sapling_crypto/

circuit.rs

//! The Sapling circuits.

use alloc::vec::Vec;
use core::fmt;
use corez::io;
use std::sync::OnceLock;

use group::{Curve, ff::PrimeField};

use bellman::{Circuit, ConstraintSystem, SynthesisError, groth16};
use bls12_381::Bls12;

use bellman::gadgets::Assignment;
use bellman::gadgets::blake2s;
use bellman::gadgets::boolean;
use bellman::gadgets::multipack;
use bellman::gadgets::num;

use self::constants::{
    note_commitment_randomness_generator, nullifier_position_generator,
    proof_generation_key_generator, spending_key_generator, value_commitment_randomness_generator,
    value_commitment_value_generator,
};
use crate::{PaymentAddress, ProofGenerationKey, value::NoteValue};

#[cfg(test)]
use group::ff::PrimeFieldBits;

mod constants;
mod ecc;
mod pedersen_hash;

/// The opening (value and randomness) of a Sapling value commitment.
#[derive(Clone)]
pub struct ValueCommitmentOpening {
    pub value: NoteValue,
    pub randomness: jubjub::Scalar,
}

#[cfg(test)]
impl ValueCommitmentOpening {
    fn commitment(&self) -> jubjub::ExtendedPoint {
        let cv = (super::constants::VALUE_COMMITMENT_VALUE_GENERATOR
            * jubjub::Fr::from(self.value.inner()))
            + (super::constants::VALUE_COMMITMENT_RANDOMNESS_GENERATOR * self.randomness);
        cv.into()
    }
}

/// This is an instance of the `Spend` circuit.
#[derive(Clone)]
pub struct Spend {
    /// The opening of a Pedersen commitment to the value being spent.
    pub value_commitment_opening: Option<ValueCommitmentOpening>,

    /// Key required to construct proofs for spending notes
    /// for a particular spending key
    pub proof_generation_key: Option<ProofGenerationKey>,

    /// The payment address associated with the note
    pub payment_address: Option<PaymentAddress>,

    /// The randomness of the note commitment
    pub commitment_randomness: Option<jubjub::Fr>,

    /// Re-randomization of the public key
    pub ar: Option<jubjub::Fr>,

    /// The authentication path of the commitment in the tree
    pub auth_path: Vec<Option<(bls12_381::Scalar, bool)>>,

    /// The anchor; the root of the tree. If the note being
    /// spent is zero-value, this can be anything.
    pub anchor: Option<bls12_381::Scalar>,
}

impl fmt::Debug for Spend {
    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
        f.debug_struct("Spend")
            .field("anchor", &self.anchor)
            .finish_non_exhaustive()
    }
}

/// This is an output circuit instance.
#[derive(Clone)]
pub struct Output {
    /// The opening of a Pedersen commitment to the value being spent.
    pub value_commitment_opening: Option<ValueCommitmentOpening>,

    /// The payment address of the recipient
    pub payment_address: Option<PaymentAddress>,

    /// The randomness used to hide the note commitment data
    pub commitment_randomness: Option<jubjub::Fr>,

    /// The ephemeral secret key for DH with recipient
    pub esk: Option<jubjub::Fr>,
}

impl fmt::Debug for Output {
    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
        f.debug_struct("Output").finish_non_exhaustive()
    }
}

/// Exposes a Pedersen commitment to the value as an
/// input to the circuit
fn expose_value_commitment<CS>(
    mut cs: CS,
    value_commitment_opening: Option<ValueCommitmentOpening>,
) -> Result<Vec<boolean::Boolean>, SynthesisError>
where
    CS: ConstraintSystem<bls12_381::Scalar>,
{
    // Booleanize the value into little-endian bit order
    let value_bits = boolean::u64_into_boolean_vec_le(
        cs.namespace(|| "value"),
        value_commitment_opening.as_ref().map(|c| c.value.inner()),
    )?;

    // Compute the note value in the exponent
    let value = ecc::fixed_base_multiplication(
        cs.namespace(|| "compute the value in the exponent"),
        value_commitment_value_generator(),
        &value_bits,
    )?;

    // Booleanize the randomness. This does not ensure
    // the bit representation is "in the field" because
    // it doesn't matter for security.
    let rcv = boolean::field_into_boolean_vec_le(
        cs.namespace(|| "rcv"),
        value_commitment_opening.as_ref().map(|c| c.randomness),
    )?;

    // Compute the randomness in the exponent
    let rcv = ecc::fixed_base_multiplication(
        cs.namespace(|| "computation of rcv"),
        value_commitment_randomness_generator(),
        &rcv,
    )?;

    // Compute the Pedersen commitment to the value
    let cv = value.add(cs.namespace(|| "computation of cv"), &rcv)?;

    // Expose the commitment as an input to the circuit
    cv.inputize(cs.namespace(|| "commitment point"))?;

