diff --git a/zcash_proofs/Cargo.toml b/zcash_proofs/Cargo.toml
index 1b7834127..8a917e2f8 100644
--- a/zcash_proofs/Cargo.toml
+++ b/zcash_proofs/Cargo.toml
@@ -14,9 +14,13 @@ edition = "2018"
 [dependencies]
 bellman = { version = "0.6", path = "../bellman", default-features = false, features = ["groth16"] }
 blake2b_simd = "0.5"
+bls12_381 = { version = "0.1", path = "../bls12_381" }
 byteorder = "1"
 directories = { version = "3", optional = true }
 ff = { version = "0.6", path = "../ff" }
+group = { version = "0.6", path = "../group" }
+jubjub = { version = "0.3", path = "../jubjub" }
+lazy_static = "1"
 minreq = { version = "2", features = ["https"], optional = true }
 pairing = { version = "0.16", path = "../pairing" }
 rand_core = "0.5.1"
diff --git a/zcash_proofs/src/constants.rs b/zcash_proofs/src/constants.rs
new file mode 100644
index 000000000..f02d8e5d0
--- /dev/null
+++ b/zcash_proofs/src/constants.rs
@@ -0,0 +1,293 @@
+//! Various constants used for the Zcash proofs.
+
+use bls12_381::Scalar;
+use ff::Field;
+use group::{Curve, Group};
+use jubjub::ExtendedPoint;
+use lazy_static::lazy_static;
+use zcash_primitives::constants::{PEDERSEN_HASH_CHUNKS_PER_GENERATOR, PEDERSEN_HASH_GENERATORS};
+
+/// The `d` constant of the twisted Edwards curve.
+pub const EDWARDS_D: Scalar = Scalar::from_raw([
+    0x0106_5fd6_d634_3eb1,
+    0x292d_7f6d_3757_9d26,
+    0xf5fd_9207_e6bd_7fd4,
+    0x2a93_18e7_4bfa_2b48,
+]);
+
+/// The `A` constant of the birationally equivalent Montgomery curve.
+pub const MONTGOMERY_A: Scalar = Scalar::from_raw([
+    0x0000_0000_0000_a002,
+    0x0000_0000_0000_0000,
+    0x0000_0000_0000_0000,
+    0x0000_0000_0000_0000,
+]);
+
+/// The scaling factor used for conversion to and from the Montgomery form.
+pub const MONTGOMERY_SCALE: Scalar = Scalar::from_raw([
+    0x8f45_35f7_cf82_b8d9,
+    0xce40_6970_3da8_8abd,
+    0x31de_341e_77d7_64e5,
+    0x2762_de61_e862_645e,
+]);
+
+/// The number of chunks needed to represent a full scalar during fixed-base
+/// exponentiation.
+const FIXED_BASE_CHUNKS_PER_GENERATOR: usize = 84;
+
+/// Reference to a circuit version of a generator for fixed-base salar multiplication.
+pub type FixedGenerator = &'static [Vec<(Scalar, Scalar)>];
+
+/// Circuit version of a generator for fixed-base salar multiplication.
+pub type FixedGeneratorOwned = Vec<Vec<(Scalar, Scalar)>>;
+
+lazy_static! {
+    pub static ref PROOF_GENERATION_KEY_GENERATOR: FixedGeneratorOwned =
+        generate_circuit_generator(zcash_primitives::constants::PROOF_GENERATION_KEY_GENERATOR);
+
+    pub static ref NOTE_COMMITMENT_RANDOMNESS_GENERATOR: FixedGeneratorOwned =
+        generate_circuit_generator(zcash_primitives::constants::NOTE_COMMITMENT_RANDOMNESS_GENERATOR);
+
+    pub static ref NULLIFIER_POSITION_GENERATOR: FixedGeneratorOwned =
+        generate_circuit_generator(zcash_primitives::constants::NULLIFIER_POSITION_GENERATOR);
+
+    pub static ref VALUE_COMMITMENT_VALUE_GENERATOR: FixedGeneratorOwned =
+        generate_circuit_generator(zcash_primitives::constants::VALUE_COMMITMENT_VALUE_GENERATOR);
+
+    pub static ref VALUE_COMMITMENT_RANDOMNESS_GENERATOR: FixedGeneratorOwned =
+        generate_circuit_generator(zcash_primitives::constants::VALUE_COMMITMENT_RANDOMNESS_GENERATOR);
+
+    pub static ref SPENDING_KEY_GENERATOR: FixedGeneratorOwned =
+        generate_circuit_generator(zcash_primitives::constants::SPENDING_KEY_GENERATOR);
+
+    /// The pre-computed window tables `[-4, 3, 2, 1, 1, 2, 3, 4]` of different magnitudes
+    /// of the Pedersen hash segment generators.
