diff --git a/crypto/fcmps/src/gadgets/interactive.rs b/crypto/fcmps/src/gadgets/interactive.rs
index 9c81c36f..fd86d15b 100644
--- a/crypto/fcmps/src/gadgets/interactive.rs
+++ b/crypto/fcmps/src/gadgets/interactive.rs
@@ -217,7 +217,7 @@ impl<C: Ciphersuite> Circuit<C> {
     claim: ClaimedPointWithDlog<C::F>,
   ) -> OnCurve {
     let ClaimedPointWithDlog { mut generator, divisor, dlog, point } = claim;
-    assert_eq!(dlog.len(), <C::F as PrimeField>::CAPACITY.try_into().unwrap());
+    assert_eq!(dlog.len(), <C::F as PrimeField>::NUM_BITS.try_into().unwrap());
 
     // Ensure this is being safely called
     let arg_iter = core::iter::once(&divisor.y).chain(divisor.yx.iter());
diff --git a/crypto/fcmps/src/lib.rs b/crypto/fcmps/src/lib.rs
index dec60249..c1bf8b45 100644
--- a/crypto/fcmps/src/lib.rs
+++ b/crypto/fcmps/src/lib.rs
@@ -3,11 +3,14 @@ use rand_core::{RngCore, CryptoRng};
 use transcript::Transcript;
 
 use ciphersuite::{
-  group::ff::{Field, PrimeField, PrimeFieldBits},
+  group::{
+    ff::{Field, PrimeField, PrimeFieldBits},
+    Group,
+  },
   Ciphersuite,
 };
 
-use ec_divisors::Poly;
+use ec_divisors::{Poly, DivisorCurve, new_divisor};
 use generalized_bulletproofs::arithmetic_circuit_proof::ArithmeticCircuitProof;
 
 #[allow(unused)] // TODO
@@ -31,14 +34,39 @@ pub struct Blinds<F: PrimeFieldBits> {
 
 /// A blind, prepared for usage within the circuit.
 #[derive(Clone, PartialEq, Eq, Debug)]
-struct PreparedBlind<F: PrimeField> {
+struct PreparedBlind<F: PrimeFieldBits> {
   bits: Vec<bool>,
   divisor: Poly<F>,
 }
 
+impl<F: PrimeFieldBits> PreparedBlind<F> {
+  fn new<C1: Ciphersuite>(blinding_generator: C1::G, blind: C1::F) -> Self
+  where
+    C1::G: DivisorCurve<FieldElement = F>,
+  {
+    let bits = blind.to_le_bits().into_iter().collect::<Vec<_>>();
+    assert_eq!(u32::try_from(bits.len()).unwrap(), C1::F::NUM_BITS);
+
+    let divisor = {
+      let mut gen_pow_2 = blinding_generator;
+      let mut points = vec![];
+      for bit in &bits {
+        if *bit {
+          points.push(gen_pow_2);
+        }
+        gen_pow_2 = gen_pow_2.double();
+      }
+      points.push(blinding_generator * -blind);
+      new_divisor::<C1::G>(&points).unwrap()
+    };
+
+    Self { bits, divisor }
+  }
+}
+
 /// The blinds used for an output, prepared for usage within the circuit.
 #[derive(Clone, PartialEq, Eq, Debug)]
-pub struct PreparedBlinds<F: PrimeField> {
+pub struct PreparedBlinds<F: PrimeFieldBits> {
   o_blind: PreparedBlind<F>,
   i_blind: PreparedBlind<F>,
   i_blind_blind: PreparedBlind<F>,
@@ -47,23 +75,10 @@ pub struct PreparedBlinds<F: PrimeField> {
 
 impl<F: PrimeFieldBits> Blinds<F> {
   pub fn new<R: RngCore + CryptoRng>(rng: &mut R) -> Self {
-    let new_blind = |rng: &mut R| -> F {
-      'outer: loop {
-        let res = F::random(&mut *rng);
-        // If this uses more bits than capacity, re-sample
-        for bit in res.to_le_bits().iter().skip(F::CAPACITY.try_into().unwrap()) {
-          if *bit {
-            continue 'outer;
-          }
-        }
-        return res;
-      }
-    };
-
-    let o_blind = new_blind(&mut *rng);
-    let i_blind = new_blind(&mut *rng);
-    let i_blind_blind = new_blind(&mut *rng);
-    let c_blind = new_blind(&mut *rng);
+    let o_blind = F::random(&mut *rng);
+    let i_blind = F::random(&mut *rng);
+    let i_blind_blind = F::random(&mut *rng);
+    let c_blind = F::random(&mut *rng);
 
     // o_blind, i_blind, c_blind are used in-circuit as negative
     let o_blind = -o_blind;
@@ -116,6 +131,17 @@ pub struct FcmpParams<C1: Ciphersuite, C2: Ciphersuite> {
   initial: CurveSpec<C2::F>,
   /// The secondary curve, defined over the initial curve's scalar field.
   secondary: CurveSpec<C1::F>,
+  /// The blinding generator for the vector commitments on the initial curve.
+  initial_blinding_generator: C1::G,
+  /// The blinding generator for the vector commitments on the secondary curve.
+  secondary_blinding_generator: C2::G,
+}
+
+#[derive(Clone, PartialEq, Eq, Debug)]
+pub struct Branches<C1: Ciphersuite, C2: Ciphersuite> {
+  leaves: Vec<Output<C1::F>>,
+  curve_2_layers: Vec<Vec<C2::F>>,
+  curve_1_layers: Vec<Vec<C1::F>>,
 }
 
