diff --git a/crypto/crypto/src/fiat_shamir/default_transcript.rs b/crypto/crypto/src/fiat_shamir/default_transcript.rs
index 8ab3eafc3..819b0f761 100644
--- a/crypto/crypto/src/fiat_shamir/default_transcript.rs
+++ b/crypto/crypto/src/fiat_shamir/default_transcript.rs
@@ -8,7 +8,7 @@ use math::{
         element::FieldElement,
         traits::{HasDefaultTranscript, IsField, IsSubFieldOf},
     },
-    traits::ByteConversion,
+    traits::AsBytes,
 };
 use rand_chacha::{ChaCha20Rng, rand_core::SeedableRng};
 
@@ -29,7 +29,7 @@ impl<F: HasDefaultTranscript> Clone for DefaultTranscript<F> {
 impl<F> DefaultTranscript<F>
 where
     F: HasDefaultTranscript,
-    FieldElement<F>: ByteConversion,
+    FieldElement<F>: AsBytes,
 {
     pub fn new(data: &[u8]) -> Self {
         let mut res = Self {
@@ -51,7 +51,7 @@ where
 impl<F> Default for DefaultTranscript<F>
 where
     F: HasDefaultTranscript,
-    FieldElement<F>: ByteConversion,
+    FieldElement<F>: AsBytes,
 {
     fn default() -> Self {
         Self::new(&[])
@@ -61,14 +61,14 @@ where
 impl<F> IsTranscript<F> for DefaultTranscript<F>
 where
     F: HasDefaultTranscript,
-    FieldElement<F>: ByteConversion,
+    FieldElement<F>: AsBytes,
 {
     fn append_bytes(&mut self, new_bytes: &[u8]) {
         self.hasher.update(new_bytes);
     }
 
     fn append_field_element(&mut self, element: &FieldElement<F>) {
-        self.append_bytes(&element.to_bytes_be());
+        element.stream_bytes(&mut |b| self.hasher.update(b));
     }
 
     fn state(&self) -> [u8; 32] {
@@ -95,7 +95,7 @@ where
 impl<F, S> IsStarkTranscript<F, S> for DefaultTranscript<F>
 where
     F: HasDefaultTranscript,
-    FieldElement<F>: ByteConversion,
+    FieldElement<F>: AsBytes,
     S: IsField + IsSubFieldOf<F>,
 {
     // nothing to implement: sample_z_ood uses the default body
diff --git a/crypto/crypto/src/merkle_tree/backends/field_element.rs b/crypto/crypto/src/merkle_tree/backends/field_element.rs
index d5d5c32d7..e8f106f5a 100644
--- a/crypto/crypto/src/merkle_tree/backends/field_element.rs
+++ b/crypto/crypto/src/merkle_tree/backends/field_element.rs
@@ -34,7 +34,7 @@ where
 
     fn hash_data(input: &FieldElement<F>) -> [u8; NUM_BYTES] {
         let mut hasher = D::new();
-        hasher.update(input.as_bytes());
+        input.stream_bytes(&mut |b| hasher.update(b));
         hasher.finalize().into()
     }
 
diff --git a/crypto/crypto/src/merkle_tree/backends/field_element_vector.rs b/crypto/crypto/src/merkle_tree/backends/field_element_vector.rs
index e6daace0d..d60419cf4 100644
--- a/crypto/crypto/src/merkle_tree/backends/field_element_vector.rs
+++ b/crypto/crypto/src/merkle_tree/backends/field_element_vector.rs
@@ -39,8 +39,8 @@ where
 
     fn hash_data(input: &[FieldElement<F>; 2]) -> [u8; NUM_BYTES] {
         let mut hasher = D::new();
-        hasher.update(input[0].as_bytes());
-        hasher.update(input[1].as_bytes());
+        input[0].stream_bytes(&mut |b| hasher.update(b));
+        input[1].stream_bytes(&mut |b| hasher.update(b));
         let mut result_hash = [0_u8; NUM_BYTES];
         result_hash.copy_from_slice(&hasher.finalize());
         result_hash
@@ -102,7 +102,7 @@ where
     pub fn hash_data_from_slices(a: &[FieldElement<F>], b: &[FieldElement<F>]) -> [u8; NUM_BYTES] {
         let mut hasher = D::new();
         for element in a.iter().chain(b.iter()) {
-            hasher.update(element.as_bytes());
+            element.stream_bytes(&mut |bytes| hasher.update(bytes));
         }
         let mut result_hash = [0_u8; NUM_BYTES];
         result_hash.copy_from_slice(&hasher.finalize());
diff --git a/crypto/math/src/field/extensions_goldilocks.rs b/crypto/math/src/field/extensions_goldilocks.rs
index d6bac98df..246a3cb87 100644
--- a/crypto/math/src/field/extensions_goldilocks.rs
+++ b/crypto/math/src/field/extensions_goldilocks.rs
@@ -554,6 +554,17 @@ impl AsBytes for FieldElement<Degree3GoldilocksExtensionField> {
     fn as_bytes(&self) -> alloc::vec::Vec<u8> {
         self.to_bytes_be()
     }
+
+    // One sink call over a stack buffer instead of three (one per limb): each
+    // sink call lands as its own `Digest::update` on the guest, and dyn dispatch
+    // here is fully devirtualized by the #[inline(always)] chain, so call count
+    // — not indirection — is the cost being cut.
+    #[inline(always)]
+    fn stream_bytes(&self, sink: &mut dyn FnMut(&[u8])) {
+        let mut buf = [0u8; 24];
+        ByteConversion::write_bytes_be(self, &mut buf);
+        sink(&buf);
+    }
 }
 
 impl HasDefaultTranscript for Degree3GoldilocksExtensionField {
diff --git a/crypto/math/src/field/goldilocks.rs b/crypto/math/src/field/goldilocks.rs
index 082d57325..1d60ee5b2 100644
--- a/crypto/math/src/field/goldilocks.rs
+++ b/crypto/math/src/field/goldilocks.rs
@@ -488,6 +488,11 @@ impl AsBytes for FieldElement<GoldilocksField> {
     fn as_bytes(&self) -> alloc::vec::Vec<u8> {
         ByteConversion::to_bytes_be(self)
     }
+
+    #[inline(always)]
+    fn stream_bytes(&self, sink: &mut dyn FnMut(&[u8])) {
+        sink(&self.canonical_u64().to_be_bytes());
+    }
 }
 
 // Implement IsPrimeField for the native Goldilocks
diff --git a/crypto/math/src/traits.rs b/crypto/math/src/traits.rs
index 0e902c6ff..e16b5bfb1 100644
--- a/crypto/math/src/traits.rs
+++ b/crypto/math/src/traits.rs
@@ -39,6 +39,12 @@ pub trait ByteConversion {
 pub trait AsBytes {
     /// Default serialize without args
     fn as_bytes(&self) -> alloc::vec::Vec<u8>;
+
+    /// Streams the byte representation to `sink` without heap-allocating a `Vec`.
+    /// Default falls back to `as_bytes`; override for zero-allocation hashing/transcript hot paths.
+    fn stream_bytes(&self, sink: &mut dyn FnMut(&[u8])) {
+        sink(&self.as_bytes());
+    }
 }
 
 #[cfg(feature = "alloc")]