diff --git a/src/tasks/mod.rs b/src/tasks/mod.rs
index 0fa72d6..b024471 100644
--- a/src/tasks/mod.rs
+++ b/src/tasks/mod.rs
@@ -11,6 +11,7 @@ use tasks01::{
     gcm::{gcm_decrypt, gcm_encrypt},
     gfmul::gfmul_task,
     pad_oracle::padding_oracle,
+    pfmath::{gfdiv, gfpoly_add, gfpoly_divmod, gfpoly_mul, gfpoly_pow, gfpoly_powmod},
     poly2block::poly2block,
     sea128::sea128,
     xex::{self, fde_xex},
@@ -83,6 +84,44 @@ pub fn task_deploy(testcase: &Testcase) -> Result<Value> {
 
             Ok(json)
         }
+        "gfpoly_add" => {
+            let result = gfpoly_add(args)?;
+            let json = json!({"S" : result.to_c_array()});
+
+            Ok(json)
+        }
+        "gfpoly_mul" => {
+            let result = gfpoly_mul(args)?;
+            let json = json!({"P" : result.to_c_array()});
+
+            Ok(json)
+        }
+        "gfpoly_pow" => {
+            let result = gfpoly_pow(args)?;
+            let json = json!({"Z" : result.to_c_array()});
+
+            Ok(json)
+        }
+        "gfdiv" => {
+            let result = gfdiv(args)?;
+            let out = BASE64_STANDARD.encode(result);
+            let json = json!({"q" : out});
+
+            Ok(json)
+        }
+        "gfpoly_divmod" => {
+            let result = gfpoly_divmod(args)?;
+            let json = json!({"Q" : result.0.to_c_array(), "R" : result.1.to_c_array()});
+
+            Ok(json)
+        }
+        "gfpoly_powmod" => {
+            let result = gfpoly_powmod(args)?;
+            let json = json!({"Z" : result.to_c_array()});
+
+            Ok(json)
+        }
+
         _ => Err(anyhow!(
             "Fatal. No compatible action found. Json data was {:?}. Arguments were; {:?}",
             testcase,
@@ -272,4 +311,22 @@ mod tests {
 
         Ok(())
     }
+
+    #[test]
+    fn test_task_gcm_gfpoly_add() -> Result<()> {
+        let json = fs::read_to_string("test_json/gcm_decrypt_sea.json").unwrap();
+        let parsed = parse_json(json).unwrap();
+
+        let expected = json!({ "responses" : { "b856d760-023d-4b00-bad2-15d2b6da22fe" : {
+        "plaintext": "RGFzIGlzdCBlaW4gVGVzdA==",
+        "authentic": true,
+        }}});
+
+        assert_eq!(
+            serde_json::to_value(task_distrubute(&parsed)?).unwrap(),
+            serde_json::to_value(expected).unwrap()
+        );
+
+        Ok(())
+    }
 }
diff --git a/src/tasks/tasks01/gfmul.rs b/src/tasks/tasks01/gfmul.rs
index 01731f6..2c1d6b8 100644
--- a/src/tasks/tasks01/gfmul.rs
+++ b/src/tasks/tasks01/gfmul.rs
@@ -16,7 +16,7 @@ pub fn gfmul_task(args: &Value) -> Result<Vec<u8>> {
 
     let semantic: String = serde_json::from_value(args["semantic"].clone())?;
 
-    let result = gfmul(poly_a, poly_b, &semantic)?;
+    let result = gfmul(&poly_a, &poly_b, &semantic)?;
 
     Ok(result)
 }
@@ -39,7 +39,7 @@ mod tests {
         let poly2_text: String = serde_json::from_value(args["b"].clone())?;
         let poly_b = BASE64_STANDARD.decode(poly2_text)?;
 
-        let result = BASE64_STANDARD.encode(gfmul(poly_a, poly_b, "xex")?);
+        let result = BASE64_STANDARD.encode(gfmul(&poly_a, &poly_b, "xex")?);
 
         assert_eq!(
             result, "hSQAAAAAAAAAAAAAAAAAAA==",
@@ -59,7 +59,7 @@ mod tests {
         let poly2_text: String = serde_json::from_value(args["b"].clone())?;
         let poly_b = BASE64_STANDARD.decode(poly2_text)?;
 