    Ok(value_bits)
}

impl Circuit<bls12_381::Scalar> for Spend {
    fn synthesize<CS: ConstraintSystem<bls12_381::Scalar>>(
        self,
        cs: &mut CS,
    ) -> Result<(), SynthesisError> {
        // Prover witnesses ak (ensures that it's on the curve)
        let ak = ecc::EdwardsPoint::witness(
            cs.namespace(|| "ak"),
            self.proof_generation_key.as_ref().map(|k| (&k.ak).into()),
        )?;

        // There are no sensible attacks on small order points
        // of ak (that we're aware of!) but it's a cheap check,
        // so we do it.
        ak.assert_not_small_order(cs.namespace(|| "ak not small order"))?;

        // Rerandomize ak and expose it as an input to the circuit
        {
            let ar = boolean::field_into_boolean_vec_le(cs.namespace(|| "ar"), self.ar)?;

            // Compute the randomness in the exponent
            let ar = ecc::fixed_base_multiplication(
                cs.namespace(|| "computation of randomization for the signing key"),
                spending_key_generator(),
                &ar,
            )?;

            let rk = ak.add(cs.namespace(|| "computation of rk"), &ar)?;

            rk.inputize(cs.namespace(|| "rk"))?;
        }

        // Compute nk = [nsk] ProofGenerationKey
        let nk;
        {
            // Witness nsk as bits
            let nsk = boolean::field_into_boolean_vec_le(
                cs.namespace(|| "nsk"),
                self.proof_generation_key.as_ref().map(|k| k.nsk),
            )?;

            // NB: We don't ensure that the bit representation of nsk
            // is "in the field" (jubjub::Fr) because it's not used
            // except to demonstrate the prover knows it. If they know
            // a congruency then that's equivalent.

            // Compute nk = [nsk] ProvingPublicKey
            nk = ecc::fixed_base_multiplication(
                cs.namespace(|| "computation of nk"),
                proof_generation_key_generator(),
                &nsk,
            )?;
        }

        // This is the "viewing key" preimage for CRH^ivk
        let mut ivk_preimage = vec![];

        // Place ak in the preimage for CRH^ivk
        ivk_preimage.extend(ak.repr(cs.namespace(|| "representation of ak"))?);

        // This is the nullifier preimage for PRF^nf
        let mut nf_preimage = vec![];

        // Extend ivk and nf preimages with the representation of
        // nk.
        {
            let repr_nk = nk.repr(cs.namespace(|| "representation of nk"))?;

            ivk_preimage.extend(repr_nk.iter().cloned());
            nf_preimage.extend(repr_nk);
        }

        assert_eq!(ivk_preimage.len(), 512);
        assert_eq!(nf_preimage.len(), 256);

        // Compute the incoming viewing key ivk
        let mut ivk = blake2s::blake2s(
            cs.namespace(|| "computation of ivk"),
            &ivk_preimage,
            super::constants::CRH_IVK_PERSONALIZATION,
        )?;

        // drop_5 to ensure it's in the field
        ivk.truncate(jubjub::Fr::CAPACITY as usize);

        // Witness g_d, checking that it's on the curve.
        let g_d = {
            ecc::EdwardsPoint::witness(
                cs.namespace(|| "witness g_d"),
                self.payment_address.as_ref().map(|a| {
                    a.diversifier()
                        .g_d()
                        .expect("checked at construction")
                        .into()
                }),
            )?
        };

        // Check that g_d is not small order. Technically, this check
        // is already done in the Output circuit, and this proof ensures
        // g_d is bound to a product of that check, but for defense in
        // depth let's check it anyway. It's cheap.
        g_d.assert_not_small_order(cs.namespace(|| "g_d not small order"))?;

        // Compute pk_d = g_d^ivk
        let pk_d = g_d.mul(cs.namespace(|| "compute pk_d"), &ivk)?;

        // Compute note contents:
        // value (in big endian) followed by g_d and pk_d
        let mut note_contents = vec![];

        // Handle the value; we'll need it later for the
        // dummy input check.
        let mut value_num = num::Num::zero();
        {
            // Get the value in little-endian bit order
            let value_bits = expose_value_commitment(
                cs.namespace(|| "value commitment"),
                self.value_commitment_opening,
            )?;

            // Compute the note's value as a linear combination
            // of the bits.
            let mut coeff = bls12_381::Scalar::one();
            for bit in &value_bits {
                value_num = value_num.add_bool_with_coeff(CS::one(), bit, coeff);
                coeff = coeff.double();
            }

            // Place the value in the note
            note_contents.extend(value_bits);
        }

        // Place g_d in the note
        note_contents.extend(g_d.repr(cs.namespace(|| "representation of g_d"))?);

