diff --git a/src/gadgets/mod.rs b/src/gadgets/mod.rs
index aa18fbeb..5ec494c7 100644
--- a/src/gadgets/mod.rs
+++ b/src/gadgets/mod.rs
@@ -3,6 +3,7 @@ pub mod arithmetic_extension;
 pub mod hash;
 pub mod insert;
 pub mod interpolation;
+pub mod nonnative;
 pub mod permutation;
 pub mod polynomial;
 pub mod random_access;
diff --git a/src/gadgets/nonnative.rs b/src/gadgets/nonnative.rs
new file mode 100644
index 00000000..6763a1a5
--- /dev/null
+++ b/src/gadgets/nonnative.rs
@@ -0,0 +1,81 @@
+use std::collections::BTreeMap;
+use std::marker::PhantomData;
+
+use crate::field::field_types::RichField;
+use crate::field::{extension_field::Extendable, field_types::Field};
+use crate::gates::switch::SwitchGate;
+use crate::iop::generator::{GeneratedValues, SimpleGenerator};
+use crate::iop::target::Target;
+use crate::iop::witness::{PartitionWitness, Witness};
+use crate::plonk::circuit_builder::CircuitBuilder;
+use crate::util::bimap::bimap_from_lists;
+
+pub struct U32Target(Target);
+
+pub struct NonNativeTarget {
+    /// The modulus of the field F' being represented.
+    modulus: BigUInt,
+    /// These F elements are assumed to contain 32-bit values.
+    limbs: Vec<U32Target>,
+}
+
+impl<F: RichField + Extendable<D>, const D: usize> CircuitBuilder<F, D> {
+    pub fn add_mul_u32(&mut self, x: U32Target, y: U32Target, z:U32Target) -> (U32Target, U32Target) {
+        
+    }
+
+    pub fn add_u32(&mut self, a: U32Target, b: U32Target) -> (U32Target, U32Target) {
+        
+    }
+
+    pub fn mul_u32(&mut self, a: U32Target, b: U32Target) -> (U32Target, U32Target) {
+        
+    }
+
+    pub fn add_nonnative(&mut self, a: NonNativeTarget, b: NonNativeTarget) -> NonNativeTarget {
+        let modulus = a.modulus;
+        let num_limbs = a.limbs.len();
+        debug_assert!(b.modulus == modulus);
+        debug_assert!(b.limbs.len() == num_limbs);
+
+        let mut combined_limbs = self.add_virtual_targets(num_limbs + 1);
+        let mut carry = self.zero();
+        for i in 0..num_limbs {
+            let gate = ComparisonGate::new(bits, num_chunks);
+            let gate_index = self.add_gate(gate.clone(), vec![]);
+
+            self.connect(Target::wire(gate_index, gate.wire_first_input()), lhs);
+            self.connect(Target::wire(gate_index, gate.wire_second_input()), rhs);
+        }
+    }
+
+    pub fn reduce_add_result(&mut self, limbs: Vec<Target>, modulus: BigUInt) -> Vec<Target> {
+        todo!()
+    }
+
+    pub fn mul_nonnative(&mut self, a: NonNativeTarget, b: NonNativeTarget) -> NonNativeTarget {
+        let modulus = a.modulus;
+        let num_limbs = a.limbs.len();
+        debug_assert!(b.modulus == modulus);
+        debug_assert!(b.limbs.len() == num_limbs);
+
+        let mut combined_limbs = self.add_virtual_targets(2 * num_limbs - 1);
+        for i in 0..num_limbs {
+            for j in 0..num_limbs {
+                let sum = builder.add(a.limbs[i], b.limbs[j]);
+                combined_limbs[i + j] = builder.add(combined_limbs[i + j], sum);
+            }
+        }
+
+        let reduced_limbs = self.reduce(combined_limbs, modulus);
+        
+        NonNativeTarget {
+            modulus,
+            limbs: reduced_limbs,
+        }
+    }
+
+    pub fn reduce_mul_result(&mut self, limbs: Vec<Target>, modulus: BigUInt) -> Vec<Target> {
+        todo!()
+    }
+}