_bits_for_head_byte = head_byte.ilog2();
-
-        // Each remaining byte in the byte decomposition requires 8 bits.
-        //
-        // Note: count will panic if it goes over usize::MAX.
-        // This may not be suitable for devices whose usize < u16
-        let tail_length = iter.count() as u32;
-
-        8 * tail_length + num_bits_for_head_byte + 1
+        let mut bit_counter = BitCounter::default();
+        self.0.serialize_uncompressed(&mut bit_counter).unwrap();
+        bit_counter.bits()
     }
 
     fn to_u128(self) -> u128 {
@@ -354,6 +338,52 @@ impl<F: PrimeField> SubAssign for FieldElement<F> {
     }
 }
 
+#[derive(Default, Debug)]
+struct BitCounter {
+    /// Total number of non-zero bytes we found.
+    count: usize,
+    /// Total bytes we found.
+    total: usize,
+    /// The last non-zero byte we found.
+    head_byte: u8,
+}
+
+impl BitCounter {
+    fn bits(&self) -> u32 {
+        // If we don't have a non-zero byte then the field element is zero,
+        // which we consider to require a single bit to represent.
+        if self.count == 0 {
+            return 1;
+        }
+
+        let num_bits_for_head_byte = self.head_byte.ilog2();
+
+        // Each remaining byte in the byte decomposition requires 8 bits.
+        //
+        // Note: count will panic if it goes over usize::MAX.
+        // This may not be suitable for devices whose usize < u16
+        let tail_length = (self.count - 1) as u32;
+        8 * tail_length + num_bits_for_head_byte + 1
+    }
+}
+
+impl Write for BitCounter {
+    fn write(&mut self, buf: &[u8]) -> ark_std::io::Result<usize> {
+        for byte in buf {
+            self.total += 1;
+            if *byte != 0 {
+                self.count = self.total;
+                self.head_byte = *byte;
+            }
+        }
+        Ok(buf.len())
+    }
+
+    fn flush(&mut self) -> ark_std::io::Result<()> {
+        Ok(())
+    }
+}
+
 #[cfg(test)]
 mod tests {
     use super::{AcirField, FieldElement};