        // Place pk_d in the note
        note_contents.extend(pk_d.repr(cs.namespace(|| "representation of pk_d"))?);

        assert_eq!(
            note_contents.len(),
            64 + // value
            256 + // g_d
            256 // p_d
        );

        // Compute the hash of the note contents
        let mut cm = pedersen_hash::pedersen_hash(
            cs.namespace(|| "note content hash"),
            pedersen_hash::Personalization::NoteCommitment,
            &note_contents,
        )?;

        {
            // Booleanize the randomness for the note commitment
            let rcm = boolean::field_into_boolean_vec_le(
                cs.namespace(|| "rcm"),
                self.commitment_randomness,
            )?;

            // Compute the note commitment randomness in the exponent
            let rcm = ecc::fixed_base_multiplication(
                cs.namespace(|| "computation of commitment randomness"),
                note_commitment_randomness_generator(),
                &rcm,
            )?;

            // Randomize the note commitment. Pedersen hashes are not
            // themselves hiding commitments.
            cm = cm.add(cs.namespace(|| "randomization of note commitment"), &rcm)?;
        }

        // This will store (least significant bit first)
        // the position of the note in the tree, for use
        // in nullifier computation.
        let mut position_bits = vec![];

        // This is an injective encoding, as cur is a
        // point in the prime order subgroup.
        let mut cur = cm.get_u().clone();

        // Ascend the merkle tree authentication path
        for (i, e) in self.auth_path.into_iter().enumerate() {
            let cs = &mut cs.namespace(|| format!("merkle tree hash {i}"));

            // Determines if the current subtree is the "right" leaf at this
            // depth of the tree.
            let cur_is_right = boolean::Boolean::from(boolean::AllocatedBit::alloc(
                cs.namespace(|| "position bit"),
                e.map(|e| e.1),
            )?);

            // Push this boolean for nullifier computation later
            position_bits.push(cur_is_right.clone());

            // Witness the authentication path element adjacent
            // at this depth.
            let path_element =
                num::AllocatedNum::alloc(cs.namespace(|| "path element"), || Ok(e.get()?.0))?;

            // Swap the two if the current subtree is on the right
            let (ul, ur) = num::AllocatedNum::conditionally_reverse(
                cs.namespace(|| "conditional reversal of preimage"),
                &cur,
                &path_element,
                &cur_is_right,
            )?;

            // We don't need to be strict, because the function is
            // collision-resistant. If the prover witnesses a congruency,
            // they will be unable to find an authentication path in the
            // tree with high probability.
            let mut preimage = vec![];
            preimage.extend(ul.to_bits_le(cs.namespace(|| "ul into bits"))?);
            preimage.extend(ur.to_bits_le(cs.namespace(|| "ur into bits"))?);

            // Compute the new subtree value
            cur = pedersen_hash::pedersen_hash(
                cs.namespace(|| "computation of pedersen hash"),
                pedersen_hash::Personalization::MerkleTree(i),
                &preimage,
            )?
            .get_u()
            .clone(); // Injective encoding
        }

        {
            let real_anchor_value = self.anchor;

            // Allocate the "real" anchor that will be exposed.
            let rt = num::AllocatedNum::alloc(cs.namespace(|| "conditional anchor"), || {
                Ok(*real_anchor_value.get()?)
            })?;

            // (cur - rt) * value = 0
            // if value is zero, cur and rt can be different
            // if value is nonzero, they must be equal
            cs.enforce(
                || "conditionally enforce correct root",
                |lc| lc + cur.get_variable() - rt.get_variable(),
                |lc| lc + &value_num.lc(bls12_381::Scalar::one()),
                |lc| lc,
            );

            // Expose the anchor
            rt.inputize(cs.namespace(|| "anchor"))?;
        }

        // Compute the cm + g^position for preventing
        // faerie gold attacks
        let mut rho = cm;
        {
            // Compute the position in the exponent
            let position = ecc::fixed_base_multiplication(
                cs.namespace(|| "g^position"),
                nullifier_position_generator(),
                &position_bits,
            )?;

            // Add the position to the commitment
            rho = rho.add(cs.namespace(|| "faerie gold prevention"), &position)?;
        }

        // Let's compute nf = BLAKE2s(nk || rho)
        nf_preimage.extend(rho.repr(cs.namespace(|| "representation of rho"))?);

        assert_eq!(nf_preimage.len(), 512);

        // Compute nf
        let nf = blake2s::blake2s(
            cs.namespace(|| "nf computation"),
            &nf_preimage,
            super::constants::PRF_NF_PERSONALIZATION,
        )?;

        multipack::pack_into_inputs(cs.namespace(|| "pack nullifier"), &nf)
    }
}

impl Circuit<bls12_381::Scalar> for Output {
    fn synthesize<CS: ConstraintSystem<bls12_381::Scalar>>(
        self,
        cs: &mut CS,
    ) -> Result<(), SynthesisError> {
        // Let's start to construct our note, which contains
        // value (big endian)
        let mut note_contents = vec![];