-        let result = BASE64_STANDARD.encode(gfmul(poly_a, poly_b, "xex")?);
+        let result = BASE64_STANDARD.encode(gfmul(&poly_a, &poly_b, "xex")?);
 
         assert_eq!(
             result, "QKgUAAAAAAAAAAAAAAAAAA==",
@@ -79,7 +79,7 @@ mod tests {
         let poly2_text: String = serde_json::from_value(args["b"].clone())?;
         let poly_b = BASE64_STANDARD.decode(poly2_text)?;
 
-        let result = BASE64_STANDARD.encode(gfmul(poly_a, poly_b, "xex")?);
+        let result = BASE64_STANDARD.encode(gfmul(&poly_a, &poly_b, "xex")?);
 
         assert_eq!(
             result, "UIAUAAAAAAAAAAAAAAAAAA==",
@@ -99,27 +99,7 @@ mod tests {
         let poly2_text: String = serde_json::from_value(args["b"].clone())?;
         let poly_b = BASE64_STANDARD.decode(poly2_text)?;
 
-        let result = BASE64_STANDARD.encode(gfmul(poly_a, poly_b, "xex")?);
-
-        assert_eq!(
-            result, "hSQAAAAAAAAAAAAAAAAAAA==",
-            "Failure. Calulated result was: {}",
-            result
-        );
-        Ok(())
-    }
-
-    #[test]
-    fn gfmul_task01_gcm() -> Result<()> {
-        let args: Value = json!({"a": "AAAAAAAAAAAAAAAQBAAAAA==", "b": "IAAAAAAAAACAAAAAAAAAAA=="});
-
-        let poly1_text: String = serde_json::from_value(args["a"].clone())?;
-        let poly_a = BASE64_STANDARD.decode(poly1_text)?;
-
-        let poly2_text: String = serde_json::from_value(args["b"].clone())?;
-        let poly_b = BASE64_STANDARD.decode(poly2_text)?;
-
-        let result = BASE64_STANDARD.encode(gfmul(poly_a, poly_b, "gcm")?);
+        let result = BASE64_STANDARD.encode(gfmul(&poly_a, &poly_b, "xex")?);
 
         assert_eq!(
             result, "hSQAAAAAAAAAAAAAAAAAAA==",
diff --git a/src/tasks/tasks01/mod.rs b/src/tasks/tasks01/mod.rs
index 479fe47..8200de5 100644
--- a/src/tasks/tasks01/mod.rs
+++ b/src/tasks/tasks01/mod.rs
@@ -2,6 +2,7 @@ pub mod block2poly;
 pub mod gcm;
 pub mod gfmul;
 pub mod pad_oracle;
+pub mod pfmath;
 pub mod poly2block;
 pub mod sea128;
 pub mod xex;
diff --git a/src/tasks/tasks01/pfmath.rs b/src/tasks/tasks01/pfmath.rs
new file mode 100644
index 0000000..4ad3ac7
--- /dev/null
+++ b/src/tasks/tasks01/pfmath.rs
@@ -0,0 +1,69 @@
+use anyhow::Result;
+use base64::{prelude::BASE64_STANDARD, Engine};
+use serde_json::Value;
+
+use crate::utils::field::{FieldElement, Polynomial};
+
+pub fn gfpoly_add(args: &Value) -> Result<Polynomial> {
+    let poly_a = Polynomial::from_c_array(&args["A"].clone());
+
+    let poly_b = Polynomial::from_c_array(&args["B"].clone());
+
+    let result = poly_a + poly_b;
+
+    Ok(result)
+}
+
+pub fn gfpoly_mul(args: &Value) -> Result<Polynomial> {
+    let poly_a = Polynomial::from_c_array(&args["A"].clone());
+
+    let poly_b = Polynomial::from_c_array(&args["B"].clone());
+
+    let result = poly_a * poly_b;
+
+    Ok(result)
+}
+
+pub fn gfpoly_pow(args: &Value) -> Result<Polynomial> {
+    let poly_a = Polynomial::from_c_array(&args["A"].clone());
+
+    let k: u128 = serde_json::from_value(args["k"].clone())?;
+
+    let result = poly_a.pow(k);
+
+    Ok(result)
+}
+
+pub fn gfdiv(args: &Value) -> Result<FieldElement> {
+    let f1_text: String = serde_json::from_value(args["a"].clone())?;
+    let f_a = FieldElement::new(BASE64_STANDARD.decode(f1_text)?);
+
+    let f2_text: String = serde_json::from_value(args["b"].clone())?;
+    let f_b = FieldElement::new(BASE64_STANDARD.decode(f2_text)?);
+
+    let result = f_a / f_b;
+
+    Ok(result)
+}
+
+pub fn gfpoly_divmod(args: &Value) -> Result<(Polynomial, Polynomial)> {
+    let poly_a = Polynomial::from_c_array(&args["A"].clone());
+
+    let poly_b = Polynomial::from_c_array(&args["B"].clone());
+
+    let result = poly_a.div(&poly_b);
+
+    Ok(result)
+}
+
+pub fn gfpoly_powmod(args: &Value) -> Result<Polynomial> {
+    let poly_a = Polynomial::from_c_array(&args["A"].clone());
+
+    let poly_m = Polynomial::from_c_array(&args["M"].clone());
+
+    let k: u128 = serde_json::from_value(args["k"].clone())?;
+
+    let result = poly_a.pow_mod(k, poly_m);
+
+    Ok(result)
+}
diff --git a/src/utils/ciphers.rs b/src/utils/ciphers.rs
index 917a1c7..333ec13 100644
--- a/src/utils/ciphers.rs
+++ b/src/utils/ciphers.rs
@@ -340,25 +340,25 @@ pub fn ghash(
     eprintln!("Ad chunks before first next {:001X?}", ad_chunks);
 
