cargo fmt zcash_proofs

This commit is contained in:
Eirik Ogilvie-Wigley
2019-08-15 10:40:07 -06:00
parent 81c58172c3
commit 272be62212
11 changed files with 595 additions and 847 deletions

View File

@@ -1,31 +1,20 @@
use ff::{Field, PrimeField, PrimeFieldRepr};
use bellman::{
SynthesisError,
ConstraintSystem,
Circuit
};
use bellman::{Circuit, ConstraintSystem, SynthesisError};
use zcash_primitives::jubjub::{
JubjubEngine,
FixedGenerators
};
use zcash_primitives::jubjub::{FixedGenerators, JubjubEngine};
use zcash_primitives::constants;
use zcash_primitives::primitives::{
ValueCommitment,
ProofGenerationKey,
PaymentAddress
};
use zcash_primitives::primitives::{PaymentAddress, ProofGenerationKey, ValueCommitment};
use bellman::gadgets::Assignment;
use bellman::gadgets::boolean;
use super::ecc;
use super::pedersen_hash;
use bellman::gadgets::blake2s;
use bellman::gadgets::num;
use bellman::gadgets::boolean;
use bellman::gadgets::multipack;
use bellman::gadgets::num;
use bellman::gadgets::Assignment;
pub const TREE_DEPTH: usize = zcash_primitives::sapling::SAPLING_COMMITMENT_TREE_DEPTH;
@@ -54,7 +43,7 @@ pub struct Spend<'a, E: JubjubEngine> {
/// The anchor; the root of the tree. If the note being
/// spent is zero-value, this can be anything.
pub anchor: Option<E::Fr>
pub anchor: Option<E::Fr>,
}
/// This is an output circuit instance.
@@ -71,7 +60,7 @@ pub struct Output<'a, E: JubjubEngine> {
pub commitment_randomness: Option<E::Fs>,
/// The ephemeral secret key for DH with recipient
pub esk: Option<E::Fs>
pub esk: Option<E::Fs>,
}
/// Exposes a Pedersen commitment to the value as an
@@ -79,15 +68,16 @@ pub struct Output<'a, E: JubjubEngine> {
fn expose_value_commitment<E, CS>(
mut cs: CS,
value_commitment: Option<ValueCommitment<E>>,
params: &E::Params
params: &E::Params,
) -> Result<Vec<boolean::Boolean>, SynthesisError>
where E: JubjubEngine,
CS: ConstraintSystem<E>
where
E: JubjubEngine,
CS: ConstraintSystem<E>,
{
// Booleanize the value into little-endian bit order
let value_bits = boolean::u64_into_boolean_vec_le(
cs.namespace(|| "value"),
value_commitment.as_ref().map(|c| c.value)
value_commitment.as_ref().map(|c| c.value),
)?;
// Compute the note value in the exponent
@@ -95,7 +85,7 @@ fn expose_value_commitment<E, CS>(
cs.namespace(|| "compute the value in the exponent"),
FixedGenerators::ValueCommitmentValue,
&value_bits,
params
params,
)?;
// Booleanize the randomness. This does not ensure
@@ -103,7 +93,7 @@ fn expose_value_commitment<E, CS>(
// it doesn't matter for security.
let rcv = boolean::field_into_boolean_vec_le(
cs.namespace(|| "rcv"),
value_commitment.as_ref().map(|c| c.randomness)
value_commitment.as_ref().map(|c| c.randomness),
)?;
// Compute the randomness in the exponent
@@ -111,15 +101,11 @@ fn expose_value_commitment<E, CS>(
cs.namespace(|| "computation of rcv"),
FixedGenerators::ValueCommitmentRandomness,
&rcv,
params
params,
)?;
// Compute the Pedersen commitment to the value
let cv = value.add(
cs.namespace(|| "computation of cv"),
&rcv,
params
)?;
let cv = value.add(cs.namespace(|| "computation of cv"), &rcv, params)?;
// Expose the commitment as an input to the circuit
cv.inputize(cs.namespace(|| "commitment point"))?;
@@ -128,43 +114,32 @@ fn expose_value_commitment<E, CS>(
}
impl<'a, E: JubjubEngine> Circuit<E> for Spend<'a, E> {
fn synthesize<CS: ConstraintSystem<E>>(self, cs: &mut CS) -> Result<(), SynthesisError>
