diff --git a/src/utils/field.rs b/src/utils/field.rs
index 37ceb74..f0da8f0 100644
--- a/src/utils/field.rs
+++ b/src/utils/field.rs
@@ -1,13 +1,104 @@
-use std::ops::{Add, Mul};
+use std::{
+    env::args,
+    ops::{Add, Mul},
+};
 
 use anyhow::{anyhow, Ok, Result};
 use base64::prelude::*;
+use serde_json::Value;
 
 use super::{math::xor_bytes, poly::gfmul};
 
+#[derive(Debug)]
+pub struct Polynomial {
+    polynomial: Vec<FieldElement>,
+}
+
+impl Polynomial {
+    pub const fn new(polynomial: Vec<FieldElement>) -> Self {
+        Self { polynomial }
+    }
+
+    pub fn from_c_array(array: &Value) -> Self {
+        let mut polynomial: Vec<FieldElement> = vec![];
+        let c_array: Vec<String> = array
+            .as_array()
+            .expect("Input is not an array")
+            .iter()
+            .map(|x| {
+                x.as_str()
+                    .expect("Array element is not a string")
+                    .to_string()
+            })
+            .collect();
+
+        eprintln!("{:?}", c_array);
+
+        for coefficient in c_array {
+            polynomial.push(FieldElement::new(
+                BASE64_STANDARD
+                    .decode(coefficient)
+                    .expect("Error on poly decode:"),
+            ));
+        }
+        Self { polynomial }
+    }
+
+    pub fn to_c_array(self) -> Vec<String> {
+        let mut output: Vec<String> = vec![];
+        for coeff in self.polynomial {
+            output.push(BASE64_STANDARD.encode(coeff));
+        }
+
+        output
+    }
+}
+
+impl Mul for Polynomial {
+    type Output = Self;
+
+    fn mul(self, rhs: Self) -> Self::Output {
+        let mut polynomial: Vec<FieldElement> =
+            vec![FieldElement::new(vec![0; 16]); self.polynomial.len() + rhs.polynomial.len() - 1];
+        for i in 0..self.polynomial.len() {
+            for j in 0..rhs.polynomial.len() {
+                polynomial[i + j] = &polynomial[i + j]
+                    + &(self.polynomial.get(i).unwrap() * rhs.polynomial.get(j).unwrap());
+            }
+        }
+        Polynomial::new(polynomial)
+    }
+}
+
+impl Add for Polynomial {
+    type Output = Self;
+    fn add(self, rhs: Self) -> Self::Output {
+        FieldElement::new(
+            xor_bytes(&self.field_element, rhs.field_element).expect("Error in poly add"),
+        )
+    }
+}
+
+/*
+impl Add for Polynomial {
+    type Output = Self;
+    fn add(self, rhs: Self) -> Self::Output {
+        FieldElement::new(
+            xor_bytes(&self.field_element, rhs.field_element).expect("Error in poly add"),
+        )
+    }
+}
+
+impl AsRef<[u8]> for Polynomial {
+    fn as_ref(&self) -> &[u8] {
+        &self.field_element.as_ref()
+    }
+}
+*/
+
 #[derive(Debug)]
 pub struct FieldElement {
-    polynomial: Vec<u8>,
+    field_element: Vec<u8>,
 }
 
 impl FieldElement {
@@ -15,8 +106,8 @@ impl FieldElement {
         87, 00, 00, 00, 00, 00, 00, 00, 00, 00, 00, 00, 00, 00, 00, 00, 01,
     ];
 
-    pub const fn new(polynomial: Vec<u8>) -> Self {
-        Self { polynomial }
+    pub const fn new(field_element: Vec<u8>) -> Self {
+        Self { field_element }
     }
 
     pub fn mul(&self, poly_a: Vec<u8>, poly_b: Vec<u8>) -> Result<Vec<u8>> {
@@ -29,7 +120,19 @@ impl Mul for FieldElement {
 