     let inter1 = xor_bytes(&output, ad_chunks.next().unwrap().to_vec())?;
-    let mut inter_loop = gfmul(inter1, auth_key_h.clone(), "gcm")?;
+    let mut inter_loop = gfmul(&inter1, &auth_key_h, "gcm")?;
     eprintln!("Ad chunks after first next {:001X?}", ad_chunks);
 
     for chunk in ad_chunks {
         eprintln!("Inside ad chunk loop");
         eprintln!("Ad chunk in loop {:001X?}", chunk);
         let inter2 = xor_bytes(&inter_loop, chunk.to_vec())?;
-        inter_loop = gfmul(inter2, auth_key_h.clone(), "gcm")?;
+        inter_loop = gfmul(&inter2, &auth_key_h, "gcm")?;
     }
 
     let cipher_chunks = ciphertext.chunks(16);
 
     for chunk in cipher_chunks {
         let inter3 = xor_bytes(&inter_loop, chunk.to_vec())?;
-        inter_loop = gfmul(inter3, auth_key_h.clone(), "gcm")?;
+        inter_loop = gfmul(&inter3, &auth_key_h, "gcm")?;
     }
 
     let inter4 = xor_bytes(&inter_loop, l_field)?;
-    inter_loop = gfmul(inter4, auth_key_h.clone(), "gcm")?;
+    inter_loop = gfmul(&inter4, &auth_key_h, "gcm")?;
 
     eprintln!("GHASH auth tag: {:001X?}", inter_loop);
 
diff --git a/src/utils/field.rs b/src/utils/field.rs
index 5645b04..fac51f2 100644
--- a/src/utils/field.rs
+++ b/src/utils/field.rs
@@ -1,7 +1,424 @@
-use anyhow::{anyhow, Ok, Result};
-use base64::Engine;
+use std::{
+    env::args,
+    ops::{Add, BitXor, Div, Mul, Rem, Sub},
+    result,
+};
 