        // Expose the value commitment and place the value
        // in the note.
        note_contents.extend(expose_value_commitment(
            cs.namespace(|| "value commitment"),
            self.value_commitment_opening,
        )?);

        // Let's deal with g_d
        {
            // Prover witnesses g_d, ensuring it's on the
            // curve.
            let g_d = ecc::EdwardsPoint::witness(
                cs.namespace(|| "witness g_d"),
                self.payment_address.as_ref().map(|a| {
                    a.diversifier()
                        .g_d()
                        .expect("checked at construction")
                        .into()
                }),
            )?;

            // g_d is ensured to be large order. The relationship
            // between g_d and pk_d ultimately binds ivk to the
            // note. If this were a small order point, it would
            // not do this correctly, and the prover could
            // double-spend by finding random ivk's that satisfy
            // the relationship.
            //
            // Further, if it were small order, epk would be
            // small order too!
            g_d.assert_not_small_order(cs.namespace(|| "g_d not small order"))?;

            // Extend our note contents with the representation of
            // g_d.
            note_contents.extend(g_d.repr(cs.namespace(|| "representation of g_d"))?);

            // Booleanize our ephemeral secret key
            let esk = boolean::field_into_boolean_vec_le(cs.namespace(|| "esk"), self.esk)?;

            // Create the ephemeral public key from g_d.
            let epk = g_d.mul(cs.namespace(|| "epk computation"), &esk)?;

            // Expose epk publicly.
            epk.inputize(cs.namespace(|| "epk"))?;
        }

        // Now let's deal with pk_d. We don't do any checks and
        // essentially allow the prover to witness any 256 bits
        // they would like.
        {
            // Just grab pk_d from the witness
            let pk_d = self
                .payment_address
                .as_ref()
                .map(|e| jubjub::ExtendedPoint::from(e.pk_d().inner()).to_affine());

            // Witness the v-coordinate, encoded as little
            // endian bits (to match the representation)
            let v_contents = boolean::field_into_boolean_vec_le(
                cs.namespace(|| "pk_d bits of v"),
                pk_d.map(|e| e.get_v()),
            )?;

            // Witness the sign bit
            let sign_bit = boolean::Boolean::from(boolean::AllocatedBit::alloc(
                cs.namespace(|| "pk_d bit of u"),
                pk_d.map(|e| e.get_u().is_odd().into()),
            )?);

            // Extend the note with pk_d representation
            note_contents.extend(v_contents);
            note_contents.push(sign_bit);
        }

        assert_eq!(
            note_contents.len(),
            64 + // value
            256 + // g_d
            256 // pk_d
        );

        // Compute the hash of the note contents
        let mut cm = pedersen_hash::pedersen_hash(
            cs.namespace(|| "note content hash"),
            pedersen_hash::Personalization::NoteCommitment,
            &note_contents,
        )?;

        {
            // Booleanize the randomness
            let rcm = boolean::field_into_boolean_vec_le(
                cs.namespace(|| "rcm"),
                self.commitment_randomness,
            )?;

            // Compute the note commitment randomness in the exponent
            let rcm = ecc::fixed_base_multiplication(
                cs.namespace(|| "computation of commitment randomness"),
                note_commitment_randomness_generator(),
                &rcm,
            )?;

            // Randomize our note commitment
            cm = cm.add(cs.namespace(|| "randomization of note commitment"), &rcm)?;
        }

        // Only the u-coordinate of the output is revealed,
        // since we know it is prime order, and we know that
        // the u-coordinate is an injective encoding for
        // elements in the prime-order subgroup.
        cm.get_u().inputize(cs.namespace(|| "commitment"))?;

        Ok(())
    }
}

/// The parameters for the Sapling Spend circuit.
pub struct SpendParameters(pub(crate) groth16::Parameters<Bls12>);

impl SpendParameters {
    /// Reads the parameters from their encoding.
    ///
    /// Only set `verify_point_encodings` to false if you are verifying the parameters in
    /// another way (such as checking the hash of the parameters file on disk).
    pub fn read<R: io::Read>(reader: R, verify_point_encodings: bool) -> io::Result<Self> {
        Ok(Self(groth16::Parameters::<Bls12>::read(
            reader,
            verify_point_encodings,
        )?))
    }

    /// Returns the verifying key for the Sapling Spend circuit.
    pub fn verifying_key(&self) -> SpendVerifyingKey {
        SpendVerifyingKey::new(self.0.vk.clone())
    }

    /// Returns the verifying key for the Sapling Spend circuit, with precomputations
    /// optimized for verifying individual proofs.
    pub fn prepared_verifying_key(&self) -> PreparedSpendVerifyingKey {
        PreparedSpendVerifyingKey(groth16::prepare_verifying_key(&self.0.vk))
    }
}

