diff --git a/src/fields/fp.rs b/src/fields/fp.rs
index 3773bc1..5ab6ca2 100644
--- a/src/fields/fp.rs
+++ b/src/fields/fp.rs
@@ -51,12 +51,6 @@ impl<P: PrimeFieldParams> Field for Fp<P> {
         }
     }
 
-    fn is_zero(&self) -> bool {
-        use num::Zero;
-
-        self.value == BigUint::zero()
-    }
-
     fn inverse(&self) -> Self {
         if self.is_zero() {
             // TODO: this should likely bleed through the abstraction layers
diff --git a/src/fields/fp12.rs b/src/fields/fp12.rs
new file mode 100644
index 0000000..434d85d
--- /dev/null
+++ b/src/fields/fp12.rs
@@ -0,0 +1,127 @@
+use ::Fq2;
+use ::Fq6;
+use rand::Rng;
+use fields::Field;
+use std::ops::{Mul,Add,Sub,Neg};
+use std::cmp::{PartialEq, Eq};
+use std::marker::PhantomData;
+use std::fmt;
+
+pub trait Fp12Params {
+    fn non_residue() -> Fq2;
+    fn name() -> &'static str;
+}
+
+pub struct Fp12<P: Fp12Params> {
+    a: Fq6,
+    b: Fq6,
+    _marker: PhantomData<P>
+}
+
+impl<P: Fp12Params> Fp12<P> {
+    pub fn new(a: Fq6, b: Fq6) -> Self {
+        Fp12 {
+            a: a,
+            b: b,
+            _marker: PhantomData
+        }
+    }
+}
+
+impl<P: Fp12Params> fmt::Debug for Fp12<P> {
+    fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
+        write!(f, "{}({:?}, {:?})", P::name(), self.a, self.b)
+    }
+}
+
+impl<P: Fp12Params> Clone for Fp12<P> {
+    fn clone(&self) -> Self {
+        Fp12 {
+            a: self.a.clone(),
+            b: self.b.clone(),
+            _marker: PhantomData
+        }
+    }
+}
+
+impl<P: Fp12Params> Field for Fp12<P> {
+    fn zero() -> Self {
+        Fp12 {
+            a: Fq6::zero(),
+            b: Fq6::zero(),
+            _marker: PhantomData
+        }
+    }
+    fn one() -> Self {
+        Fp12 {
+            a: Fq6::one(),
+            b: Fq6::zero(),
+            _marker: PhantomData
+        }
+    }
+    fn random<R: Rng>(rng: &mut R) -> Self {
+        Fp12 {
+            a: Fq6::random(rng),
+            b: Fq6::random(rng),
+            _marker: PhantomData
+        }
+    }
+    
+    fn inverse(&self) -> Self {
+        let t = (self.a.squared() - (self.b.squared().mul_by_nonresidue(&P::non_residue()))).inverse();
+
+        Fp12 {
+            a: &self.a * &t,
+            b: -(&self.b * &t),
+            _marker: PhantomData
+        }
+    }
+    
+    fn squared(&self) -> Self {
+        let a = &self.a; let b = &self.b;
+        let ab = &(a * b);
+
+        Fp12 {
+            a: (b.mul_by_nonresidue(&P::non_residue()) + a) * (a + b) - ab - ab.mul_by_nonresidue(&P::non_residue()),
+            b: ab + ab,
+            _marker: PhantomData
+        }
+    }
+    
+    fn eq(&self, other: &Self) -> bool {
+        self.a == other.a && self.b == other.b
+    }
+    fn neg(&self) -> Self {
+        Fp12 {
+            a: -(&self.a),
+            b: -(&self.b),
+            _marker: PhantomData
+        }
+    }
+    fn mul(&self, other: &Self) -> Self {
+        let a_a = &(&self.a * &other.a);
+        let b_b = &(&self.b * &other.b);
+
+        Fp12 {
+            a: b_b.mul_by_nonresidue(&P::non_residue()) + a_a,
+            b: (&self.a + &self.b) * (&other.a + &other.b) - a_a - b_b,
+            _marker: PhantomData
+        }
+    }
+    fn sub(&self, other: &Self) -> Self {
+        Fp12 {
+            a: &self.a - &other.a,
+            b: &self.b - &other.b,
+            _marker: PhantomData
+        }
+    }
+    fn add(&self, other: &Self) -> Self {
+        Fp12 {
+            a: &self.a + &other.a,
+            b: &self.b + &other.b,
+            _marker: PhantomData
+        }
+    }
+}
+
+forward_ops_to_field_ops!(impl(P: Fp12Params) Fp12<P>);
diff --git a/src/fields/fp2.rs b/src/fields/fp2.rs
index a28d234..c885e42 100644
--- a/src/fields/fp2.rs
+++ b/src/fields/fp2.rs
@@ -1,6 +1,5 @@
 use ::Fq;
 use rand::Rng;
-use fields::fp::PrimeFieldParams;
 use fields::Field;
 use std::ops::{Mul,Add,Sub,Neg};
 use std::cmp::{PartialEq, Eq};
@@ -66,9 +65,7 @@ impl<P: Fp2Params> Field for Fp2<P> {
             _marker: PhantomData
         }
     }
-    fn is_zero(&self) -> bool {
-        self == &Self::zero()
-    }
+    
     fn inverse(&self) -> Self {
         let t = (self.a.squared() - (self.b.squared() * P::non_residue())).inverse();
 