-use super::poly::gfmul;
+use anyhow::{anyhow, Ok, Result};
+use base64::prelude::*;
+use serde_json::Value;
+
+use crate::{tasks::tasks01::poly2block::poly2block, utils::poly::polynomial_2_block};
+
+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
+    }
+
+    pub fn pow(&self, mut exponent: u128) -> Polynomial {
+        if exponent == 0 {
+            return Polynomial::new(vec![FieldElement::new(vec![0])]);
+        }
+
+        let base = self.clone();
+        let mut result = base.clone();
+        exponent -= 1;
+        while exponent > 0 {
+            result = result * base.clone();
+            exponent -= 1;
+        }
+
+        result
+    }
+
+    pub fn pow_mod(mut self, mut exponent: u128, modulus: Polynomial) -> Polynomial {
+        let mut result: Polynomial = Polynomial::new(vec![FieldElement::new(
+            polynomial_2_block(vec![0], "gcm").unwrap(),
+        )]);
+
+        //eprintln!("Initial result: {:?}", result);
+        while exponent > 0 {
+            //eprintln!("Current exponent: {:02X}", exponent);
+            if exponent & 1 == 1 {
+                let temp = &self * &result;
+                //eprintln!("After multiplication: {:?}", temp);
+                result = temp.div(&modulus).1;
+                //eprintln!("After mod: {:?}", result);
+            }
+            let temp_square = &self * &self;
+            //eprintln!("After squaring: {:?}", temp_square);
+            self = temp_square.div(&modulus).1;
+            //eprintln!("After mod: {:?}", self);
+            exponent >>= 1;
+        }
+        result
+    }
+
+    // Returns (quotient, remainder)
+    pub fn div(self, rhs: &Self) -> (Self, Self) {
+        // Div by zero check ommitted since data is guaranteed to be non 0
+
+        let mut remainder = self.clone();
+        let divisor = rhs;
+        let dividend_deg = remainder.polynomial.len() - 1;
+        let divisor_deg = divisor.polynomial.len() - 1;
+
+        if dividend_deg < divisor_deg {
+            return (
+                Polynomial::new(vec![FieldElement::new(
+                    polynomial_2_block(vec![0; 16], "gcm").unwrap(),
+                )]),
+                remainder,
+            );
+        }
+
+        let mut quotient_coeffs =
+            vec![
+                FieldElement::new(polynomial_2_block(vec![0; 16], "gcm").unwrap());
+                dividend_deg - divisor_deg + 1
+            ];
+
+        while remainder.polynomial.len() >= divisor.polynomial.len() {
+            let deg_diff = remainder.polynomial.len() - divisor.polynomial.len();
+
+            let leading_dividend = remainder.polynomial.last().unwrap();
+            let leading_divisor = divisor.polynomial.last().unwrap();
+            let quot_coeff = leading_dividend / leading_divisor;
+
+            quotient_coeffs[deg_diff] = quot_coeff.clone();
+
+            let mut subtrahend =
+                vec![FieldElement::new(polynomial_2_block(vec![0; 16], "gcm").unwrap()); deg_diff];
+            subtrahend.extend(
+                divisor
+                    .polynomial
+                    .iter()
+                    .map(|x| x.clone() * quot_coeff.clone()),
+            );
+            let subtrahend_poly = Polynomial::new(subtrahend);
+
+            remainder = remainder + subtrahend_poly;
+
+            while !remainder.polynomial.is_empty()
+                && remainder
+                    .polynomial
+                    .last()
+                    .unwrap()
+                    .as_ref()
+                    .iter()
+                    .all(|&x| x == 0)
+            {
+                remainder.polynomial.pop();
+            }
+        }
+
+        (Polynomial::new(quotient_coeffs), remainder)
+    }
+}
+
+impl Clone for Polynomial {
+    fn clone(&self) -> Self {
+        Polynomial {
+            polynomial: self.polynomial.clone(),
+        }
+    }
+}
+
+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 Mul for &Polynomial {
+    type Output = Polynomial;
+    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 {
+        let mut polynomial: Vec<FieldElement>;
+
+        if self.polynomial.len() > rhs.polynomial.len() {
+            polynomial = self.polynomial.clone();
+            for i in 0..rhs.polynomial.len() {
+                polynomial[i] = polynomial[i].clone() + rhs.polynomial[i].clone();
+            }
+        } else {
+            polynomial = rhs.polynomial.clone();
+            for i in 0..self.polynomial.len() {
