diff --git a/src/circuit/mod.rs b/src/circuit/mod.rs
index a81d6c7..b407b69 100644
--- a/src/circuit/mod.rs
+++ b/src/circuit/mod.rs
@@ -22,7 +22,6 @@ use bellman::{
 
 use jubjub::{
     JubjubEngine,
-    Unknown,
     PrimeOrder,
     FixedGenerators,
     edwards
@@ -55,9 +54,9 @@ pub struct Spend<'a, E: JubjubEngine> {
     /// The public key that will be re-randomized for
     /// use as a nullifier and signing key for the
     /// transaction.
-    pub ak: Option<edwards::Point<E, Unknown>>,
+    pub ak: Option<edwards::Point<E, PrimeOrder>>,
     /// The diversified base used to compute pk_d.
-    pub g_d: Option<edwards::Point<E, Unknown>>,
+    pub g_d: Option<edwards::Point<E, PrimeOrder>>,
     /// The randomness used to hide the note commitment data
     pub commitment_randomness: Option<E::Fs>,
     /// The authentication path of the commitment in the tree
@@ -482,7 +481,7 @@ impl<'a, E: JubjubEngine> Circuit<E> for Output<'a, E> {
 
 #[test]
 fn test_input_circuit_with_bls12_381() {
-    use pairing::{Field};
+    use pairing::{Field, BitIterator};
     use pairing::bls12_381::*;
     use rand::{SeedableRng, Rng, XorShiftRng};
     use ::circuit::test::*;
@@ -495,10 +494,34 @@ fn test_input_circuit_with_bls12_381() {
 
     let value: u64 = 1;
     let value_randomness: fs::Fs = rng.gen();
-    let ak: edwards::Point<Bls12, Unknown> = edwards::Point::rand(rng, params);
-    let g_d: edwards::Point<Bls12, Unknown> = edwards::Point::rand(rng, params);
-    let commitment_randomness: fs::Fs = rng.gen();
+
     let rsk: fs::Fs = rng.gen();
+    let ak: edwards::Point<Bls12, PrimeOrder> = edwards::Point::rand(rng, params).mul_by_cofactor(params);
+
+    let proof_generation_key = ::primitives::ProofGenerationKey {
+        ak: ak.clone(),
+        rsk: rsk.clone()
+    };
+
+    let viewing_key = proof_generation_key.into_viewing_key(params);
+
+    let payment_address;
+
+    loop {
+        let diversifier = ::primitives::Diversifier(rng.gen());
+
+        if let Some(p) = viewing_key.into_payment_address(
+            diversifier,
+            params
+        )
+        {
+            payment_address = p;
+            break;
+        }
+    }
+
+    let g_d = payment_address.diversifier.g_d(params).unwrap();
+    let commitment_randomness: fs::Fs = rng.gen();
     let auth_path = vec![Some((rng.gen(), rng.gen())); tree_depth];
 
     {
@@ -510,7 +533,7 @@ fn test_input_circuit_with_bls12_381() {
             value_randomness: Some(value_randomness),
             rsk: Some(rsk),
             ak: Some(ak),
-            g_d: Some(g_d),
+            g_d: Some(g_d.clone()),
             commitment_randomness: Some(commitment_randomness),
             auth_path: auth_path.clone()
         };
@@ -535,9 +558,54 @@ fn test_input_circuit_with_bls12_381() {
         assert_eq!(cs.get_input(1, "value commitment/x/input variable"), expected_value_cm_xy.0);
         assert_eq!(cs.get_input(2, "value commitment/y/input variable"), expected_value_cm_xy.1);
 
