feat: add the gcm crack

Example testcase is working

src/utils/dff.rs

@@ -25,20 +25,14 @@ pub fn ddf(f: Polynomial) -> Vec<(Polynomial, u128)> {
 
         let g = gcd(&h, &f_star);
         if g != one_cmp {
-            eprintln!("d is: {}", d);
-            eprintln!("g is: {:?}", &g.clone().to_c_array());
-
             z.push((g.clone(), d));
             f_star = f_star.div(&g).0;
         }
-        eprintln!("d outer is: {}", d);
-        eprintln!("F star degree is {:?}", &f_star.degree());
 
         d += 1;
     }
 
     if f_star != one_cmp {
-        eprintln!("fstar not one");
         z.push((f_star.clone(), f_star.degree() as u128));
     } else if z.len() == 0 {
         z.push((f.clone(), 1));

src/utils/field.rs

@@ -39,6 +39,18 @@ impl FieldElement {
         FieldElement::new_no_convert(vec![0x01, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0])
     }
 
+    pub fn to_vec(&self) -> Vec<u8> {
+        self.field_element.clone()
+    }
+
+    /*
+    pub fn padd(&mut self) {
+        if self.field_element.len() % 16 != 0 || ad.is_empty() {
+            ad.append(vec![0u8; 16 - (ad.len() % 16)].as_mut());
+        }
+    }
+    */
+
     pub fn new(field_element: Vec<u8>) -> Self {
         Self {
             field_element: reverse_bits_in_bytevec(field_element),

src/utils/poly.rs

@@ -1,7 +1,7 @@
 use crate::utils::field::ByteArray;
 use base64::prelude::*;
 
-use num::traits::FromBytes;
+use num::traits::{FromBytes, ToBytes};
 use num::{BigInt, BigUint, One, Zero};
 
 use std::{str::FromStr, u128, u8, usize};
@@ -31,6 +31,10 @@ impl Polynomial {
         self.polynomial.len() - 1
     }
 
+    pub fn empty() -> Polynomial {
+        Polynomial::new(vec![])
+    }
+
     pub fn one() -> Self {
         Polynomial::new(vec![FieldElement::one()])
     }
@@ -373,6 +377,10 @@ impl Polynomial {
 
         self
     }
+
+    pub fn extract_component(&self, i: u32) -> FieldElement {
+        self.polynomial[i as usize].clone()
+    }
 }
 
 impl Clone for Polynomial {