+                polynomial[i] = polynomial[i].clone() + self.polynomial[i].clone();
+            }
+        }
+
+        Polynomial::new(polynomial)
+    }
+}
+
+// Helper implementation for subtraction
+impl Sub for &FieldElement {
+    type Output = FieldElement;
+
+    fn sub(self, rhs: Self) -> FieldElement {
+        // In a field of characteristic 2, addition and subtraction are the same operation (XOR)
+        self + rhs
+    }
+}
+
+// Helper trait for checking emptiness
+trait IsEmpty {
+    fn is_empty(&self) -> bool;
+}
+
+impl IsEmpty for Polynomial {
+    fn is_empty(&self) -> bool {
+        self.polynomial.is_empty()
+    }
+}
+impl AsRef<[FieldElement]> for Polynomial {
+    fn as_ref(&self) -> &[FieldElement] {
+        &self.polynomial
+    }
+}
+
+#[derive(Debug)]
+pub struct FieldElement {
+    field_element: Vec<u8>,
+}
+
+impl FieldElement {
+    pub const IRREDUCIBLE_POLYNOMIAL: [u8; 17] = [
+        87, 00, 00, 00, 00, 00, 00, 00, 00, 00, 00, 00, 00, 00, 00, 00, 01,
+    ];
+
+    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>> {
+        gfmul(&poly_a, &poly_b, "gcm")
+    }
+
+    pub fn to_b64(&self) -> String {
+        BASE64_STANDARD.encode(&self.field_element)
+    }
+
+    pub fn pow(&self, mut exponent: u128) -> FieldElement {
+        if exponent == 0 {
+            // Return polynomial with coefficient 1
+            return FieldElement::new(vec![1]);
+        }
+
+        let base = self.clone();
+        let mut result = base.clone();
+        exponent -= 1; // Subtract 1 because we already set result to base
+
+        while exponent > 0 {
+            result = result * base.clone();
+            exponent -= 1;
+        }
+
+        result
+    }
+
+    pub fn inv(mut self) -> Self {
+        let mut inverser: u128 = 0xfffffffffffffffffffffffffffffffe;
+        let mut inverse: Vec<u8> = polynomial_2_block(vec![0], "gcm").unwrap();
+        //eprintln!("Inverse start {:02X?}", inverse);
+
+        while inverser > 0 {
+            //eprintln!("{:02X}", inverser);
+            if inverser & 1 == 1 {
+                inverse = gfmul(&self.field_element, &inverse, "gcm").unwrap();
+            }
+            inverser >>= 1;
+            self.field_element = gfmul(&self.field_element, &self.field_element, "gcm")
+                .expect("Error in sqrmul sqr");
+        }
+        //eprintln!("Inverse rhs {:?}", inverse);
+        FieldElement::new(inverse)
+    }
+}
+
+impl Mul for FieldElement {
+    type Output = Self;
+
+    fn mul(self, rhs: Self) -> Self::Output {
+        FieldElement::new(
+            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, &rhs.field_element, "gcm")
+                .expect("Error during multiplication"),
+        )
+    }
+}
+
+impl Add for FieldElement {
+    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 &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.field_element.as_ref()
+    }
+}
+
+impl Clone for FieldElement {
+    fn clone(&self) -> Self {
+        FieldElement {
+            field_element: self.field_element.clone(),
+        }
+    }
+}
+
+impl BitXor for FieldElement {
+    type Output = Self;
+    fn bitxor(self, rhs: Self) -> Self::Output {
+        let result: Vec<u8> = self
+            .field_element
+            .iter()
+            .zip(rhs.field_element.iter())
+            .map(|(&x1, &x2)| x1 ^ x2)
+            .collect();
+        FieldElement::new(result)
+    }
+}
+
+impl Div for FieldElement {
+    type Output = Self;
+    fn div(self, rhs: Self) -> Self::Output {
+        eprintln!("RHS in div{:02X?}", &rhs);
+
+        let inverse = rhs.inv();
+        eprintln!("Inverse in div{:02X?}", inverse);
+        self.clone() * inverse
+    }
+}
+
+impl Div for &FieldElement {
+    type Output = FieldElement;
+
+    fn div(self, rhs: Self) -> Self::Output {
+        // First clone and invert the divisor (rhs)
+        let rhs_inv = rhs.clone().inv();
+        // Multiply original number by the inverse
+        self.clone() * rhs_inv
+    }
+}
+
+/*
+impl Rem for FieldElement {
+    type Output = Self;
+    fn rem(self, rhs: Self) -> Self::Output {
+        let result: FieldElement = self.field_element;
+
+        while self.field_element[15] != 0x00 {
+            self.field_element
+        }
+        todo!();
+    }
+}
+*/
+/*
+impl BitXor for FieldElement {
+    fn bitxor(self, rhs: Self) -> Self::Output {
+        FieldElement
+    }
+}
+*/
+
+/*
+impl From<Vec<u8>> for FieldElement {
+    fn from(item: Vec<u8>) -> Self {
+        FieldElement { bytes: item }
+    }
+}
+*/
 