/// The verifying key for the Sapling Spend circuit.
pub struct SpendVerifyingKey(
    pub(crate) groth16::VerifyingKey<Bls12>,
    OnceLock<groth16::batch::PreparedBatchG2<Bls12>>,
);

impl SpendVerifyingKey {
    pub(crate) fn new(vk: groth16::VerifyingKey<Bls12>) -> Self {
        Self(vk, OnceLock::new())
    }

    pub(crate) fn prepared_batch(
        &self,
    ) -> Result<groth16::batch::PreparedBatchVerifyingKey<'_, Bls12>, bellman::VerificationError>
    {
        let g2 = self
            .1
            .get_or_init(|| groth16::batch::PreparedBatchG2::from(&self.0));
        groth16::batch::PreparedBatchVerifyingKey::from_cached(&self.0, g2)
    }

    /// Performs precomputations optimized for verifying individual proofs.
    pub fn prepare(&self) -> PreparedSpendVerifyingKey {
        PreparedSpendVerifyingKey(groth16::prepare_verifying_key(&self.0))
    }
}

/// The verifying key for the Sapling Spend circuit, with precomputations optimized for
/// verifying individual proofs.
pub struct PreparedSpendVerifyingKey(pub(crate) groth16::PreparedVerifyingKey<Bls12>);

/// The parameters for the Sapling Output circuit.
pub struct OutputParameters(pub(crate) groth16::Parameters<Bls12>);

impl OutputParameters {
    /// Reads the parameters from their encoding.
    ///
    /// Only set `verify_point_encodings` to false if you are verifying the parameters in
    /// another way (such as checking the hash of the parameters file on disk).
    pub fn read<R: io::Read>(reader: R, verify_point_encodings: bool) -> io::Result<Self> {
        groth16::Parameters::<Bls12>::read(reader, verify_point_encodings).map(Self)
    }

    /// Returns the verifying key for the Sapling Output circuit.
    pub fn verifying_key(&self) -> OutputVerifyingKey {
        OutputVerifyingKey::new(self.0.vk.clone())
    }

    /// Returns the verifying key for the Sapling Output circuit, with precomputations
    /// optimized for verifying individual proofs.
    pub fn prepared_verifying_key(&self) -> PreparedOutputVerifyingKey {
        PreparedOutputVerifyingKey(groth16::prepare_verifying_key(&self.0.vk))
    }
}

/// The verifying key for the Sapling Output circuit.
pub struct OutputVerifyingKey(
    pub(crate) groth16::VerifyingKey<Bls12>,
    OnceLock<groth16::batch::PreparedBatchG2<Bls12>>,
);

impl OutputVerifyingKey {
    pub(crate) fn new(vk: groth16::VerifyingKey<Bls12>) -> Self {
        Self(vk, OnceLock::new())
    }

    pub(crate) fn prepared_batch(
        &self,
    ) -> Result<groth16::batch::PreparedBatchVerifyingKey<'_, Bls12>, bellman::VerificationError>
    {
        let g2 = self
            .1
            .get_or_init(|| groth16::batch::PreparedBatchG2::from(&self.0));
        groth16::batch::PreparedBatchVerifyingKey::from_cached(&self.0, g2)
    }

    /// Performs precomputations optimized for verifying individual proofs.
    pub fn prepare(&self) -> PreparedOutputVerifyingKey {
        PreparedOutputVerifyingKey(groth16::prepare_verifying_key(&self.0))
    }
}

/// The verifying key for the Sapling Output circuit, with precomputations optimized for
/// verifying individual proofs.
pub struct PreparedOutputVerifyingKey(pub(crate) groth16::PreparedVerifyingKey<Bls12>);

#[test]
fn test_input_circuit_with_bls12_381() {
    use crate::{
        Diversifier, Note, ProofGenerationKey, Rseed, keys::SpendValidatingKey, pedersen_hash,
    };

    use bellman::gadgets::test::*;
    use group::ff::Field;
    use rand_core::{Rng, SeedableRng};
    use rand_xorshift::XorShiftRng;

    let mut rng = XorShiftRng::from_seed([
        0x58, 0x62, 0xbe, 0x3d, 0x76, 0x3d, 0x31, 0x8d, 0x17, 0xdb, 0x37, 0x32, 0x54, 0x06, 0xbc,
        0xe5,
    ]);

    let tree_depth = 32;

    for _ in 0..10 {
        let value_commitment = ValueCommitmentOpening {
            value: NoteValue::from_raw(rng.next_u64()),
            randomness: jubjub::Fr::random(&mut rng),
        };

        let proof_generation_key = ProofGenerationKey {
            ak: SpendValidatingKey::fake_random(&mut rng),
            nsk: jubjub::Fr::random(&mut rng),
        };

        let viewing_key = proof_generation_key.to_viewing_key();

        let payment_address;

        loop {
            let diversifier = {
                let mut d = [0; 11];
                rng.fill_bytes(&mut d);
                Diversifier(d)
            };

            if let Some(p) = viewing_key.to_payment_address(diversifier) {
                payment_address = p;
                break;
            }
        }

        let commitment_randomness = jubjub::Fr::random(&mut rng);
        let auth_path = vec![
            Some((
                bls12_381::Scalar::random(&mut rng),
                !rng.next_u32().is_multiple_of(2),
            ));
            tree_depth
        ];
        let ar = jubjub::Fr::random(&mut rng);

