diff --git a/src/utils/field.rs b/src/utils/field.rs
index 82234da..184b2c6 100644
--- a/src/utils/field.rs
+++ b/src/utils/field.rs
@@ -36,21 +36,46 @@ impl FieldElement {
         BASE64_STANDARD.encode(&self.field_element)
     }
 
-    pub fn pow(&self, mut exponent: u128) -> FieldElement {
+    pub fn pow(mut self, mut exponent: u128) -> FieldElement {
+        let mut result: FieldElement =
+            FieldElement::new(polynomial_2_block(vec![0], "gcm").unwrap());
+
+        if exponent == 1 {
+            eprintln!("special case 1: {:02X?}", self.clone());
+
+            return self;
+        }
+
         if exponent == 0 {
-            // Return polynomial with coefficient 1
-            return FieldElement::new(vec![1]);
+            let result = FieldElement::new(polynomial_2_block(vec![0], "gcm").unwrap());
+
+            eprintln!("Returned value is: {:02X?}", result);
+            return result;
         }
 
-        let base = self.clone();
-        let mut result = base.clone();
-        exponent -= 1; // Subtract 1 because we already set result to base
-
+        //eprintln!("Initial result: {:?}", result);
         while exponent > 0 {
-            result = result * base.clone();
-            exponent -= 1;
+            //eprintln!("Current exponent: {:02X}", exponent);
+            if exponent & 1 == 1 {
+                let temp = &self * &result;
+                eprintln!("Mult");
+                eprintln!("After mod: {:?}", temp);
+
+                result = temp
+            }
+            let temp_square = &self * &self;
+            eprintln!("Square");
+
+            eprintln!("After squaring: {:?}", temp_square);
+            self = temp_square;
+            //eprintln!("After mod: {:?}", self);
+            exponent >>= 1;
         }
 
+        eprintln!("result in powmod before reduction: {:02X?}", result);
+
+        eprintln!("result in powmod after reduction: {:02X?}", result);
+
         result
     }
 
diff --git a/src/utils/poly.rs b/src/utils/poly.rs
index e624361..642be5c 100644
--- a/src/utils/poly.rs
+++ b/src/utils/poly.rs
@@ -56,19 +56,63 @@ impl Polynomial {
         output
     }
 
-    pub fn pow(&self, mut exponent: u128) -> Polynomial {
-        if exponent == 0 {
-            return Polynomial::new(vec![FieldElement::new(
-                polynomial_2_block(vec![0], "gcm").unwrap(),
-            )]);
+    pub fn pow(mut self, mut exponent: u128) -> Polynomial {
+        let mut result: Polynomial = Polynomial::new(vec![FieldElement::new(
+            polynomial_2_block(vec![0], "gcm").unwrap(),
+        )]);
+
+        if exponent == 1 {
+            eprintln!("special case 1: {:02X?}", self.clone());
+
+            return self;
         }
 
-        let base = self.clone();
-        let mut result = base.clone();
-        exponent -= 1;
+        if exponent == 0 {
+            let result = Polynomial::new(vec![FieldElement::new(
+                polynomial_2_block(vec![0], "gcm").unwrap(),
+            )]);
+
+            eprintln!("Returned value is: {:02X?}", result);
+            return result;
+        }
+
+        //eprintln!("Initial result: {:?}", result);
         while exponent > 0 {
-            result = result * base.clone();
-            exponent -= 1;
+            //eprintln!("Current exponent: {:02X}", exponent);
+            if exponent & 1 == 1 {
+                let temp = &self * &result;
+                eprintln!("Mult");
+                eprintln!("After mod: {:?}", temp);
+
+                result = temp
+            }
+            let temp_square = &self * &self;
+            eprintln!("Square");
+
+            eprintln!("After squaring: {:?}", temp_square);
+            self = temp_square;
+            //eprintln!("After mod: {:?}", self);
+            exponent >>= 1;
+        }
+
+        eprintln!("result in powmod before reduction: {:02X?}", result);
+
+        while !result.polynomial.is_empty()
+            && result
+                .polynomial
+                .last()
+                .unwrap()
+                .as_ref()
+                .iter()
+                .all(|&x| x == 0)
+        {
+            result.polynomial.pop();
+        }
+
+        eprintln!("result in powmod after reduction: {:02X?}", result);
+
+        if result.is_empty() {
+            result = Polynomial::new(vec![FieldElement::new(vec![0; 16])]);
         }
 
         result
@@ -237,6 +281,18 @@ impl Polynomial {
 
         self
     }
+
+    fn sqrt(self) -> Self {
+        let mut result = vec![];
+
+        for (position, element) in self.polynomial.iter().enumerate() {
+            if position % 2 == 0 {
+                result.push(element.clone().pow(2u128.pow(127)));
+            }
+        }
+
+        Polynomial::new(result)
+    }
 }
 
 impl Clone for Polynomial {
@@ -1112,4 +1168,29 @@ mod tests {
 
         assert_eq!(json!(result.to_c_array()), expected);
     }
+
+    #[test]
+    fn test_poly_poly_sqrt() {
+        let json1 = json!([
+            "5TxUxLHO1lHE/rSFquKIAg==",
+            "AAAAAAAAAAAAAAAAAAAAAA==",
+            "0DEUJYdHlmd4X7nzzIdcCA==",
+            "AAAAAAAAAAAAAAAAAAAAAA==",
+            "PKUa1+JHTxHE8y3LbuKIIA==",
+            "AAAAAAAAAAAAAAAAAAAAAA==",
+            "Ds96KiAKKoigKoiKiiKAiA=="
+        ]);
+        let expected = json!([
+            "NeverGonnaGiveYouUpAAA==",
+            "NeverGonnaLetYouDownAA==",
+            "NeverGonnaRunAroundAAA==",
+            "AndDesertYouAAAAAAAAAA=="
+        ]);
+        let element1: Polynomial = Polynomial::from_c_array(&json1);
+        eprintln!("Starting poly sqrt");
+
+        let result = element1.sqrt();
+
+        assert_eq!(json!(result.to_c_array()), expected);
+    }
 }