 #[derive(Debug)]
 pub struct ByteArray(pub Vec<u8>);
@@ -37,13 +454,13 @@ impl ByteArray {
                 let alpha_poly: Vec<u8> = base64::prelude::BASE64_STANDARD
                     .decode("AgAAAAAAAAAAAAAAAAAAAA==")
                     .expect("Decode failed");
-                self.0 = gfmul(self.0.clone(), alpha_poly, "xex").unwrap();
+                self.0 = gfmul(&self.0, &alpha_poly, "xex").unwrap();
             }
             "gcm" => {
                 let alpha_poly: Vec<u8> = base64::prelude::BASE64_STANDARD
                     .decode("AgAAAAAAAAAAAAAAAAAAAA==")
                     .expect("Decode failed");
-                self.0 = gfmul(self.0.clone(), alpha_poly, "gcm").unwrap();
+                self.0 = gfmul(&self.0, &alpha_poly, "gcm").unwrap();
             }
             _ => {}
         }
@@ -105,6 +522,8 @@ impl ByteArray {
 #[cfg(test)]
 mod tests {
     use super::*;
+    use base64::prelude::*;
+    use serde_json::json;
     use std::fs;
 
     #[test]
@@ -199,4 +618,184 @@ mod tests {
 
         assert_eq!(byte_array.0, vec![0x55, 0x55]);
     }
+
+    #[test]
+    fn test_field_add_01() {
+        let element1: FieldElement =
+            FieldElement::new(BASE64_STANDARD.decode("NeverGonnaGiveYouUpAAA==").unwrap());
+        let element2: FieldElement =
+            FieldElement::new(BASE64_STANDARD.decode("KryptoanalyseAAAAAAAAA==").unwrap());
+        let sum = element2 + element1;
+
+        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!(
+            sum.to_c_array(),
+            vec![
+                "H1d3GuyA9/0OxeYouUpAAA==",
+                "OZuIncPAGEp4tYouDownAA==",
+                "NeverGonnaRunAroundAAA==",
+                "AndDesertYouAAAAAAAAAA=="
+            ]
+        );
+    }
+
+    #[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;
+
+        assert_eq!(
+            result.to_c_array(),
+            vec![
+                "MoAAAAAAAAAAAAAAAAAAAA==",
+                "sUgAAAAAAAAAAAAAAAAAAA==",
+                "MbQAAAAAAAAAAAAAAAAAAA==",
+                "AAhAAAAAAAAAAAAAAAAAAA=="
+            ]
+        );
+        //assert_eq!(BASE64_STANDARD.encode(product), "MoAAAAAAAAAAAAAAAAAAAA==");
+    }
+
+    #[test]
+    fn test_field_pow_01() {
+        let json1 = json!([
+            "JAAAAAAAAAAAAAAAAAAAAA==",
+            "wAAAAAAAAAAAAAAAAAAAAA==",
+            "ACAAAAAAAAAAAAAAAAAAAA=="
+        ]);
+        let element1: Polynomial = Polynomial::from_c_array(&json1);
+
+        let result = element1.pow(3);
+
+        assert_eq!(
+            result.to_c_array(),
+            vec![
+                "AkkAAAAAAAAAAAAAAAAAAA==",
+                "DDAAAAAAAAAAAAAAAAAAAA==",
+                "LQIIAAAAAAAAAAAAAAAAAA==",
+                "8AAAAAAAAAAAAAAAAAAAAA==",
+                "ACgCQAAAAAAAAAAAAAAAAA==",
+                "AAAMAAAAAAAAAAAAAAAAAA==",
+                "AAAAAgAAAAAAAAAAAAAAAA=="
+            ]
+        );
+        //assert_eq!(BASE64_STANDARD.encode(product), "MoAAAAAAAAAAAAAAAAAAAA==");
