feat: add the gcm crack

Example testcase is working

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 {