diff --git a/Cargo.toml b/Cargo.toml
index 754e310..0a7c98b 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -6,5 +6,9 @@ edition = "2018"
 # See more keys and their definitions at https://doc.rust-lang.org/cargo/reference/manifest.html
 
 [dependencies]
-rand_core = "0.6.0"
-rand ="0.8.3"
\ No newline at end of file
+rand_core = { version = "0.6", default-features = false }
+rand ="0.8.3"
+subtle = "2.4.1"
+byteorder = "1.4.3"
+bitvec = "0.22.3"
+ff = { version = "0.10", features = ["derive"] }
\ No newline at end of file
diff --git a/README.md b/README.md
index f46fcd6..7cb0818 100644
--- a/README.md
+++ b/README.md
@@ -7,9 +7,9 @@ This package contains a toy implementation of an (s-t)Detectable Hash Function a
 
 ### How it Works
 
-A client creates new `Generator` which instantiates the secret key behind the scenes.
+A client creates new `HashKey` which instantiates the secret key behind the scenes.
 
-A client can then use this `Generator` to produce two kinds of `Hash`. 
+A client can then use this `HashKey` to produce two kinds of `Hash`. 
 
 The first kind of hash (`Hash(x)`) "a true hash" multiplies the given `x` by the secret key (treating the secret key as a `s x t` matrix of polynomials (`p_1..p_s`)). `DHF(k,x):=(x,p_1(x),...,p_s(x))`
 
diff --git a/src/domain.rs b/src/domain.rs
deleted file mode 100644
index 0d5e17c..0000000
--- a/src/domain.rs
+++ /dev/null
@@ -1,85 +0,0 @@
-use std::fmt::{Display, Formatter, Result};
-use std::ops::{Add, Mul, Sub};
-
-/// Did I really implement an awfully hacky prime order field to play with this
-/// Yes...yes I did...
-#[derive(Clone, Copy, Debug)]
-pub struct PrimeOrderDomain<const ORDER: u64> {
-    val: u64,
-}
-
-impl<const ORDER: u64> Display for PrimeOrderDomain<{ ORDER }> {
-    fn fmt(&self, f: &mut Formatter<'_>) -> Result {
-        write!(f, "{:20}", self.val)
-    }
-}
-
-impl<const ORDER: u64> PrimeOrderDomain<{ ORDER }> {
-    pub fn new(val: u64) -> PrimeOrderDomain<{ ORDER }> {
-        PrimeOrderDomain { val }
-    }
-
-    pub fn is_zero(&self) -> bool {
-        self.val == 0
-    }
-
-    pub fn gt(&self, rhs: &Self) -> bool {
-        self.val > rhs.val
-    }
-
-    pub fn inverse(&self) -> Self {
-        self.pow(ORDER - 2) // at least it is faster an iterating...
-    }
-
-    // exponentiation by squaring
-    pub fn pow(&self, exp: u64) -> Self {
-        if exp == 0 {
-            return PrimeOrderDomain::new(1);
-        }
-        if exp == 1 {
-            return self.clone();
-        }
-
-        if exp % 2 == 0 {
-            (*self * *self).pow(exp / 2)
-        } else {
-            *self * self.pow(2).pow((exp - 1) / 2)
-        }
-    }
-}
-
-impl<const ORDER: u64> Add for PrimeOrderDomain<{ ORDER }> {
-    type Output = Self;
-
-    fn add(self, rhs: Self) -> Self::Output {
-        PrimeOrderDomain {
-            val: ((self.val as u128 + rhs.val as u128) % ORDER as u128) as u64,
-        }
-    }
-}
-
-impl<const ORDER: u64> Sub for PrimeOrderDomain<{ ORDER }> {
-    type Output = Self;
-
-    fn sub(self, rhs: Self) -> Self::Output {
-        if rhs.val > self.val {
-            return PrimeOrderDomain {
-                val: ((ORDER - rhs.val) + self.val) % ORDER,
-            };
-        }
-
-        PrimeOrderDomain {
-            val: (self.val - rhs.val) % ORDER,
-        }
-    }
-}
-
-impl<const ORDER: u64> Mul for PrimeOrderDomain<{ ORDER }> {
-    type Output = Self;
-
-    fn mul(self, rhs: Self) -> Self::Output {
-        PrimeOrderDomain {
-            val: ((self.val as u128 * rhs.val as u128) % ORDER as u128) as u64,
-        }
-    }
-}
diff --git a/src/lib.rs b/src/lib.rs
index c02c20f..1a152a6 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -1,76 +1,86 @@
-use crate::domain::PrimeOrderDomain;
+extern crate ff;
 use crate::matrix::Matrix;
-use rand::Rng;
+use ff::PrimeField;
 use rand_core::{CryptoRng, RngCore};
+use std::fmt::Display;
 
-pub const PRIME_ORDER: u64 = 18446744073709551557; // picked because largest 64 bit prime...
+mod matrix;
 