+    }
+
+    #[test]
+    fn test_field_pow_mod_01() {
+        let json1 = json!([
+            "JAAAAAAAAAAAAAAAAAAAAA==",
+            "wAAAAAAAAAAAAAAAAAAAAA==",
+            "ACAAAAAAAAAAAAAAAAAAAA=="
+        ]);
+        let element1: Polynomial = Polynomial::from_c_array(&json1);
+
+        let result = element1.pow(3);
+
+        assert_eq!(
+            result.to_c_array(),
+            vec![
+                "AkkAAAAAAAAAAAAAAAAAAA==",
+                "DDAAAAAAAAAAAAAAAAAAAA==",
+                "LQIIAAAAAAAAAAAAAAAAAA==",
+                "8AAAAAAAAAAAAAAAAAAAAA==",
+                "ACgCQAAAAAAAAAAAAAAAAA==",
+                "AAAMAAAAAAAAAAAAAAAAAA==",
+                "AAAAAgAAAAAAAAAAAAAAAA=="
+            ]
+        );
+        //assert_eq!(BASE64_STANDARD.encode(product), "MoAAAAAAAAAAAAAAAAAAAA==");
+    }
+
+    #[test]
+    fn test_poly_div_01() {
+        let element1 =
+            FieldElement::new(BASE64_STANDARD.decode("JAAAAAAAAAAAAAAAAAAAAA==").unwrap());
+
+        let element2 =
+            FieldElement::new(BASE64_STANDARD.decode("wAAAAAAAAAAAAAAAAAAAAA==").unwrap());
+
+        let result = element1 / element2;
+
+        assert_eq!(BASE64_STANDARD.encode(result), "OAAAAAAAAAAAAAAAAAAAAA==");
+    }
+
+    #[test]
+    fn test_field_poly_div_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);
+
+        println!("Beginning the new division");
+        let (result, remainder) = element1.div(&element2);
+
+        assert_eq!(
+            result.to_c_array(),
+            vec!["nAIAgCAIAgCAIAgCAIAgCg==", "m85znOc5znOc5znOc5znOQ=="]
+        );
+        assert_eq!(remainder.to_c_array(), vec!["lQNA0DQNA0DQNA0DQNA0Dg=="]);
+        //assert_eq!(BASE64_STANDARD.encode(product), "MoAAAAAAAAAAAAAAAAAAAA==");
+    }
+
+    #[test]
+    fn test_field_poly_powmod_01() {
+        let json1 = json!([
+            "JAAAAAAAAAAAAAAAAAAAAA==",
+            "wAAAAAAAAAAAAAAAAAAAAA==",
+            "ACAAAAAAAAAAAAAAAAAAAA=="
+        ]);
+        let json2 = json!(["KryptoanalyseAAAAAAAAA==", "DHBWMannheimAAAAAAAAAA=="]);
+        let element1: Polynomial = Polynomial::from_c_array(&json1);
+        let modulus: Polynomial = Polynomial::from_c_array(&json2);
+
+        let result = element1.pow_mod(1000, modulus);
+
+        eprintln!("Result is: {:02X?}", result);
+        assert_eq!(result.to_c_array(), vec!["XrEhmKuat+Glt5zZWtMo6g=="]);
+    }
 }
diff --git a/src/utils/poly.rs b/src/utils/poly.rs
index 78889c8..6425577 100644
--- a/src/utils/poly.rs
+++ b/src/utils/poly.rs
@@ -7,14 +7,14 @@ use std::{str::FromStr, u128, u8, usize};
 use super::{field, math::reverse_bits_in_bytevec};
 pub const RED_POLY: u128 = 0x87000000_00000000_00000000_00000000;
 
-pub fn gfmul(poly_a: Vec<u8>, poly_b: Vec<u8>, semantic: &str) -> Result<Vec<u8>> {
+pub fn gfmul(poly_a: &Vec<u8>, poly_b: &Vec<u8>, semantic: &str) -> Result<Vec<u8>> {
     let mut red_poly_bytes: ByteArray = ByteArray(RED_POLY.to_be_bytes().to_vec());
     red_poly_bytes.0.push(0x01);
 