-        cs.get_input(3, "anchor/input variable");
-        cs.get_input(4, "nullifier/x/input variable");
-        cs.get_input(5, "nullifier/y/input variable");
+        let note = ::primitives::Note {
+            value: value,
+            g_d: g_d.clone(),
+            pk_d: payment_address.pk_d.clone(),
+            r: commitment_randomness.clone()
+        };
+
+        let mut position = 0u64;
+        let mut cur = note.cm(params);
+
+        assert_eq!(cs.get("randomization of note commitment/x3/num"), cur);
+
+        for (i, val) in auth_path.into_iter().enumerate()
+        {
+            let (uncle, b) = val.unwrap();
+
+            let mut lhs = cur;
+            let mut rhs = uncle;
+
+            if b {
+                ::std::mem::swap(&mut lhs, &mut rhs);
+            }
+
+            let mut lhs: Vec<bool> = BitIterator::new(lhs.into_repr()).collect();
+            let mut rhs: Vec<bool> = BitIterator::new(rhs.into_repr()).collect();
+
+            lhs.reverse();
+            rhs.reverse();
+
+            cur = ::pedersen_hash::pedersen_hash::<Bls12, _>(
+                ::pedersen_hash::Personalization::MerkleTree(i),
+                lhs.into_iter()
+                   .take(Fr::NUM_BITS as usize)
+                   .chain(rhs.into_iter().take(Fr::NUM_BITS as usize)),
+                params
+            ).into_xy().0;
+
+            if b {
+                position |= 1 << i;
+            }
+        }
+
+        let expected_nf = note.nf(&viewing_key, position, params);
+        let expected_nf_xy = expected_nf.into_xy();
+
+        assert_eq!(cs.get_input(3, "anchor/input variable"), cur);
+        assert_eq!(cs.get_input(4, "nullifier/x/input variable"), expected_nf_xy.0);
+        assert_eq!(cs.get_input(5, "nullifier/y/input variable"), expected_nf_xy.1);
     }
 }
 
diff --git a/src/lib.rs b/src/lib.rs
index 686f93a..100bbb0 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -25,6 +25,8 @@ const PRF_NR_PERSONALIZATION: &'static [u8; 8]  = b"WhatTheH";
 // Group hash personalizations
 /// BLAKE2s Personalization for Pedersen hash generators.
 const PEDERSEN_HASH_GENERATORS_PERSONALIZATION: &'static [u8; 8] = b"PEDERSEN";
+/// BLAKE2s Personalization for the group hash for key diversification
+const KEY_DIVERSIFICATION_PERSONALIZATION: &'static [u8; 8] = b"Zcash_gh";
 /// BLAKE2s Personalization for the proof generation key base point
 const PROOF_GENERATION_KEY_BASE_GENERATOR_PERSONALIZATION: &'static [u8; 8] = b"12345678";
 /// BLAKE2s Personalization for the note commitment randomness generator
diff --git a/src/primitives/mod.rs b/src/primitives/mod.rs
index 237b633..d5bb550 100644
--- a/src/primitives/mod.rs
+++ b/src/primitives/mod.rs
@@ -1,3 +1,10 @@
+use pairing::{
+    PrimeField,
+    PrimeFieldRepr
+};
+
+use group_hash::group_hash;
+
 use pedersen_hash::{
     pedersen_hash,
     Personalization
@@ -16,6 +23,83 @@ use jubjub::{
     FixedGenerators
 };
 
