diff --git a/lib/ak-381/groth16.ak b/lib/ak-381/groth16.ak
index 96e661c..02ead42 100644
--- a/lib/ak-381/groth16.ak
+++ b/lib/ak-381/groth16.ak
@@ -1,9 +1,8 @@
 use aiken/builtin.{
-  bls12_381_final_verify, bls12_381_g1_add, bls12_381_g1_compress,
-  bls12_381_g1_scalar_mul, bls12_381_g1_uncompress, bls12_381_g2_uncompress,
-  bls12_381_miller_loop, bls12_381_mul_miller_loop_result,
+  bls12_381_final_verify, bls12_381_g1_add, bls12_381_g1_scalar_mul,
+  bls12_381_g1_uncompress, bls12_381_g2_uncompress, bls12_381_miller_loop,
+  bls12_381_mul_miller_loop_result,
 }
-use aiken/list.{head, map, map2, reduce, tail}
 
 pub type SnarkVerificationKey {
   nPublic: Int,
@@ -23,7 +22,7 @@ pub type SnarkVerificationKey {
 
 //
 pub type Proof {
-  // G1Element 
+  // G1Element
   piA: ByteArray,
   // G2Element
   piB: ByteArray,
@@ -38,6 +37,29 @@ pub fn pairing(g1: ByteArray, g2: ByteArray) {
   )
 }
 
+pub fn derive(
+  vk_ic: List<ByteArray>,
+  public: List<Int>,
+  result: G1Element,
+) -> G1Element {
+  when vk_ic is {
+    [] -> result
+    [i, ..vk_ic] ->
+      when public is {
+        [] -> fail
+        [scalar, ..public] ->
+          derive(
+            vk_ic,
+            public,
+            bls12_381_g1_add(
+              result,
+              bls12_381_g1_scalar_mul(scalar, bls12_381_g1_uncompress(i)),
+            ),
+          )
+      }
+  }
+}
+
 pub fn groth_verify(
   vk: SnarkVerificationKey,
   proof: Proof,
@@ -47,14 +69,13 @@ pub fn groth_verify(
   let eAB = pairing(proof.piA, proof.piB)
   let eAlphaBeta = pairing(vk.vkAlpha, vk.vkBeta)
 
-  expect Some(vk_ic_head) = head(vk.vkIC)
-  expect Some(vk_ic_tail) = tail(vk.vkIC)
-  let vkICHead: G1Element = bls12_381_g1_uncompress(vk_ic_head)
-  let vkICTail: List<G1Element> =
-    map(vk_ic_tail, fn(n) { bls12_381_g1_uncompress(n) })
-  let derived_vkIC = map2(public, vkICTail, bls12_381_g1_scalar_mul)
-  let vkI = reduce(derived_vkIC, vkICHead, bls12_381_g1_add)
-  let eIGamma = pairing(bls12_381_g1_compress(vkI), vk.vkGamma)
+  let vkI =
+    when vk.vkIC is {
+      [] -> fail @"empty vkIC?"
+      [head, ..tail] -> derive(tail, public, bls12_381_g1_uncompress(head))
+    }
+
+  let eIGamma = bls12_381_miller_loop(vkI, bls12_381_g2_uncompress(vk.vkGamma))
   let eCDelta = pairing(proof.piC, vk.vkDelta)
 
   // * Miller functions