diff --git a/src/fields/fp6.rs b/src/fields/fp6.rs
new file mode 100644
index 0000000..1d88aba
--- /dev/null
+++ b/src/fields/fp6.rs
@@ -0,0 +1,147 @@
+use ::Fq2;
+use rand::Rng;
+use fields::Field;
+use std::ops::{Mul,Add,Sub,Neg};
+use std::cmp::{PartialEq, Eq};
+use std::marker::PhantomData;
+use std::fmt;
+
+pub trait Fp6Params {
+    fn non_residue() -> Fq2;
+    fn name() -> &'static str;
+}
+
+pub struct Fp6<P: Fp6Params> {
+    a: Fq2,
+    b: Fq2,
+    c: Fq2,
+    _marker: PhantomData<P>
+}
+
+impl<P: Fp6Params> Fp6<P> {
+    pub fn new(a: Fq2, b: Fq2, c: Fq2) -> Self {
+        Fp6 {
+            a: a,
+            b: b,
+            c: c,
+            _marker: PhantomData
+        }
+    }
+}
+
+impl<P: Fp6Params> fmt::Debug for Fp6<P> {
+    fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
+        write!(f, "{}({:?}, {:?}, {:?})", P::name(), self.a, self.b, self.c)
+    }
+}
+
+impl<P: Fp6Params> Clone for Fp6<P> {
+    fn clone(&self) -> Self {
+        Fp6 {
+            a: self.a.clone(),
+            b: self.b.clone(),
+            c: self.c.clone(),
+            _marker: PhantomData
+        }
+    }
+}
+
+impl<P: Fp6Params> Field for Fp6<P> {
+    fn zero() -> Self {
+        Fp6 {
+            a: Fq2::zero(),
+            b: Fq2::zero(),
+            c: Fq2::zero(),
+            _marker: PhantomData
+        }
+    }
+
+    fn one() -> Self {
+        Fp6 {
+            a: Fq2::one(),
+            b: Fq2::zero(),
+            c: Fq2::zero(),
+            _marker: PhantomData
+        }
+    }
+
+    fn random<R: Rng>(rng: &mut R) -> Self {
+        Fp6 {
+            a: Fq2::random(rng),
+            b: Fq2::random(rng),
+            c: Fq2::random(rng),
+            _marker: PhantomData
+        }
+    }
+
+    fn inverse(&self) -> Self {
+        let c0 = self.a.squared() - &self.b * &self.c * P::non_residue();
+        let c1 = self.c.squared() * P::non_residue() - &self.a * &self.b;
+        let c2 = self.b.squared() - &self.a * &self.c;
+        let t = ((&self.c * &c1 + &self.b * &c2) * P::non_residue() + &self.a * &c0).inverse();
+
+        Fp6 {
+            a: &t * &c0,
+            b: &t * &c1,
+            c: &t * &c2,
+            _marker: PhantomData
+        }
+    }
+
+    fn eq(&self, other: &Self) -> bool {
+        self.a == other.a && self.b == other.b && self.c == other.c
+    }
+
+    fn neg(&self) -> Self {
+        Fp6 {
+        	a: -(&self.a),
+        	b: -(&self.b),
+        	c: -(&self.c),
+        	_marker: PhantomData
+        }
+    }
+
+    fn mul(&self, other: &Self) -> Self {
+        let a_a = &self.a * &other.a;
+        let b_b = &self.b * &other.b;
+        let c_c = &self.c * &other.c;
+
+        Fp6 {
+        	a: ((&self.b + &self.c) * (&other.b + &other.c) - &b_b - &c_c) * P::non_residue() + &a_a,
+        	b: (&self.a + &self.b) * (&other.a + &other.b) - &a_a - &b_b + &c_c * P::non_residue(),
+        	c: (&self.a + &self.c) * (&other.a + &other.c) - &a_a + &b_b - &c_c,
+        	_marker: PhantomData
+        }
+    }
+
+    fn sub(&self, other: &Self) -> Self {
+        Fp6 {
+            a: &self.a - &other.a,
+            b: &self.b - &other.b,
+            c: &self.c - &other.c,
+            _marker: PhantomData
+        }
+    }
+
+    fn add(&self, other: &Self) -> Self {
+        Fp6 {
+            a: &self.a + &other.a,
+            b: &self.b + &other.b,
+            c: &self.c + &other.c,
+            _marker: PhantomData
+        }
+    }
+}
+
+impl<P: Fp6Params> Fp6<P> {
+	pub fn mul_by_nonresidue(&self, other: &Fq2) -> Fp6<P> {
+		Fp6 {
+			a: &self.c * other,
+			b: self.a.clone(),
+			c: self.b.clone(),
+			_marker: PhantomData
+		}
+	}
+}
+
+forward_ops_to_field_ops!(impl(P: Fp6Params) Fp6<P>);
diff --git a/src/fields/mod.rs b/src/fields/mod.rs
index bfb5610..0c24f0e 100644
--- a/src/fields/mod.rs
+++ b/src/fields/mod.rs
@@ -3,6 +3,8 @@ mod macros;
 
