diff --git a/src/zk/w_trusted_setup/pinocchio/crs.rs b/src/zk/w_trusted_setup/pinocchio/crs.rs
index 1292ba7..594d9c9 100644
--- a/src/zk/w_trusted_setup/pinocchio/crs.rs
+++ b/src/zk/w_trusted_setup/pinocchio/crs.rs
@@ -22,7 +22,7 @@ pub struct VerificationKeys {
   pub one_g1: G1Point,
   pub one_g2: G2Point,
   pub alpha_v: G2Point,
-  pub alpha_w: G2Point,
+  pub alpha_w: G1Point,
   pub alpha_y: G2Point,
   pub gamma: G2Point,
   pub beta_gamma: G2Point,
@@ -30,6 +30,9 @@ pub struct VerificationKeys {
   pub vk_io: Vec<G1Point>,
   pub wk_io: Vec<G2Point>,
   pub yk_io: Vec<G1Point>,
+
+  pub alpha_v_t: G1Point,
+  pub alpha_y_t: G1Point,
 }
 
 pub struct CRS {
@@ -100,9 +103,9 @@ impl CRS {
     println!("----> Computing verification keys...");
     let one_g1 = g1 * f.elem(&1u8);
     let one_g2 = g2 * f.elem(&1u8);
-    let alpha_v = g2 * alpha_v;
-    let alpha_w = g2 * alpha_w;
-    let alpha_y = g2 * alpha_y;
+    let alpha_v_pt = g2 * alpha_v;
+    let alpha_w = g1 * alpha_w;
+    let alpha_y_pt = g2 * alpha_y;
     let gamma_pt = g2 * gamma;
     let beta_gamma = g2 * gamma * beta;
 
@@ -123,18 +126,23 @@ impl CRS {
       beta_vwy_k_mid,
     };
 
+    let alpha_v_t: G1Point = &t * alpha_v;
+    let alpha_y_t: G1Point = &t * alpha_y;
+
     let vk = VerificationKeys {
       one_g1,
       one_g2,
-      alpha_v,
+      alpha_v: alpha_v_pt,
       alpha_w,
-      alpha_y,
+      alpha_y: alpha_y_pt,
       gamma: gamma_pt,
       beta_gamma,
       t,
       vk_io,
       wk_io,
       yk_io,
+      alpha_v_t,
+      alpha_y_t,
     };
 
     CRS {
diff --git a/src/zk/w_trusted_setup/pinocchio/pinocchio_prover.rs b/src/zk/w_trusted_setup/pinocchio/pinocchio_prover.rs
index e9d07d2..c470449 100644
--- a/src/zk/w_trusted_setup/pinocchio/pinocchio_prover.rs
+++ b/src/zk/w_trusted_setup/pinocchio/pinocchio_prover.rs
@@ -91,17 +91,16 @@ impl PinocchioProver {
     println!("--> Generating proof...");
     let witness_mid = &self.witness.mid();
 
-    let ek = &crs.ek;
+    let (ek, vk) = (&crs.ek, &crs.vk);
     let delta_v = &self.f.rand_elem(true);
     let delta_y = &self.f.rand_elem(true);
-    let t = &crs.vk.t;
 
-    let mut v_mid_s = t * delta_v;  // randomize v
+    let mut v_mid_s = &vk.t * delta_v;  // randomize v
     let mut w_mid_s = G2Point::zero();
-    let mut y_mid_s = t * delta_y;  // randomize y
-    let mut alpha_v_mid_s = t * delta_v; // G1Point::zero();
+    let mut y_mid_s = &vk.t * delta_y;  // randomize y
+    let mut alpha_v_mid_s = &vk.alpha_v_t * delta_v;
     let mut alpha_w_mid_s = G1Point::zero();
-    let mut alpha_y_mid_s = G1Point::zero();
+    let mut alpha_y_mid_s = &vk.alpha_y_t * delta_y;
     let mut beta_vwy_mid_s = G1Point::zero();
   
     for i in 0..witness_mid.size_in_usize() {
diff --git a/src/zk/w_trusted_setup/pinocchio/pinocchio_verifier.rs b/src/zk/w_trusted_setup/pinocchio/pinocchio_verifier.rs
index 8f5fe4d..1f45edc 100644
--- a/src/zk/w_trusted_setup/pinocchio/pinocchio_verifier.rs
+++ b/src/zk/w_trusted_setup/pinocchio/pinocchio_verifier.rs
@@ -44,40 +44,41 @@ impl PinocchioVerifier {
     // }
 
     // KC of v, w and y
-    // {
-    //   let lhs = e(&p.alpha_v_mid_s, &vk.one_g2);
-    //   let rhs = e(&p.v_mid_s, &vk.alpha_v); 
-    //   if lhs != rhs { return false; }
-    // }
-    // {
-    //   let lhs = e(&p.alpha_w_mid_s, &vk.one_g2);
-    //   let rhs = e(&p.g1_w_mid_s, &vk.alpha_w); 
-    //   if lhs != rhs { return false; }
-    // }
-    // {
-    //   let lhs = e(&p.alpha_y_mid_s, &vk.one_g2);
-    //   let rhs = e(&p.y_mid_s, &vk.alpha_y); 
-    //   if lhs != rhs { return false; }
-    // }
+    {
+      let lhs = e(&p.alpha_v_mid_s, &vk.one_g2);
+      let rhs = e(&p.v_mid_s, &vk.alpha_v); 
+      if lhs != rhs { return false; }
+    }
+    {
+      let lhs = e(&p.alpha_w_mid_s, &vk.one_g2);
+      let rhs = e(&vk.alpha_w, &p.w_mid_s); 
+      if lhs != rhs { return false; }
+    }
+    {
+      let lhs = e(&p.alpha_y_mid_s, &vk.one_g2);
+      let rhs = e(&p.y_mid_s, &vk.alpha_y); 
+      if lhs != rhs { return false; }
+    }
+    true
 
     // QAP divisibility check
-    {
-      let mut v_s = p.v_mid_s.clone();
-      let mut w_s = p.w_mid_s.clone();
-      let mut y_s = p.y_mid_s.clone();
-
-      for i in 0..witness_io.size_in_usize() {
-        let w = &witness_io[&i];
-        v_s = v_s + &vk.vk_io[i] * w;
-        w_s = w_s + &vk.wk_io[i] * w;
-        y_s = y_s + &vk.yk_io[i] * w;
-      }
-
-      let lhs = e(&v_s, &w_s);
-      let rhs = e(&vk.t, &p.h_s) * e(&y_s, &vk.one_g2);
-
-      lhs == rhs
-    }
+    // {
+    //   let mut v_s = p.v_mid_s.clone();
+    //   let mut w_s = p.w_mid_s.clone();
+    //   let mut y_s = p.y_mid_s.clone();
+    // 
+    //   for i in 0..witness_io.size_in_usize() {
+    //     let w = &witness_io[&i];
+    //     v_s = v_s + &vk.vk_io[i] * w;
+    //     w_s = w_s + &vk.wk_io[i] * w;
+    //     y_s = y_s + &vk.yk_io[i] * w;
+    //   }
+    // 
+    //   let lhs = e(&v_s, &w_s);
+    //   let rhs = e(&vk.t, &p.h_s) * e(&y_s, &vk.one_g2);
+    // 
+    //   lhs == rhs
+    // }
   }
 }