diff --git a/libcrux-ml-kem/src/simd/simd256.rs b/libcrux-ml-kem/src/simd/simd256.rs
index 3a0f14d81..510e2ce4d 100644
--- a/libcrux-ml-kem/src/simd/simd256.rs
+++ b/libcrux-ml-kem/src/simd/simd256.rs
@@ -1,4 +1,8 @@
 use crate::{
+    arithmetic::{
+        BARRETT_MULTIPLIER, BARRETT_R, BARRETT_SHIFT, INVERSE_OF_MODULUS_MOD_MONTGOMERY_R,
+        MONTGOMERY_SHIFT,
+    },
     constants::FIELD_MODULUS,
     simd::{portable, simd_trait::*},
 };
@@ -9,6 +13,13 @@ pub(crate) struct SIMD256Vector {
     elements: __m256i,
 }
 
+#[allow(dead_code)]
+fn print_m256i_as_i32s(a: __m256i, prefix: String) {
+    let mut a_bytes = [0i32; 8];
+    unsafe { _mm256_store_si256(a_bytes.as_mut_ptr() as *mut __m256i, a) };
+    println!("{}: {:?}", prefix, a_bytes);
+}
+
 #[allow(non_snake_case)]
 #[inline(always)]
 fn ZERO() -> SIMD256Vector {
@@ -111,18 +122,52 @@ fn cond_subtract_3329(mut v: SIMD256Vector) -> SIMD256Vector {
 
 #[inline(always)]
 fn barrett_reduce(v: SIMD256Vector) -> SIMD256Vector {
-    let input = portable::PortableVector::from_i32_array(to_i32_array(v));
-    let output = portable::PortableVector::barrett_reduce(input);
+    let reduced = unsafe {
+        let barrett_multiplier = _mm256_set1_epi32(BARRETT_MULTIPLIER as i32);
+        let barrett_r_halved = _mm256_set1_epi64x(BARRETT_R >> 1);
+        let field_modulus = _mm256_set1_epi32(FIELD_MODULUS);
 
-    from_i32_array(portable::PortableVector::to_i32_array(output))
+        let mut t_low = _mm256_mul_epi32(v.elements, barrett_multiplier);
+        t_low = _mm256_add_epi64(t_low, barrett_r_halved);
+        let quotient_low = _mm256_srli_epi64(t_low, BARRETT_SHIFT as i32);
+
+        let mut t_high = _mm256_shuffle_epi32(v.elements, 0b00_11_00_01);
+        t_high = _mm256_mul_epi32(t_high, barrett_multiplier);
+        t_high = _mm256_add_epi64(t_high, barrett_r_halved);
+        let quotient_high = _mm256_slli_epi64(t_high, 6);
+
+        let quotient = _mm256_blend_epi32(quotient_low, quotient_high, 0b1_0_1_0_1_0_1_0);
+        let quotient = _mm256_mullo_epi32(quotient, field_modulus);
+
+        _mm256_sub_epi32(v.elements, quotient)
+    };
+
+    SIMD256Vector { elements: reduced }
 }
 
 #[inline(always)]
 fn montgomery_reduce(v: SIMD256Vector) -> SIMD256Vector {
-    let input = portable::PortableVector::from_i32_array(to_i32_array(v));
-    let output = portable::PortableVector::montgomery_reduce(input);
+    let reduced = unsafe {
+        let montgomery_shift_mask = _mm256_set1_epi32((1 << MONTGOMERY_SHIFT) - 1);
+        let field_modulus = _mm256_set1_epi32(FIELD_MODULUS);
+        let inverse_of_modulus_mod_montgomery_r =
+            _mm256_set1_epi32(INVERSE_OF_MODULUS_MOD_MONTGOMERY_R as i32);
 
-    from_i32_array(portable::PortableVector::to_i32_array(output))
+        let t = _mm256_and_si256(v.elements, montgomery_shift_mask);
+        let t = _mm256_mullo_epi32(t, inverse_of_modulus_mod_montgomery_r);
+
+        let k = _mm256_and_si256(t, montgomery_shift_mask);
+        let k = _mm256_slli_epi32(k, 16);
+        let k = _mm256_srai_epi32(k, 16);
+
+        let k_times_modulus = _mm256_mullo_epi32(k, field_modulus);
+        let c = _mm256_srai_epi32(k_times_modulus, MONTGOMERY_SHIFT as i32);
+        let value_high = _mm256_srai_epi32(v.elements, MONTGOMERY_SHIFT as i32);
+
+        _mm256_sub_epi32(value_high, c)
+    };
+
+    SIMD256Vector { elements: reduced }
 }
 
 #[inline(always)]
@@ -185,12 +230,31 @@ fn inv_ntt_layer_2_step(v: SIMD256Vector, zeta: i32) -> SIMD256Vector {
 
 #[inline(always)]
 fn ntt_multiply(lhs: &SIMD256Vector, rhs: &SIMD256Vector, zeta0: i32, zeta1: i32) -> SIMD256Vector {
-    let input1 = portable::PortableVector::from_i32_array(to_i32_array(*lhs));
-    let input2 = portable::PortableVector::from_i32_array(to_i32_array(*rhs));
+    let result = unsafe {
+        // Calculate the first element of the output binomial
+        let zetas = _mm256_set_epi32(-zeta1, 0, zeta1, 0, -zeta0, 0, zeta0, 0);
 
-    let output = portable::PortableVector::ntt_multiply(&input1, &input2, zeta0, zeta1);
+        let left = _mm256_mullo_epi32(lhs.elements, rhs.elements);
+        let right = montgomery_reduce(SIMD256Vector { elements: left });
 
-    from_i32_array(portable::PortableVector::to_i32_array(output))
+        let right = _mm256_mullo_epi32(right.elements, zetas);
+
+        let right = _mm256_shuffle_epi32(right, 0b00_11_00_01);
+
+        let result_0 = _mm256_add_epi32(left, right);
+
+        // Calculate the second element in the output binomial
+        let rhs_adjacent_swapped = _mm256_shuffle_epi32(rhs.elements, 0b10_11_00_01);
+        let result_1 = _mm256_mullo_epi32(lhs.elements, rhs_adjacent_swapped);
+
+        let swapped = _mm256_shuffle_epi32(result_1, 0b10_00_00_00);
+        let result_1 = _mm256_add_epi32(result_1, swapped);
+
+        // Put them together
+        _mm256_blend_epi32(result_0, result_1, 0b1_0_1_0_1_0_1_0)
+    };
+
+    montgomery_reduce(SIMD256Vector { elements: result })
 }
 
 #[inline(always)]