 pub mod fp;
 pub mod fp2;
+pub mod fp6;
+pub mod fp12;
 
 #[cfg(test)]
 pub mod tests;
@@ -15,7 +17,9 @@ pub trait Field: Sized + Clone + Debug {
     fn zero() -> Self;
     fn one() -> Self;
     fn random<R: Rng>(rng: &mut R) -> Self;
-    fn is_zero(&self) -> bool;
+    fn is_zero(&self) -> bool {
+        self.eq(&Self::zero())
+    }
     fn inverse(&self) -> Self;
     fn squared(&self) -> Self {
         self.mul(self)
diff --git a/src/lib.rs b/src/lib.rs
index 219db22..e0c205d 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -8,13 +8,17 @@ mod groups;
 
 pub use fields::fp::Fp;
 pub use fields::fp2::Fp2;
-pub use params::{FrParams,FqParams,Fq2Params,G1Params,G2Params};
+pub use fields::fp6::Fp6;
+pub use fields::fp12::Fp12;
+pub use params::{FrParams,FqParams,Fq2Params,G1Params,G2Params,Fq6Params,Fq12Params};
 pub use fields::Field;
 pub use groups::Jacobian;
 
 pub type Fr = Fp<FrParams>;
 pub type Fq = Fp<FqParams>;
 pub type Fq2 = Fp2<Fq2Params>;
+pub type Fq6 = Fp6<Fq6Params>;
+pub type Fq12 = Fp12<Fq12Params>;
 
 pub type Scalar = Fr;
 pub type G1 = Jacobian<G1Params>;
diff --git a/src/params.rs b/src/params.rs
index 567f783..397508d 100644
--- a/src/params.rs
+++ b/src/params.rs
@@ -2,7 +2,9 @@ use num::{Num,BigUint};
 use fields::Field;
 use fields::fp::PrimeFieldParams;
 use fields::fp2::Fp2Params;
-use super::{Fr,Fq,Fq2,G1,G2};
+use fields::fp6::Fp6Params;
+use fields::fp12::Fp12Params;
+use super::{Fr,Fq,Fq2,Fq6,Fq12,G1,G2};
 use groups::*;
 