        {
            let rk = jubjub::AffinePoint::from_bytes(viewing_key.rk(ar).into()).unwrap();
            let expected_value_commitment = value_commitment.commitment().to_affine();
            let note = Note::from_parts(
                payment_address,
                value_commitment.value,
                Rseed::BeforeZip212(commitment_randomness),
            );

            let mut position = 0u64;
            let cmu = note.cmu();
            let mut cur = bls12_381::Scalar::from_bytes(&cmu.to_bytes()).unwrap();

            for (i, val) in auth_path.clone().into_iter().enumerate() {
                let (uncle, b) = val.unwrap();

                let mut lhs = cur;
                let mut rhs = uncle;

                if b {
                    ::core::mem::swap(&mut lhs, &mut rhs);
                }

                let lhs = lhs.to_le_bits();
                let rhs = rhs.to_le_bits();

                cur = jubjub::ExtendedPoint::from(pedersen_hash::pedersen_hash(
                    pedersen_hash::Personalization::MerkleTree(i),
                    lhs.iter()
                        .by_vals()
                        .take(bls12_381::Scalar::NUM_BITS as usize)
                        .chain(
                            rhs.iter()
                                .by_vals()
                                .take(bls12_381::Scalar::NUM_BITS as usize),
                        ),
                ))
                .to_affine()
                .get_u();

                if b {
                    position |= 1 << i;
                }
            }

            let expected_nf = note.nf(&viewing_key.nk, position);
            let expected_nf = multipack::bytes_to_bits_le(&expected_nf.0);
            let expected_nf = multipack::compute_multipacking(&expected_nf);
            assert_eq!(expected_nf.len(), 2);

            let mut cs = TestConstraintSystem::new();

            let instance = Spend {
                value_commitment_opening: Some(value_commitment.clone()),
                proof_generation_key: Some(proof_generation_key.clone()),
                payment_address: Some(payment_address),
                commitment_randomness: Some(commitment_randomness),
                ar: Some(ar),
                auth_path: auth_path.clone(),
                anchor: Some(cur),
            };

            instance.synthesize(&mut cs).unwrap();

            assert!(cs.is_satisfied());
            assert_eq!(cs.num_constraints(), 98777);
            assert_eq!(
                cs.hash(),
                "d37c738e83df5d9b0bb6495ac96abf21bcb2697477e2c15c2c7916ff7a3b6a89"
            );

            assert_eq!(
                cs.get("randomization of note commitment/u3/num").to_repr(),
                cmu.to_bytes()
            );

            assert_eq!(cs.num_inputs(), 8);
            assert_eq!(cs.get_input(0, "ONE"), bls12_381::Scalar::one());
            assert_eq!(cs.get_input(1, "rk/u/input variable"), rk.get_u());
            assert_eq!(cs.get_input(2, "rk/v/input variable"), rk.get_v());
            assert_eq!(
                cs.get_input(3, "value commitment/commitment point/u/input variable"),
                expected_value_commitment.get_u()
            );
            assert_eq!(
                cs.get_input(4, "value commitment/commitment point/v/input variable"),
                expected_value_commitment.get_v()
            );
            assert_eq!(
                cs.get_input(5, "anchor/input variable").to_repr(),
                cur.to_bytes()
            );
            assert_eq!(cs.get_input(6, "pack nullifier/input 0"), expected_nf[0]);
            assert_eq!(cs.get_input(7, "pack nullifier/input 1"), expected_nf[1]);
        }
    }
}

#[test]
fn test_input_circuit_with_bls12_381_external_test_vectors() {
    use crate::{
        Diversifier, Note, ProofGenerationKey, Rseed, keys::SpendValidatingKey, pedersen_hash,
    };

    use bellman::gadgets::test::*;
    use group::ff::Field;
    use rand_core::{Rng, SeedableRng};
    use rand_xorshift::XorShiftRng;

    let mut rng = XorShiftRng::from_seed([
        0x59, 0x62, 0xbe, 0x3d, 0x76, 0x3d, 0x31, 0x8d, 0x17, 0xdb, 0x37, 0x32, 0x54, 0x06, 0xbc,
        0xe5,
    ]);

    let tree_depth = 32;