+use blake2_rfc::blake2s::Blake2s;
+
+pub struct ProofGenerationKey<E: JubjubEngine> {
+    pub ak: edwards::Point<E, PrimeOrder>,
+    pub rsk: E::Fs
+}
+
+impl<E: JubjubEngine> ProofGenerationKey<E> {
+    pub fn into_viewing_key(&self, params: &E::Params) -> ViewingKey<E> {
+        ViewingKey {
+            ak: self.ak.clone(),
+            rk: params.generator(FixedGenerators::ProofGenerationKey)
+                      .mul(self.rsk, params)
+        }
+    }
+}
+
+pub struct ViewingKey<E: JubjubEngine> {
+    pub ak: edwards::Point<E, PrimeOrder>,
+    pub rk: edwards::Point<E, PrimeOrder>
+}
+
+impl<E: JubjubEngine> ViewingKey<E> {
+    fn ivk(&self) -> E::Fs {
+        let mut preimage = [0; 64];
+
+        self.ak.write(&mut preimage[0..32]).unwrap();
+        self.rk.write(&mut preimage[32..64]).unwrap();
+
+        let mut h = Blake2s::with_params(32, &[], &[], ::CRH_IVK_PERSONALIZATION);
+        h.update(&preimage);
+        let mut h = h.finalize().as_ref().to_vec();
+
+        // Drop the first five bits, so it can be interpreted as a scalar.
+        h[0] &= 0b0000_0111;
+
+        let mut e = <E::Fs as PrimeField>::Repr::default();
+        e.read_be(&h[..]).unwrap();
+
+        E::Fs::from_repr(e).expect("should be a valid scalar")
+    }
+
+    pub fn into_payment_address(
+        &self,
+        diversifier: Diversifier,
+        params: &E::Params
+    ) -> Option<PaymentAddress<E>>
+    {
+        diversifier.g_d(params).map(|g_d| {
+            let pk_d = g_d.mul(self.ivk(), params);
+
+            PaymentAddress {
+                pk_d: pk_d,
+                diversifier: diversifier
+            }
+        })
+    }
+}
+
+#[derive(Copy, Clone)]
+pub struct Diversifier(pub [u8; 11]);
+
+impl Diversifier {
+    pub fn g_d<E: JubjubEngine>(
+        &self,
+        params: &E::Params
+    ) -> Option<edwards::Point<E, PrimeOrder>>
+    {
+        group_hash::<E>(&self.0, ::KEY_DIVERSIFICATION_PERSONALIZATION, params)
+    }
+}
+
+pub struct PaymentAddress<E: JubjubEngine> {
+    pub pk_d: edwards::Point<E, PrimeOrder>,
+    pub diversifier: Diversifier
+}
+
 pub struct Note<E: JubjubEngine> {
     /// The value of the note
     pub value: u64,
@@ -28,8 +112,8 @@ pub struct Note<E: JubjubEngine> {
 }
 
 impl<E: JubjubEngine> Note<E> {
-    /// Computes the note commitment
-    pub fn cm(&self, params: &E::Params) -> E::Fr
+    /// Computes the note commitment, returning the full point.
+    fn cm_full_point(&self, params: &E::Params) -> edwards::Point<E, PrimeOrder>
     {
         // Calculate the note contents, as bytes
         let mut note_contents = vec![];
@@ -56,12 +140,53 @@ impl<E: JubjubEngine> Note<E> {
         );
 
         // Compute final commitment
-        let cm = params.generator(FixedGenerators::NoteCommitmentRandomness)
-                       .mul(self.r, params)
-                       .add(&hash_of_contents, params);
+        params.generator(FixedGenerators::NoteCommitmentRandomness)
+              .mul(self.r, params)
+              .add(&hash_of_contents, params)
+    }
 
+    /// Computes the nullifier given the viewing key and
+    /// note position
+    pub fn nf(
+        &self,
+        viewing_key: &ViewingKey<E>,
+        position: u64,
+        params: &E::Params
+    ) -> edwards::Point<E, PrimeOrder>
+    {
+        // Compute cm + position
+        let cm_plus_position = self
+            .cm_full_point(params)
+            .add(
+                &params.generator(FixedGenerators::NullifierPosition)
+                       .mul(position, params),
+                params
+            );
+
+        // Compute nr = drop_5(BLAKE2s(rk | cm_plus_position))
+        let mut nr_preimage = [0u8; 64];
+        viewing_key.rk.write(&mut nr_preimage[0..32]).unwrap();
+        cm_plus_position.write(&mut nr_preimage[32..64]).unwrap();
+        let mut h = Blake2s::with_params(32, &[], &[], ::PRF_NR_PERSONALIZATION);
+        h.update(&nr_preimage);
+        let mut h = h.finalize().as_ref().to_vec();
+
+        // Drop the first five bits, so it can be interpreted as a scalar.
+        h[0] &= 0b0000_0111;
+
+        let mut e = <E::Fs as PrimeField>::Repr::default();
+        e.read_be(&h[..]).unwrap();
+
+        let nr = E::Fs::from_repr(e).expect("should be a valid scalar");
+
+        viewing_key.ak.mul(nr, params)
+    }
+
+    /// Computes the note commitment
+    pub fn cm(&self, params: &E::Params) -> E::Fr
+    {
         // The commitment is in the prime order subgroup, so mapping the
         // commitment to the x-coordinate is an injective encoding.
-        cm.into_xy().0
+        self.cm_full_point(params).into_xy().0
     }
 }