 /// The full-chain membership proof.
@@ -125,19 +151,103 @@ pub struct Fcmp<C1: Ciphersuite, C2: Ciphersuite> {
   proof_2: ArithmeticCircuitProof<C2>,
   proof_2_vcs: Vec<C2::G>,
 }
-impl<C1: Ciphersuite, C2: Ciphersuite> Fcmp<C1, C2> {
+impl<C1: Ciphersuite, C2: Ciphersuite> Fcmp<C1, C2>
+where
+  C1::G: DivisorCurve<FieldElement = C2::F>,
+  C2::G: DivisorCurve<FieldElement = C1::F>,
+{
   pub fn prove<R: RngCore + CryptoRng, T: Transcript>(
     rng: &mut R,
     transcript: &mut T,
     params: &FcmpParams<C1, C2>,
-    tree_root: TreeRoot<C1, C2>,
-    depth: u32,
+    tree: Tree<C1, C2>,
     output: Output<C1::F>,
-    blinds: PreparedBlinds<C1::F>,
+    output_blinds: PreparedBlinds<C1::F>,
+    mut branches: Branches<C1, C2>,
   ) -> Self {
+    // Assert the depth is greater than or equal to two, and we'll actually use both proofs
+    assert!(tree.depth >= 2);
     // If depth = 1, there's one layer after the leaves
     // That makes the tree root a C1 point
-    assert_eq!(depth % 2, u32::from(u8::from(matches!(tree_root, TreeRoot::C1(_)))));
+    assert_eq!(tree.depth % 2, u32::from(u8::from(matches!(tree.root, TreeRoot::C1(_)))));
+
+    // Re-format the leaves into the expected branch format
+    let mut branches_1 = vec![vec![]];
+    for leaf in branches.leaves {
+      branches_1[0].extend(&[leaf.O.0, leaf.I.0, leaf.I.1, leaf.C.0]);
+    }
+
+    // Append the rest of the branches
+    let branches_2 = branches.curve_2_layers;
+    branches_1.append(&mut branches.curve_1_layers);
+
+    // Accumulate a blind into a witness vector
+    fn accum_blind<C: Ciphersuite>(witness: &mut Vec<C::F>, prepared_blind: PreparedBlind<C::F>) {
+      // Bits
+      assert_eq!(prepared_blind.bits.len(), usize::try_from(C::F::NUM_BITS).unwrap());
+      for bit in &prepared_blind.bits {
+        witness.push(if *bit { C::F::ONE } else { C::F::ZERO });
+      }
+
+      // Divisor y
+      witness.push(*prepared_blind.divisor.y_coefficients.first().unwrap_or(&C::F::ZERO));
+
+      // Divisor yx
+      // We have `(p / 2) - 2` yx coeffs, where p is the amount of points
+      let p = prepared_blind.bits.len() + 1;
+      let empty_vec = vec![];
+      let yx = prepared_blind.divisor.yx_coefficients.first().unwrap_or(&empty_vec);
+      for i in 0 .. (p / 2).saturating_sub(2) {
+        witness.push(*yx.get(i).unwrap_or(&C::F::ZERO));
+      }
+
+      // Divisor x
+      // We have `p / 2` x coeffs
+      assert_eq!(prepared_blind.divisor.x_coefficients[0], C::F::ONE);
+      // Transcript from 1 given we expect a normalization of the first coefficient
+      for i in 1 .. (p / 2) {
+        witness.push(*prepared_blind.divisor.x_coefficients.get(i).unwrap_or(&C::F::ZERO));
+      }
+
+      // Divisor 0
+      witness.push(prepared_blind.divisor.zero_coefficient);
+    }
+
+    // Decide blinds for each branch
+    let mut branches_1_blinds = vec![];
+    let mut branches_1_blinds_prepared = vec![];
+    for _ in 0 .. branches_1.len() {
+      let blind = C1::F::random(&mut *rng);
+      branches_1_blinds.push(blind);
+      branches_1_blinds_prepared
+        .push(PreparedBlind::<_>::new::<C1>(params.initial_blinding_generator, blind));
+    }
+
+    let mut branches_2_blinds = vec![];
+    let mut branches_2_blinds_prepared = vec![];
+    for _ in 0 .. branches_2.len() {
+      let blind = C2::F::random(&mut *rng);
+      branches_2_blinds.push(blind);
+      branches_2_blinds_prepared
+        .push(PreparedBlind::<_>::new::<C2>(params.secondary_blinding_generator, blind));
+    }
+
+    // interactive_witness_1 gets the leaves' openings/divisors, along with the standard witness
+    // for the relevant branches
+    let mut interactive_witness_1 = vec![];
+    accum_blind::<C1>(&mut interactive_witness_1, output_blinds.o_blind);
+    accum_blind::<C1>(&mut interactive_witness_1, output_blinds.i_blind);
+    accum_blind::<C1>(&mut interactive_witness_1, output_blinds.i_blind_blind);
+    accum_blind::<C1>(&mut interactive_witness_1, output_blinds.c_blind);
+    for blind in branches_2_blinds_prepared {
+      accum_blind::<C1>(&mut interactive_witness_1, blind);
+    }
+
+    // interactive_witness_2 gets the witness for the relevant branches
+    let mut interactive_witness_2 = vec![];
+    for blind in branches_1_blinds_prepared {
+      accum_blind::<C2>(&mut interactive_witness_2, blind);
+    }
 
     todo!("TODO")
   }