    let expected_commitment_us = [
        "43821661663052659750276289184181083197337192946256245809816728673021647664276",
        "7220807656052227578299730541645543434083158611414003423211850718229633594616",
        "13239753550660714843257636471668037031928211668773449453628093339627668081697",
        "10900524635678389360790699587556574797582192824300145558807405770494079767974",
        "1411013767457690636461779630023011774660680126764323588543800715293173598850",
        "32334206652383066267661379202183359608706535021387905923603014648832344657662",
        "20206750741605167608500278423400565295188703622528437817438897624149653579380",
        "46716485782200334735478719487356079850582051575003452698983255860512578229998",
        "31221372899739042781372142393132358519434268512685538373976981051223051220367",
        "18269767207277008186871145355531741929166733260352590789136389380124992250945",
    ];

    let expected_commitment_vs = [
        "27630722367128086497290371604583225252915685718989450292520883698391703910",
        "23310648738313092772044712773481584369462075017189681529702825235349449805260",
        "25709635353183537915646348052945798827495141780341329896098121888376871589480",
        "10516315852014492141081718791576479298042117442649432716255936672048164184691",
        "23970713991179488695004801139667700217127937225554773561645815034212389459772",
        "3256052161046564597126736968199320852691566092694819239485673781545479548450",
        "18887250722195819674378865377623103071236046274361890247643850134985809137409",
        "36501156873031641173054592888886902104303750771545647842488588827138867116570",
        "21927526310070011864833939629345235038589128172309792087590183778192091594775",
        "32959334601512756708397683646222389414681003290313255304927423560477040775488",
    ];

    for i in 0..10 {
        let value_commitment = ValueCommitmentOpening {
            value: NoteValue::from_raw(i),
            randomness: jubjub::Fr::from(1000 * (i + 1)),
        };

        let proof_generation_key = ProofGenerationKey {
            ak: SpendValidatingKey::fake_random(&mut rng),
            nsk: jubjub::Fr::random(&mut rng),
        };

        let viewing_key = proof_generation_key.to_viewing_key();

        let payment_address;

        loop {
            let diversifier = {
                let mut d = [0; 11];
                rng.fill_bytes(&mut d);
                Diversifier(d)
            };

            if let Some(p) = viewing_key.to_payment_address(diversifier) {
                payment_address = p;
                break;
            }
        }

        let commitment_randomness = jubjub::Fr::random(&mut rng);
        let auth_path = vec![
            Some((
                bls12_381::Scalar::random(&mut rng),
                !rng.next_u32().is_multiple_of(2),
            ));
            tree_depth
        ];
        let ar = jubjub::Fr::random(&mut rng);

        {
            let rk = jubjub::AffinePoint::from_bytes(viewing_key.rk(ar).into()).unwrap();
            let expected_value_commitment = value_commitment.commitment().to_affine();
            assert_eq!(
                expected_value_commitment.get_u(),
                bls12_381::Scalar::from_str_vartime(expected_commitment_us[i as usize]).unwrap()
            );
            assert_eq!(
                expected_value_commitment.get_v(),
                bls12_381::Scalar::from_str_vartime(expected_commitment_vs[i as usize]).unwrap()
            );
            let note = Note::from_parts(
                payment_address,
                value_commitment.value,
                Rseed::BeforeZip212(commitment_randomness),
            );

            let mut position = 0u64;
            let cmu = note.cmu();
            let mut cur = bls12_381::Scalar::from_bytes(&cmu.to_bytes()).unwrap();

            for (i, val) in auth_path.clone().into_iter().enumerate() {
                let (uncle, b) = val.unwrap();

                let mut lhs = cur;
                let mut rhs = uncle;

                if b {
                    ::core::mem::swap(&mut lhs, &mut rhs);
                }

                let lhs = lhs.to_le_bits();
                let rhs = rhs.to_le_bits();

                cur = jubjub::ExtendedPoint::from(pedersen_hash::pedersen_hash(
                    pedersen_hash::Personalization::MerkleTree(i),
                    lhs.iter()
                        .by_vals()
                        .take(bls12_381::Scalar::NUM_BITS as usize)
                        .chain(
                            rhs.iter()
                                .by_vals()
                                .take(bls12_381::Scalar::NUM_BITS as usize),
                        ),
                ))
                .to_affine()
                .get_u();

                if b {
                    position |= 1 << i;
                }
            }

            let expected_nf = note.nf(&viewing_key.nk, position);
            let expected_nf = multipack::bytes_to_bits_le(&expected_nf.0);
            let expected_nf = multipack::compute_multipacking(&expected_nf);
            assert_eq!(expected_nf.len(), 2);

            let mut cs = TestConstraintSystem::new();

            let instance = Spend {
                value_commitment_opening: Some(value_commitment.clone()),
                proof_generation_key: Some(proof_generation_key.clone()),
                payment_address: Some(payment_address),
                commitment_randomness: Some(commitment_randomness),
                ar: Some(ar),
                auth_path: auth_path.clone(),
                anchor: Some(cur),
            };