-    let mut poly1: ByteArray = ByteArray(poly_a);
+    let mut poly1: ByteArray = ByteArray(poly_a.to_owned());
     poly1.0.push(0x00);
 
-    let mut poly2: ByteArray = ByteArray(poly_b);
+    let mut poly2: ByteArray = ByteArray(poly_b.to_owned());
     poly2.0.push(0x00);
 
     if semantic == "gcm" {
diff --git a/test_json/pfmath_tests.json b/test_json/pfmath_tests.json
new file mode 100644
index 0000000..b9cc6e0
--- /dev/null
+++ b/test_json/pfmath_tests.json
@@ -0,0 +1,98 @@
+{
+  "testcases": {
+    "gfpoly_add": {
+      "action": "gfpoly_add",
+      "arguments": {
+        "A": [
+          "NeverGonnaGiveYouUpAAA==",
+          "NeverGonnaLetYouDownAA==",
+          "NeverGonnaRunAroundAAA==",
+          "AndDesertYouAAAAAAAAAA=="
+        ],
+        "B": [
+          "KryptoanalyseAAAAAAAAA==",
+          "DHBWMannheimAAAAAAAAAA=="
+        ]
+      }
+    },
+    "gfpoly_mul": {
+      "action": "gfpoly_mul",
+      "arguments": {
+        "A": [
+          "JAAAAAAAAAAAAAAAAAAAAA==",
+          "wAAAAAAAAAAAAAAAAAAAAA==",
+          "ACAAAAAAAAAAAAAAAAAAAA=="
+        ],
+        "B": [
+          "0AAAAAAAAAAAAAAAAAAAAA==",
+          "IQAAAAAAAAAAAAAAAAAAAA=="
+        ]
+      }
+    },
+    "gfpoly_mul_10": {
+      "action": "gfpoly_mul",
+      "arguments": {
+        "A": [
+          "JAAAAAAAAAAAAAAAAAAAAA==",
+          "wAAAAAAAAAAAAAAAAAAAAA==",
+          "ACAAAAAAAAAAAAAAAAAAAA=="
+        ],
+        "B": [
+          "AAAAAAAAAAAAAAAAAAAAAA=="
+        ]
+      }
+    },
+    "gfpoly_mul_01": {
+      "action": "gfpoly_mul",
+      "arguments": {
+        "A": [
+          "AAAAAAAAAAAAAAAAAAAAAA=="
+        ],
+        "B": [
+          "0AAAAAAAAAAAAAAAAAAAAA==",
+          "IQAAAAAAAAAAAAAAAAAAAA=="
+        ]
+      }
+    },
+    "gfpoly_pow": {
+      "action": "gfpoly_pow",
+      "arguments": {
+        "A": [
+          "JAAAAAAAAAAAAAAAAAAAAA==",
+          "wAAAAAAAAAAAAAAAAAAAAA==",
+          "ACAAAAAAAAAAAAAAAAAAAA=="
+        ],
+        "k": 3
+      }
+    },
+    "gfpoly_pow_k0": {
+      "action": "gfpoly_pow",
+      "arguments": {
+        "A": [
+          "JAAAAAAAAAAAAAAAAAAAAA==",
+          "wAAAAAAAAAAAAAAAAAAAAA==",
+          "ACAAAAAAAAAAAAAAAAAAAA=="
+        ],
+        "k": 0
+      }
+    },
+    "gfpoly_pow_k1": {
+      "action": "gfpoly_pow",
+      "arguments": {
+        "A": [
+          "JAAAAAAAAAAAAAAAAAAAAA==",
+          "wAAAAAAAAAAAAAAAAAAAAA==",
+          "ACAAAAAAAAAAAAAAAAAAAA=="
+        ],
+        "k": 1
+      }
+    },
+    "gfdiv": {
+      "action": "gfdiv",
+      "arguments": {
+        "a": "JAAAAAAAAAAAAAAAAAAAAA==",
+        "b": "wAAAAAAAAAAAAAAAAAAAAA=="
+      }
+    }
+  }
+}