 pub struct FrParams;
@@ -166,3 +168,127 @@ fn g2_test_vector() {
 
     assert_eq!(expect, e);
 }
+
+pub struct Fq6Params;
+
+impl Fp6Params for Fq6Params {
+    fn non_residue() -> Fq2 {
+        Fq2::new(Fq::from("9"), Fq::from("1"))
+    }
+    fn name() -> &'static str {
+        "Fq6"
+    }
+}
+
+#[test]
+fn test_fq6() {
+    use fields;
+
+    fields::tests::field_trials::<Fq6>();
+}
+
+pub struct Fq12Params;
+
+impl Fp12Params for Fq12Params {
+    fn non_residue() -> Fq2 {
+        Fq2::new(Fq::from("9"), Fq::from("1"))
+    }
+    fn name() -> &'static str {
+        "Fq12"
+    }
+}
+
+#[test]
+fn test_fq12() {
+    use fields;
+
+    fields::tests::field_trials::<Fq12>();
+}
+
+#[test]
+fn fq12_test_vector() {
+    let start = Fq12::new(
+        Fq6::new(
+            Fq2::new(
+                Fq::from("19797905000333868150253315089095386158892526856493194078073564469188852136946"),
+                Fq::from("10509658143212501778222314067134547632307419253211327938344904628569123178733")
+            ),
+            Fq2::new(
+                Fq::from("208316612133170645758860571704540129781090973693601051684061348604461399206"),
+                Fq::from("12617661120538088237397060591907161689901553895660355849494983891299803248390")
+            ),
+            Fq2::new(
+                Fq::from("2897490589776053688661991433341220818937967872052418196321943489809183508515"),
+                Fq::from("2730506433347642574983433139433778984782882168213690554721050571242082865799")
+            )
+        ),
+        Fq6::new(
+            Fq2::new(
+                Fq::from("17870056122431653936196746815433147921488990391314067765563891966783088591110"),
+                Fq::from("14314041658607615069703576372547568077123863812415914883625850585470406221594")
+            ),
+            Fq2::new(
+                Fq::from("10123533891707846623287020000407963680629966110211808794181173248765209982878"),
+                Fq::from("5062091880848845693514855272640141851746424235009114332841857306926659567101")
+            ),
+            Fq2::new(
+                Fq::from("9839781502639936537333620974973645053542086898304697594692219798017709586567"),
+                Fq::from("1583892292110602864638265389721494775152090720173641072176370350017825640703")
+            )
+        )
+    );
+
+    // Do a bunch of arbitrary stuff to the element
+
+    let mut next = start.clone();
+    for _ in 0..100 {
+        next = &next * &start;
+    }
+
+    let mut cpy = next.clone();
+
+    for _ in 0..10 {
+        next = next.squared();
+    }
+
+    for _ in 0..10 {
+        next = &next + &start;
+        next = &next - &cpy;
+        next = -&next;
+    }
+
+    next = next.squared();
+
+    let finally = Fq12::new(
+        Fq6::new(
+            Fq2::new(
+                Fq::from("18388750939593263065521177085001223024106699964957029146547831509155008229833"),
+                Fq::from("18370529854582635460997127698388761779167953912610241447912705473964014492243")
+            ),
+            Fq2::new(
+                Fq::from("3691824277096717481466579496401243638295254271265821828017111951446539785268"),
+                Fq::from("20513494218085713799072115076991457239411567892860153903443302793553884247235")
+            ),
+            Fq2::new(
+                Fq::from("12214155472433286415803224222551966441740960297013786627326456052558698216399"),
+                Fq::from("10987494248070743195602580056085773610850106455323751205990078881956262496575")
+            )
+        ),
+        Fq6::new(
+            Fq2::new(
+                Fq::from("5134522153456102954632718911439874984161223687865160221119284322136466794876"),
+                Fq::from("20119236909927036376726859192821071338930785378711977469360149362002019539920")
+            ),
+            Fq2::new(
+                Fq::from("8839766648621210419302228913265679710586991805716981851373026244791934012854"),
+                Fq::from("9103032146464138788288547957401673544458789595252696070370942789051858719203")
+            ),
+            Fq2::new(
+                Fq::from("10378379548636866240502412547812481928323945124508039853766409196375806029865"),
+                Fq::from("9021627154807648093720460686924074684389554332435186899318369174351765754041")
+            )
+        )
+    );
+
+    assert_eq!(finally, next);
+}