-pub mod domain;
-pub mod matrix;
-
-struct Generator {
+struct HashKey<PF>
+where
+    PF: PrimeField,
+{
     synthetic_max: u64,
     threshold: u64,
-    key: Vec<Vec<PrimeOrderDomain<PRIME_ORDER>>>,
+    key: Vec<Vec<PF>>,
 }
 
 #[derive(Debug)]
-struct Hash(Vec<PrimeOrderDomain<PRIME_ORDER>>);
+struct Hash<PF>(Vec<PF>)
+where
+    PF: PrimeField;
 
-impl Generator {
-    pub fn generate<R: RngCore + CryptoRng>(
-        rng: &mut R,
+impl<PF> HashKey<PF>
+where
+    PF: PrimeField,
+{
+    pub fn new<R: RngCore + CryptoRng + Copy>(
+        rng: R,
         synthetic_max: u64,
         threshold: u64,
-    ) -> Generator {
+    ) -> HashKey<PF> {
         let mut k = vec![];
         for _i in 0..synthetic_max {
             let mut p_i = vec![];
             for _j in 0..threshold {
-                let p = rng.gen_range(0..PRIME_ORDER);
-                p_i.push(PrimeOrderDomain::<PRIME_ORDER>::new(p));
+                p_i.push(PF::random(rng));
             }
             k.push(p_i);
         }
-        Generator {
+        HashKey {
             synthetic_max,
             threshold,
             key: k,
         }
     }
 
-    pub fn hash(&self, value: PrimeOrderDomain<PRIME_ORDER>) -> Hash {
+    pub fn generate_hash(&self, value: PF) -> Hash<PF> {
         let mut hash = vec![value];
 
         for i in 0..self.synthetic_max as usize {
             // Here evaluate our polynomial key[i]*X key[i]*X^2 key[i]*X^3 etc....
-            let mut result = PrimeOrderDomain::new(0);
+            let mut result = PF::zero();
             for j in 0..self.threshold as usize {
-                result = result + (self.key[i][j].clone() * value.pow(j as u64));
+                result = result + (self.key[i][j].clone() * value.pow_vartime(&[j as u64]));
             }
             hash.push(result);
         }
         Hash(hash)
     }
 
-    pub fn random<R: RngCore + CryptoRng>(&self, rng: &mut R) -> Hash {
-        let mut hash = vec![PrimeOrderDomain::new(rng.gen_range(0..PRIME_ORDER))];
+    pub fn random<R: RngCore + CryptoRng + Copy>(&self, rng: R) -> Hash<PF> {
+        let mut hash = vec![PF::random(rng)];
         for _i in 0..self.synthetic_max as usize {
-            let mut result = PrimeOrderDomain::new(rng.gen_range(0..PRIME_ORDER));
-            hash.push(result);
+            hash.push(PF::random(rng));
         }
         Hash(hash)
     }
 }
 
-struct Solver {
+struct Solver<PF>
+where
+    PF: PrimeField,
+{
     synthetic_max: u64,
     threshold: u64,
-    expanded_hashes: Vec<Hash>,
+    expanded_hashes: Vec<Hash<PF>>,
 }
 
-impl Solver {
-    pub fn new(synthetic_max: u64, threshold: u64) -> Solver {
+impl<PF> Solver<PF>
+where
+    PF: PrimeField + PartialOrd + Display,
+{
+    pub fn new(synthetic_max: u64, threshold: u64) -> Solver<PF> {
         Solver {
             synthetic_max,
             threshold,
@@ -79,13 +89,13 @@ impl Solver {
     }
 
     /// Add a new hash to be evaluated by the solver...
-    pub fn add_hash(&mut self, hash: Hash) {
+    pub fn add_hash(&mut self, hash: Hash<PF>) {
         println!("Hash {}: {:?}", self.expanded_hashes.len(), hash);
 
         // To expand a Hash we take DHF(x0,p1..ps) and produce DHF(1,x0,x0^1..x0^t-1,p1..ps)
         let mut expanded_hash = vec![];
         for i in 0..self.threshold {
-            expanded_hash.push(hash.0[0].pow(i))
+            expanded_hash.push(hash.0[0].pow_vartime(&[i]))
         }
         for element in hash.0.iter().skip(1) {
             expanded_hash.push(element.clone())
@@ -106,7 +116,7 @@ impl Solver {
         }
         // Append the identity matrix...
         for (i, r) in (m..m + self.expanded_hashes.len()).enumerate() {
-            augmented_matrix.update(r as usize, i, PrimeOrderDomain::new(1));
+            augmented_matrix.update(r as usize, i, PF::one());
         }
 
