diff --git a/g16ckt/examples/pairing_gate_counts.rs b/g16ckt/examples/pairing_gate_counts.rs
index 6b140d0..0100c99 100644
--- a/g16ckt/examples/pairing_gate_counts.rs
+++ b/g16ckt/examples/pairing_gate_counts.rs
@@ -326,7 +326,7 @@ fn main() {
                     let b = Fq2::as_montgomery(ark::g2::Config::COEFF_B);
                     let y2 = Fq2::add_constant(ctx, &x3, &b);
                     let y = Fq2::sqrt_general_montgomery(ctx, &y2);
-                    let neg_y = Fq2::neg(ctx, y.clone());
+                    let neg_y = Fq2::neg(ctx, &y);
                     let y0 = gsv::gadgets::bigint::select(
                         ctx,
                         y.c0(),
diff --git a/g16ckt/src/gadgets/bn254/fq12.rs b/g16ckt/src/gadgets/bn254/fq12.rs
index f1bbf4c..b4f2798 100644
--- a/g16ckt/src/gadgets/bn254/fq12.rs
+++ b/g16ckt/src/gadgets/bn254/fq12.rs
@@ -175,10 +175,7 @@ impl Fq12 {
     }
 
     pub fn neg<C: CircuitContext>(circuit: &mut C, a: &Fq12) -> Fq12 {
-        Fq12::from_components(
-            Fq6::neg(circuit, a.0[0].clone()),
-            Fq6::neg(circuit, a.0[1].clone()),
-        )
+        Fq12::from_components(Fq6::neg(circuit, &a.0[0]), Fq6::neg(circuit, &a.0[1]))
     }
 
     pub fn sub<C: CircuitContext>(circuit: &mut C, a: &Fq12, b: &Fq12) -> Fq12 {
@@ -421,7 +418,7 @@ impl Fq12 {
         let inverse_norm = Fq6::inverse_montgomery(circuit, &norm);
 
         let res_c0 = Fq6::mul_montgomery(circuit, a.c0(), &inverse_norm);
-        let neg_a_c1 = Fq6::neg(circuit, a.c1().clone());
+        let neg_a_c1 = Fq6::neg(circuit, a.c1());
         let res_c1 = Fq6::mul_montgomery(circuit, &inverse_norm, &neg_a_c1);
 
         Fq12::from_components(res_c0, res_c1)
@@ -442,7 +439,7 @@ impl Fq12 {
     }
 
     pub fn conjugate<C: CircuitContext>(circuit: &mut C, a: &Fq12) -> Fq12 {
-        let new_c1 = Fq6::neg(circuit, a.c1().clone());
+        let new_c1 = Fq6::neg(circuit, a.c1());
         Fq12::from_components(a.c0().clone(), new_c1)
     }
 }
diff --git a/g16ckt/src/gadgets/bn254/fq2.rs b/g16ckt/src/gadgets/bn254/fq2.rs
index d1f6100..4bbab7f 100644
--- a/g16ckt/src/gadgets/bn254/fq2.rs
+++ b/g16ckt/src/gadgets/bn254/fq2.rs
@@ -176,7 +176,7 @@ impl Fq2 {
         Fq2::from_components(c0, c1)
     }
 
-    pub fn neg<C: CircuitContext>(circuit: &mut C, a: Fq2) -> Fq2 {
+    pub fn neg<C: CircuitContext>(circuit: &mut C, a: &Fq2) -> Fq2 {
         assert_eq!(a.c0().len(), Self::N_BITS / 2);
         assert_eq!(a.c1().len(), Self::N_BITS / 2);
 
@@ -597,7 +597,7 @@ mod tests {
             10_000,
             |ctx, input| {
                 let [a] = input;
-                Fq2::neg(ctx, a.clone())
+                Fq2::neg(ctx, a)
             },
         );
 
diff --git a/g16ckt/src/gadgets/bn254/fq6.rs b/g16ckt/src/gadgets/bn254/fq6.rs
index e4d982e..d36bac2 100644
--- a/g16ckt/src/gadgets/bn254/fq6.rs
+++ b/g16ckt/src/gadgets/bn254/fq6.rs
@@ -159,11 +159,11 @@ impl Fq6 {
         )
     }
 
-    pub fn neg<C: CircuitContext>(circuit: &mut C, a: Fq6) -> Fq6 {
+    pub fn neg<C: CircuitContext>(circuit: &mut C, a: &Fq6) -> Fq6 {
         Fq6::from_components(
-            Fq2::neg(circuit, a.0[0].clone()),
-            Fq2::neg(circuit, a.0[1].clone()),
-            Fq2::neg(circuit, a.0[2].clone()),
+            Fq2::neg(circuit, &a.0[0]),
+            Fq2::neg(circuit, &a.0[1]),
+            Fq2::neg(circuit, &a.0[2]),
         )
     }
 