     fn mul(self, rhs: Self) -> Self::Output {
         FieldElement::new(
-            gfmul(self.polynomial, rhs.polynomial, "gcm").expect("Error during multiplication"),
+            gfmul(self.field_element, rhs.field_element, "gcm")
+                .expect("Error during multiplication"),
+        )
+    }
+}
+
+impl Mul for &FieldElement {
+    type Output = FieldElement;
+
+    fn mul(self, rhs: &FieldElement) -> FieldElement {
+        FieldElement::new(
+            gfmul(self.field_element.clone(), rhs.field_element.clone(), "gcm")
+                .expect("Error during multiplication"),
         )
     }
 }
@@ -37,13 +140,32 @@ impl Mul for FieldElement {
 impl Add for FieldElement {
     type Output = Self;
     fn add(self, rhs: Self) -> Self::Output {
-        FieldElement::new(xor_bytes(&self.polynomial, rhs.polynomial).expect("Error in poly add"))
+        FieldElement::new(
+            xor_bytes(&self.field_element, rhs.field_element).expect("Error in poly add"),
+        )
+    }
+}
+
+impl Add for &FieldElement {
+    type Output = FieldElement;
+    fn add(self, rhs: Self) -> Self::Output {
+        FieldElement::new(
+            xor_bytes(&self.field_element, rhs.field_element.clone()).expect("Error in poly add"),
+        )
     }
 }
 
 impl AsRef<[u8]> for FieldElement {
     fn as_ref(&self) -> &[u8] {
-        &self.polynomial.as_ref()
+        &self.field_element.as_ref()
+    }
+}
+
+impl Clone for FieldElement {
+    fn clone(&self) -> Self {
+        FieldElement {
+            field_element: self.field_element.clone(),
+        }
     }
 }
 
@@ -158,6 +280,7 @@ impl ByteArray {
 mod tests {
     use super::*;
     use base64::prelude::*;
+    use serde_json::json;
     use std::fs;
 
     #[test]
@@ -263,4 +386,53 @@ mod tests {
 
         assert_eq!(BASE64_STANDARD.encode(sum), "H1d3GuyA9/0OxeYouUpAAA==");
     }
+
+    #[test]
+    fn test_field_add_02() {
+        let element1: FieldElement =
+            FieldElement::new(BASE64_STANDARD.decode("NeverGonnaLetYouDownAA==").unwrap());
+        let element2: FieldElement =
+            FieldElement::new(BASE64_STANDARD.decode("DHBWMannheimAAAAAAAAAA==").unwrap());
+        let sum = element2 + element1;
+
+        assert_eq!(BASE64_STANDARD.encode(sum), "OZuIncPAGEp4tYouDownAA==");
+    }
+
+    #[test]
+    fn test_field_add_03() {
+        let json1 = json!([
+            "NeverGonnaGiveYouUpAAA==",
+            "NeverGonnaLetYouDownAA==",
+            "NeverGonnaRunAroundAAA==",
+            "AndDesertYouAAAAAAAAAA=="
+        ]);
+        let json2 = json!(["KryptoanalyseAAAAAAAAA==", "DHBWMannheimAAAAAAAAAA=="]);
+        let element1: Polynomial = Polynomial::from_c_array(&json1);
+        let element2: Polynomial = Polynomial::from_c_array(&json2);
+
+        let sum = element2 + element1;
+
+        assert_eq!(BASE64_STANDARD.encode(sum), "OZuIncPAGEp4tYouDownAA==");
+    }
+
+    #[test]
+    fn test_field_mul_01() {
+        let json1 = json!([
+            "JAAAAAAAAAAAAAAAAAAAAA==",
+            "wAAAAAAAAAAAAAAAAAAAAA==",
+            "ACAAAAAAAAAAAAAAAAAAAA=="
+        ]);
+        let json2 = json!(["0AAAAAAAAAAAAAAAAAAAAA==", "IQAAAAAAAAAAAAAAAAAAAA=="]);
+        let element1: Polynomial = Polynomial::from_c_array(&json1);
+        let element2: Polynomial = Polynomial::from_c_array(&json2);
+
+        //eprintln!("{:?}", element1);
+
+        let result = element1 * element2;
+
+        eprintln!("Result = {:?}", result.to_c_array());
+
+        assert!(false);
+        //assert_eq!(BASE64_STANDARD.encode(product), "MoAAAAAAAAAAAAAAAAAAAA==");
+    }
 }