         // Transpose for row reduction...
@@ -131,7 +141,7 @@ impl Solver {
             let mut i_max = h;
             let mut i_max_v = augmented_matrix.at(h, k);
             for x in h + 1..rows {
-                if augmented_matrix.at(x, k).gt(&i_max_v) {
+                if augmented_matrix.at(x, k) > i_max_v {
                     i_max = x;
                     i_max_v = augmented_matrix.at(x, k)
                 }
@@ -141,8 +151,8 @@ impl Solver {
             } else {
                 augmented_matrix.swap_rows(h, i_max);
                 for i in h + 1..rows {
-                    let f = augmented_matrix.at(i, k) * augmented_matrix.at(h, k).inverse();
-                    augmented_matrix.update(i, k, PrimeOrderDomain::new(0));
+                    let f = augmented_matrix.at(i, k) * augmented_matrix.at(h, k).invert().unwrap();
+                    augmented_matrix.update(i, k, PF::zero());
                     for j in k + 1..cols {
                         let val = augmented_matrix.at(i, j) - augmented_matrix.at(h, j) * f;
                         augmented_matrix.update(i, j, val);
@@ -217,17 +227,31 @@ impl Solver {
 
 #[cfg(test)]
 mod tests {
-    use crate::domain::PrimeOrderDomain;
-    use crate::{Generator, Solver, PRIME_ORDER};
-    use rand::Rng;
+    use crate::ff::Field;
+    use crate::{HashKey, Solver};
+    use ff::PrimeField;
     use rand_core::OsRng;
+    use std::fmt::{Display, Formatter};
+
+    // Generate a Prime Field to Test with...
+    #[derive(PrimeField)]
+    #[PrimeFieldModulus = "65537"]
+    #[PrimeFieldGenerator = "3"]
+    #[PrimeFieldReprEndianness = "little"]
+    struct Fp([u64; 1]);
+
+    impl Display for Fp {
+        fn fmt(&self, f: &mut Formatter<'_>) -> std::fmt::Result {
+            write!(f, "{:10}", self.0[0])
+        }
+    }
 
     #[test]
     fn it_works() {
-        let mut rng = OsRng;
+        let rng = OsRng;
         let s = 3u64;
         let t = 6u64;
-        let dhf = Generator::generate(&mut rng, s, t);
+        let dhf = HashKey::<Fp>::new(rng, s, t);
 
         let mut solver = Solver::new(s, t);
         for i in 0..10 {
@@ -237,11 +261,11 @@ mod tests {
             // If |random hashes| > s this this procedure will *not* work
             // There is an extended algorithm for extract assuming |true hashes| > t though - we do not implement it.
             if i != 2 && i != 5 && i != 8 {
-                let x0: u64 = rng.gen_range(0..PRIME_ORDER);
-                let hash = dhf.hash(PrimeOrderDomain::new(x0));
+                let x0 = Fp::random(rng);
+                let hash = dhf.generate_hash(x0);
                 solver.add_hash(hash);
             } else {
-                solver.add_hash(dhf.random(&mut rng));
+                solver.add_hash(dhf.random(rng));
             }
         }
 
diff --git a/src/matrix.rs b/src/matrix.rs
index e187732..fb8d14a 100644
--- a/src/matrix.rs
+++ b/src/matrix.rs
@@ -1,21 +1,26 @@
-use crate::domain::PrimeOrderDomain;
-use crate::PRIME_ORDER;
+use ff::PrimeField;
 
 /// A dense matrix. Apple have said t and s are going to be on the order of 30 so I feel
 /// you can probably always get away with a dense representation
-pub struct Matrix {
+pub struct Matrix<PF>
+where
+    PF: PrimeField,
+{
     rows: usize,
     cols: usize,
-    vals: Vec<Vec<PrimeOrderDomain<PRIME_ORDER>>>,
+    vals: Vec<Vec<PF>>,
 }
 
-impl Matrix {
-    pub fn new(rows: usize, cols: usize) -> Matrix {
+impl<PF> Matrix<PF>
+where
+    PF: PrimeField,
+{
+    pub fn new(rows: usize, cols: usize) -> Matrix<PF> {
         let mut vals = vec![];
         for _i in 0..rows {
             let mut row = vec![];
             for _j in 0..cols {
-                row.push(PrimeOrderDomain::new(0))
+                row.push(PF::zero())
             }
             vals.push(row)
         }
@@ -30,15 +35,15 @@ impl Matrix {
         self.cols
     }
 
-    pub fn update(&mut self, row: usize, col: usize, val: PrimeOrderDomain<PRIME_ORDER>) {
+    pub fn update(&mut self, row: usize, col: usize, val: PF) {
         self.vals[row][col] = val
     }
 
-    pub fn at(&self, row: usize, col: usize) -> PrimeOrderDomain<PRIME_ORDER> {
+    pub fn at(&self, row: usize, col: usize) -> PF {
         self.vals[row][col]
     }
 
-    pub fn transpose(&self) -> Matrix {
+    pub fn transpose(&self) -> Matrix<PF> {
         let mut m = Matrix::new(self.cols, self.rows);
         for i in 0..self.cols {
             for j in 0..self.rows {