            instance.synthesize(&mut cs).unwrap();

            assert!(cs.is_satisfied());
            assert_eq!(cs.num_constraints(), 98777);
            assert_eq!(
                cs.hash(),
                "d37c738e83df5d9b0bb6495ac96abf21bcb2697477e2c15c2c7916ff7a3b6a89"
            );

            assert_eq!(
                cs.get("randomization of note commitment/u3/num").to_repr(),
                cmu.to_bytes()
            );

            assert_eq!(cs.num_inputs(), 8);
            assert_eq!(cs.get_input(0, "ONE"), bls12_381::Scalar::one());
            assert_eq!(cs.get_input(1, "rk/u/input variable"), rk.get_u());
            assert_eq!(cs.get_input(2, "rk/v/input variable"), rk.get_v());
            assert_eq!(
                cs.get_input(3, "value commitment/commitment point/u/input variable"),
                expected_value_commitment.get_u()
            );
            assert_eq!(
                cs.get_input(4, "value commitment/commitment point/v/input variable"),
                expected_value_commitment.get_v()
            );
            assert_eq!(
                cs.get_input(5, "anchor/input variable").to_repr(),
                cur.to_bytes()
            );
            assert_eq!(cs.get_input(6, "pack nullifier/input 0"), expected_nf[0]);
            assert_eq!(cs.get_input(7, "pack nullifier/input 1"), expected_nf[1]);
        }
    }
}

#[test]
fn test_output_circuit_with_bls12_381() {
    use crate::{Diversifier, ProofGenerationKey, Rseed, keys::SpendValidatingKey};

    use bellman::gadgets::test::*;
    use group::ff::Field;
    use rand_core::{Rng, SeedableRng};
    use rand_xorshift::XorShiftRng;

    let mut rng = XorShiftRng::from_seed([
        0x58, 0x62, 0xbe, 0x3d, 0x76, 0x3d, 0x31, 0x8d, 0x17, 0xdb, 0x37, 0x32, 0x54, 0x06, 0xbc,
        0xe5,
    ]);

    for _ in 0..100 {
        let value_commitment = ValueCommitmentOpening {
            value: NoteValue::from_raw(rng.next_u64()),
            randomness: jubjub::Fr::random(&mut rng),
        };

        let nsk = jubjub::Fr::random(&mut rng);
        let ak = SpendValidatingKey::fake_random(&mut rng);

        let proof_generation_key = ProofGenerationKey { ak, nsk };

        let viewing_key = proof_generation_key.to_viewing_key();

        let payment_address;

        loop {
            let diversifier = {
                let mut d = [0; 11];
                rng.fill_bytes(&mut d);
                Diversifier(d)
            };

            if let Some(p) = viewing_key.to_payment_address(diversifier) {
                payment_address = p;
                break;
            }
        }

        let commitment_randomness = jubjub::Fr::random(&mut rng);
        let esk = jubjub::Fr::random(&mut rng);

        {
            let mut cs = TestConstraintSystem::new();

            let instance = Output {
                value_commitment_opening: Some(value_commitment.clone()),
                payment_address: Some(payment_address),
                commitment_randomness: Some(commitment_randomness),
                esk: Some(esk),
            };

            instance.synthesize(&mut cs).unwrap();

            assert!(cs.is_satisfied());
            assert_eq!(cs.num_constraints(), 7827);
            assert_eq!(
                cs.hash(),
                "c26d5cdfe6ccd65c03390902c02e11393ea6bb96aae32a7f2ecb12eb9103faee"
            );

            let expected_cmu = payment_address
                .create_note(
                    value_commitment.value,
                    Rseed::BeforeZip212(commitment_randomness),
                )
                .cmu();

            let expected_value_commitment = value_commitment.commitment().to_affine();

            let expected_epk = jubjub::ExtendedPoint::from(
                payment_address
                    .diversifier()
                    .g_d()
                    .expect("should be valid")
                    * esk,
            )
            .to_affine();

            assert_eq!(cs.num_inputs(), 6);
            assert_eq!(cs.get_input(0, "ONE"), bls12_381::Scalar::one());
            assert_eq!(
                cs.get_input(1, "value commitment/commitment point/u/input variable"),
                expected_value_commitment.get_u()
            );
            assert_eq!(
                cs.get_input(2, "value commitment/commitment point/v/input variable"),
                expected_value_commitment.get_v()
            );
            assert_eq!(
                cs.get_input(3, "epk/u/input variable"),
                expected_epk.get_u()
            );
            assert_eq!(
                cs.get_input(4, "epk/v/input variable"),
                expected_epk.get_v()
            );
            assert_eq!(
                cs.get_input(5, "commitment/input variable").to_repr(),
                expected_cmu.to_bytes()
            );
        }
    }
}