diff --git a/plonky2_verifier/hash.go b/plonky2_verifier/hash.go
new file mode 100644
index 0000000..fff7e20
--- /dev/null
+++ b/plonky2_verifier/hash.go
@@ -0,0 +1,42 @@
+package plonky2_verifier
+
+import (
+	"fmt"
+	. "gnark-ed25519/field"
+
+	"github.com/consensys/gnark/frontend"
+)
+
+type Hash = [4]F
+
+func SelectHash(fieldAPI frontend.API, bit frontend.Variable, leftHash, rightHash Hash) Hash {
+	var returnHash Hash
+	for i := 0; i < 4; i++ {
+		returnHash[i] = fieldAPI.Select(bit, leftHash[i], rightHash[i]).(F)
+	}
+
+	return returnHash
+}
+
+func Lookup2Hash(fieldAPI frontend.API, b0 frontend.Variable, b1 frontend.Variable, h0, h1, h2, h3 Hash) Hash {
+	var returnHash Hash
+
+	for i := 0; i < 4; i++ {
+		returnHash[i] = fieldAPI.Lookup2(b0, b1, h0[i], h1[i], h2[i], h3[i]).(F)
+	}
+
+	return returnHash
+}
+
+func AssertIsEqualHash(fieldAPI frontend.API, h1, h2 Hash) {
+	for i := 0; i < 4; i++ {
+		fieldAPI.AssertIsEqual(h1[0], h2[0])
+	}
+}
+
+func PrintHash(f frontend.API, h Hash) {
+	for i := 0; i < 4; i++ {
+		fmt.Println("Hash Limb", i)
+		f.Println(h[i])
+	}
+}
diff --git a/plonky2_verifier/quadratic_extension.go b/plonky2_verifier/quadratic_extension.go
index 31a3f9c..f841469 100644
--- a/plonky2_verifier/quadratic_extension.go
+++ b/plonky2_verifier/quadratic_extension.go
@@ -2,7 +2,6 @@ package plonky2_verifier
 
 import (
 	"fmt"
-	"gnark-ed25519/field"
 	. "gnark-ed25519/field"
 	"math/bits"
 
@@ -67,7 +66,7 @@ func (c *QuadraticExtensionAPI) InverseExtension(a QuadraticExtension) Quadratic
 	a1_is_zero := c.fieldAPI.IsZero(a[1])
 
 	// assert that a0_is_zero OR a1_is_zero == false
-	c.fieldAPI.AssertIsEqual(c.fieldAPI.Mul(a0_is_zero, a1_is_zero).(F), field.ZERO_F)
+	c.fieldAPI.AssertIsEqual(c.fieldAPI.Mul(a0_is_zero, a1_is_zero).(F), ZERO_F)
 
 	a_pow_r_minus_1 := QuadraticExtension{a[0], c.fieldAPI.Mul(a[1], c.DTH_ROOT).(F)}
 	a_pow_r := c.MulExtension(a_pow_r_minus_1, a)
@@ -79,7 +78,7 @@ func (c *QuadraticExtensionAPI) ScalarMulExtension(a QuadraticExtension, scalar
 }
 
 func (c *QuadraticExtensionAPI) FieldToQE(a F) QuadraticExtension {
-	return QuadraticExtension{a, field.ZERO_F}
+	return QuadraticExtension{a, ZERO_F}
 }
 
 // / Exponentiate `base` to the power of a known `exponent`.
@@ -110,6 +109,22 @@ func (c *QuadraticExtensionAPI) ExpU64Extension(a QuadraticExtension, exponent u
 	return product
 }
 
+func (c *QuadraticExtensionAPI) reduceWithPowers(terms []QuadraticExtension, scalar QuadraticExtension) QuadraticExtension {
+	sum := c.ZERO_QE
+
+	for i := len(terms) - 1; i >= 0; i-- {
+		sum = c.AddExtension(
+			c.MulExtension(
+				sum,
+				scalar,
+			),
+			terms[i],
+		)
+	}
+
+	return sum
+}
+
 func (c *QuadraticExtensionAPI) Println(a QuadraticExtension) {
 	fmt.Print("Degree 0 coefficient")
 	c.fieldAPI.Println(a[0])
diff --git a/plonky2_verifier/utils.go b/plonky2_verifier/utils.go
index 226a97e..ae69bfe 100644
--- a/plonky2_verifier/utils.go
+++ b/plonky2_verifier/utils.go
@@ -2,28 +2,9 @@ package plonky2_verifier
 
 import (
 	"fmt"
-	. "gnark-ed25519/field"
 	"math/bits"
-
-	"github.com/consensys/gnark/frontend"
 )
 
-func reduceWithPowers(qe *QuadraticExtensionAPI, terms []QuadraticExtension, scalar QuadraticExtension) QuadraticExtension {
-	sum := qe.ZERO_QE
-
-	for i := len(terms) - 1; i >= 0; i-- {
-		sum = qe.AddExtension(
-			qe.MulExtension(
-				sum,
-				scalar,
-			),
-			terms[i],
-		)
-	}
-
-	return sum
-}
-
 // Computes `log_2(n)`, panicking if `n` is not a power of two.
 func log2Strict(n uint) int {
 	res := bits.TrailingZeros(n)
@@ -32,35 +13,3 @@ func log2Strict(n uint) int {
 	}
 	return res
 }
-
-func SelectHash(fieldAPI frontend.API, bit frontend.Variable, leftHash, rightHash Hash) Hash {
-	var returnHash Hash
-	for i := 0; i < 4; i++ {
-		returnHash[i] = fieldAPI.Select(bit, leftHash[i], rightHash[i]).(F)
-	}
-
-	return returnHash
-}
-
-func Lookup2Hash(fieldAPI frontend.API, b0 frontend.Variable, b1 frontend.Variable, h0, h1, h2, h3 Hash) Hash {
-	var returnHash Hash
-
-	for i := 0; i < 4; i++ {
-		returnHash[i] = fieldAPI.Lookup2(b0, b1, h0[i], h1[i], h2[i], h3[i]).(F)
-	}
-
-	return returnHash
-}
-
-func AssertIsEqualHash(fieldAPI frontend.API, h1, h2 Hash) {
-	for i := 0; i < 4; i++ {
-		fieldAPI.AssertIsEqual(h1[0], h2[0])
-	}
-}
-
-func PrintHash(f frontend.API, h Hash) {
-	for i := 0; i < 4; i++ {
-		fmt.Println("Hash Limb", i)
-		f.Println(h[i])
-	}
-}