+    pub static ref PEDERSEN_CIRCUIT_GENERATORS: Vec<Vec<Vec<(Scalar, Scalar)>>> =
+        generate_pedersen_circuit_generators();
+}
+
+/// Creates the 3-bit window table `[0, 1, ..., 8]` for different magnitudes of a fixed
+/// generator.
+fn generate_circuit_generator(mut gen: jubjub::SubgroupPoint) -> FixedGeneratorOwned {
+    let mut windows = vec![];
+
+    for _ in 0..FIXED_BASE_CHUNKS_PER_GENERATOR {
+        let mut coeffs = vec![(Scalar::zero(), Scalar::one())];
+        let mut g = gen.clone();
+        for _ in 0..7 {
+            let g_affine = jubjub::ExtendedPoint::from(g).to_affine();
+            coeffs.push((g_affine.get_u(), g_affine.get_v()));
+            g += gen;
+        }
+        windows.push(coeffs);
+
+        // gen = gen * 8
+        gen = g;
+    }
+
+    windows
+}
+
+/// Returns the coordinates of this point's Montgomery curve representation, or `None` if
+/// it is the point at infinity.
+pub(crate) fn to_montgomery_coords(g: ExtendedPoint) -> Option<(Scalar, Scalar)> {
+    let g = g.to_affine();
+    let (x, y) = (g.get_u(), g.get_v());
+
+    if y == Scalar::one() {
+        // The only solution for y = 1 is x = 0. (0, 1) is the neutral element, so we map
+        // this to the point at infinity.
+        None
+    } else {
+        // The map from a twisted Edwards curve is defined as
+        // (x, y) -> (u, v) where
+        //      u = (1 + y) / (1 - y)
+        //      v = u / x
+        //
+        // This mapping is not defined for y = 1 and for x = 0.
+        //
+        // We have that y != 1 above. If x = 0, the only
+        // solutions for y are 1 (contradiction) or -1.
+        if x.is_zero() {
+            // (0, -1) is the point of order two which is not
+            // the neutral element, so we map it to (0, 0) which is
+            // the only affine point of order 2.
+            Some((Scalar::zero(), Scalar::zero()))
+        } else {
+            // The mapping is defined as above.
+            //
+            // (x, y) -> (u, v) where
+            //      u = (1 + y) / (1 - y)
+            //      v = u / x
+
+            let u = (Scalar::one() + y) * (Scalar::one() - y).invert().unwrap();
+            let v = u * x.invert().unwrap();
+
+            // Scale it into the correct curve constants
+            // scaling factor = sqrt(4 / (a - d))
+            Some((u, v * MONTGOMERY_SCALE))
+        }
+    }
+}
+
+/// Creates the 2-bit window table lookups for each 4-bit "chunk" in each segment of the
+/// Pedersen hash.
+fn generate_pedersen_circuit_generators() -> Vec<Vec<Vec<(Scalar, Scalar)>>> {
+    // Process each segment
+    PEDERSEN_HASH_GENERATORS
+        .iter()
+        .cloned()
+        .map(|mut gen| {
+            let mut windows = vec![];
+
+            for _ in 0..PEDERSEN_HASH_CHUNKS_PER_GENERATOR {
+                // Create (x, y) coeffs for this chunk
+                let mut coeffs = vec![];
+                let mut g = gen.clone();
+
+                // coeffs = g, g*2, g*3, g*4
+                for _ in 0..4 {
+                    coeffs.push(
+                        to_montgomery_coords(g.into())
+                            .expect("we never encounter the point at infinity"),
+                    );
+                    g += gen;
+                }
+                windows.push(coeffs);
+
+                // Our chunks are separated by 2 bits to prevent overlap.