@@ -718,7 +718,7 @@ mod tests {
         let result =
             CircuitBuilder::streaming_execute::<_, _, Fq6Output>(input, 10_000, |ctx, input| {
                 let [a] = input;
-                Fq6::neg(ctx, a.clone())
+                Fq6::neg(ctx, a)
             });
         assert_eq!(result.output_value.value, expected);
     }
diff --git a/g16ckt/src/gadgets/bn254/g2.rs b/g16ckt/src/gadgets/bn254/g2.rs
index 441a9e8..d690183 100644
--- a/g16ckt/src/gadgets/bn254/g2.rs
+++ b/g16ckt/src/gadgets/bn254/g2.rs
@@ -520,7 +520,7 @@ impl G2Projective {
     pub fn neg<C: CircuitContext>(circuit: &mut C, p: &G2Projective) -> G2Projective {
         G2Projective {
             x: p.x.clone(),
-            y: Fq2::neg(circuit, p.y.clone()),
+            y: Fq2::neg(circuit, &p.y),
             z: p.z.clone(),
         }
     }
diff --git a/g16ckt/src/gadgets/bn254/pairing.rs b/g16ckt/src/gadgets/bn254/pairing.rs
index 00e5b24..0c3d73b 100644
--- a/g16ckt/src/gadgets/bn254/pairing.rs
+++ b/g16ckt/src/gadgets/bn254/pairing.rs
@@ -247,7 +247,7 @@ fn g2_frobenius_map_affine<C: CircuitContext>(
             let y_f2 = Fq2::frobenius_montgomery(circuit, &y1, 1);
             let x2 = Fq2::mul_by_constant_montgomery(circuit, &x_f2, &Fq2::as_montgomery(cx));
             let mut y2 = Fq2::mul_by_constant_montgomery(circuit, &y_f2, &Fq2::as_montgomery(cy));
-            y2 = Fq2::neg(circuit, y2);
+            y2 = Fq2::neg(circuit, &y2);
             G2Projective {
                 x: x2,
                 y: y2,
@@ -285,7 +285,7 @@ fn g2_line_coeffs_double<C: CircuitContext>(
     let one_c0 = Fq::new_constant(&Fq::as_montgomery(ark_bn254::Fq::ONE)).expect("const one");
     let zero_c1 = Fq::new_constant(&Fq::as_montgomery(ark_bn254::Fq::ZERO)).expect("const zero");
     let c0 = Fq2::from_components(one_c0, zero_c1);
-    let c1 = Fq2::neg(circuit, lambda.clone());
+    let c1 = Fq2::neg(circuit, &lambda);
     let lambda_x = Fq2::mul_montgomery(circuit, &lambda, &x);
     let c2 = Fq2::sub(circuit, &lambda_x, &y);
 
@@ -323,7 +323,7 @@ fn g2_line_coeffs_add<C: CircuitContext>(
     let one_c0 = Fq::new_constant(&Fq::as_montgomery(ark_bn254::Fq::ONE)).expect("const one");
     let zero_c1 = Fq::new_constant(&Fq::as_montgomery(ark_bn254::Fq::ZERO)).expect("const zero");
     let c0 = Fq2::from_components(one_c0, zero_c1);
-    let c1 = Fq2::neg(circuit, lambda.clone());
+    let c1 = Fq2::neg(circuit, &lambda);
     let lambda_xr = Fq2::mul_montgomery(circuit, &lambda, &xr);
     let c2 = Fq2::sub(circuit, &lambda_xr, &yr);
 
@@ -394,7 +394,7 @@ pub fn double_in_place_circuit_montgomery<C: CircuitContext>(
     let gs = Fq2::square_montgomery(circuit, &g);
     let new_y = Fq2::sub(circuit, &gs, &es_triple);
     let new_z = Fq2::mul_montgomery(circuit, &b, &h);
-    let hn = Fq2::neg(circuit, h);
+    let hn = Fq2::neg(circuit, &h);
 
     (
         G2Projective {
@@ -438,7 +438,7 @@ pub fn add_in_place_montgomery(
     let wires_4 = Fq2::double(circuit, &g);
     let h = Fq2::sub(circuit, &wires_3, &wires_4);
 
-    let neg_theta = Fq2::neg(circuit, theta.clone());
+    let neg_theta = Fq2::neg(circuit, &theta);
 
     let wires_5 = Fq2::mul_montgomery(circuit, &theta, qx);
     let wires_6 = Fq2::mul_montgomery(circuit, &lambda, qy);
@@ -468,7 +468,7 @@ pub fn g2_affine_neg_evaluate<C: CircuitContext>(
     q: &G2Projective,
 ) -> G2Projective {
     let mut result = q.clone();
-    result.y = Fq2::neg(circuit, q.y.clone());
+    result.y = Fq2::neg(circuit, &q.y);
     result
 }
 
diff --git a/g16ckt/src/gadgets/groth16.rs b/g16ckt/src/gadgets/groth16.rs
index 80f0d57..52d1a65 100644
--- a/g16ckt/src/gadgets/groth16.rs
+++ b/g16ckt/src/gadgets/groth16.rs
@@ -161,7 +161,7 @@ pub fn decompress_g2_from_compressed<C: CircuitContext>(
 
     let y = Fq2Wire::sqrt_general_montgomery(circuit, &y2);
 
-    let neg_y = Fq2Wire::neg(circuit, y.clone());
+    let neg_y = Fq2Wire::neg(circuit, &y);
 
     let final_y_0 = bigint::select(circuit, y.c0(), neg_y.c0(), *y_flag);
     let final_y_1 = bigint::select(circuit, y.c1(), neg_y.c1(), *y_flag);