+                for _ in 0..4 {
+                    gen = gen.double();
+                }
+            }
+
+            windows
+        })
+        .collect()
+}
+
+#[cfg(test)]
+mod tests {
+    use bls12_381::Scalar;
+    use ff::PrimeField;
+    use pairing::bls12_381::Fr;
+    use zcash_primitives::{
+        jubjub::{FixedGenerators, JubjubParams},
+        JUBJUB,
+    };
+
+    use super::*;
+
+    fn check_scalar(expected: Fr, actual: Scalar) {
+        assert_eq!(expected.to_repr().0, actual.to_bytes());
+    }
+
+    fn check_generator(expected: FixedGenerators, actual: FixedGenerator) {
+        let expected = JUBJUB.circuit_generators(expected);
+
+        // Same number of windows per generator.
+        assert_eq!(expected.len(), actual.len());
+        for (expected, actual) in expected.iter().zip(actual) {
+            // Same size table per window.
+            assert_eq!(expected.len(), actual.len());
+            for (expected, actual) in expected.iter().zip(actual) {
+                // Same coordinates.
+                check_scalar(expected.0, actual.0);
+                check_scalar(expected.1, actual.1);
+            }
+        }
+    }
+
+    #[test]
+    fn edwards_d() {
+        check_scalar(*JUBJUB.edwards_d(), EDWARDS_D);
+    }
+
+    #[test]
+    fn montgomery_a() {
+        check_scalar(*JUBJUB.montgomery_a(), MONTGOMERY_A);
+    }
+
+    #[test]
+    fn montgomery_scale() {
+        check_scalar(*JUBJUB.scale(), MONTGOMERY_SCALE);
+    }
+
+    #[test]
+    fn fixed_base_chunks_per_generator() {
+        assert_eq!(
+            JUBJUB.fixed_base_chunks_per_generator(),
+            FIXED_BASE_CHUNKS_PER_GENERATOR
+        );
+    }
+
+    #[test]
+    fn proof_generation_key_base_generator() {
+        check_generator(
+            FixedGenerators::ProofGenerationKey,
+            &PROOF_GENERATION_KEY_GENERATOR,
+        );
+    }
+
+    #[test]
+    fn note_commitment_randomness_generator() {
+        check_generator(
+            FixedGenerators::NoteCommitmentRandomness,
+            &NOTE_COMMITMENT_RANDOMNESS_GENERATOR,
+        );
+    }
+
+    #[test]
+    fn nullifier_position_generator() {
+        check_generator(
+            FixedGenerators::NullifierPosition,
+            &NULLIFIER_POSITION_GENERATOR,
+        );
+    }
+
+    #[test]
+    fn value_commitment_value_generator() {
+        check_generator(
+            FixedGenerators::ValueCommitmentValue,
+            &VALUE_COMMITMENT_VALUE_GENERATOR,
+        );
+    }
+
+    #[test]
+    fn value_commitment_randomness_generator() {
+        check_generator(
+            FixedGenerators::ValueCommitmentRandomness,
+            &VALUE_COMMITMENT_RANDOMNESS_GENERATOR,
+        );
+    }
+
+    #[test]
+    fn spending_key_generator() {
+        check_generator(
+            FixedGenerators::SpendingKeyGenerator,
+            &SPENDING_KEY_GENERATOR,
+        );
+    }
+
+    #[test]
+    fn pedersen_circuit_generators() {
+        let expected = JUBJUB.pedersen_circuit_generators();
+        let actual = &PEDERSEN_CIRCUIT_GENERATORS;
+
+        // Same number of Pedersen hash generators.
+        assert_eq!(expected.len(), actual.len());
+        for (expected, actual) in expected.iter().zip(actual.iter()) {
+            // Same number of windows per generator.
+            assert_eq!(expected.len(), actual.len());
+            for (expected, actual) in expected.iter().zip(actual) {
+                // Same size table per window.
+                assert_eq!(expected.len(), actual.len());
+                for (expected, actual) in expected.iter().zip(actual) {
+                    // Same coordinates.
+                    check_scalar(expected.0, actual.0);
+                    check_scalar(expected.1, actual.1);
+                }
+            }
+        }
+    }
+}
diff --git a/zcash_proofs/src/lib.rs b/zcash_proofs/src/lib.rs
index 7c574c295..a94c4a589 100644
--- a/zcash_proofs/src/lib.rs
+++ b/zcash_proofs/src/lib.rs
@@ -18,6 +18,7 @@ use directories::BaseDirs;
 use std::path::PathBuf;
 
 pub mod circuit;
+mod constants;
 mod hashreader;
 pub mod sapling;
 pub mod sprout;