{
fn synthesize<CS: ConstraintSystem<E>>(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.clone()),
self.params
self.params,
)?;
// 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"),
self.params
)?;
ak.assert_not_small_order(cs.namespace(|| "ak not small order"), self.params)?;
// Rerandomize ak and expose it as an input to the circuit
{
let ar = boolean::field_into_boolean_vec_le(
cs.namespace(|| "ar"),
self.ar
)?;
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"),
FixedGenerators::SpendingKeyGenerator,
&ar,
self.params
self.params,
)?;
let rk = ak.add(
cs.namespace(|| "computation of rk"),
&ar,
self.params
)?;
let rk = ak.add(cs.namespace(|| "computation of rk"), &ar, self.params)?;
rk.inputize(cs.namespace(|| "rk"))?;
}
@@ -175,7 +150,7 @@ impl<'a, E: JubjubEngine> Circuit<E> for Spend<'a, E> {
// 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.clone())
self.proof_generation_key.as_ref().map(|k| k.nsk.clone()),
)?;
// NB: We don't ensure that the bit representation of nsk
@@ -188,7 +163,7 @@ impl<'a, E: JubjubEngine> Circuit<E> for Spend<'a, E> {
cs.namespace(|| "computation of nk"),
FixedGenerators::ProofGenerationKey,
&nsk,
self.params
self.params,
)?;
}
@@ -196,9 +171,7 @@ impl<'a, E: JubjubEngine> Circuit<E> for Spend<'a, E> {
let mut ivk_preimage = vec![];
// Place ak in the preimage for CRH^ivk
ivk_preimage.extend(
ak.repr(cs.namespace(|| "representation of ak"))?
);
ivk_preimage.extend(ak.repr(cs.namespace(|| "representation of ak"))?);
// This is the nullifier preimage for PRF^nf
let mut nf_preimage = vec![];
@@ -206,9 +179,7 @@ impl<'a, E: JubjubEngine> Circuit<E> for Spend<'a, E> {
// Extend ivk and nf preimages with the representation of
// nk.
{
let repr_nk = nk.repr(
cs.namespace(|| "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);
@@ -221,7 +192,7 @@ impl<'a, E: JubjubEngine> Circuit<E> for Spend<'a, E> {
let mut ivk = blake2s::blake2s(
cs.namespace(|| "computation of ivk"),
&ivk_preimage,
constants::CRH_IVK_PERSONALIZATION
constants::CRH_IVK_PERSONALIZATION,
)?;
// drop_5 to ensure it's in the field
@@ -239,7 +210,7 @@ impl<'a, E: JubjubEngine> Circuit<E> for Spend<'a, E> {
ecc::EdwardsPoint::witness(
cs.namespace(|| "witness g_d"),
self.payment_address.as_ref().and_then(|a| a.g_d(params)),
self.params
self.params,
)?
};
@@ -247,17 +218,10 @@ impl<'a, E: JubjubEngine> Circuit<E> for Spend<'a, E> {
// 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"),
self.params
)?;
g_d.assert_not_small_order(cs.namespace(|| "g_d not small order"), self.params)?;
// Compute pk_d = g_d^ivk
let pk_d = g_d.mul(
cs.namespace(|| "compute pk_d"),
&ivk,
self.params
)?;
let pk_d = g_d.mul(cs.namespace(|| "compute pk_d"), &ivk, self.params)?;
// Compute note contents:
// value (in big endian) followed by g_d and pk_d
@@ -271,18 +235,14 @@ impl<'a, E: JubjubEngine> Circuit<E> for Spend<'a, E> {
let value_bits = expose_value_commitment(
cs.namespace(|| "value commitment"),
self.value_commitment,
self.params
self.params,
)?;
// Compute the note's value as a linear combination
// of the bits.
let mut coeff = E::Fr::one();
for bit in &value_bits {
value_num = value_num.add_bool_with_coeff(
CS::one(),
bit,
coeff
);
value_num = value_num.add_bool_with_coeff(CS::one(), bit, coeff);
coeff.double();
}
@@ -291,14 +251,10 @@ impl<'a, E: JubjubEngine> Circuit<E> for Spend<'a, E> {
}
// Place g_d in the note
note_contents.extend(
g_d.repr(cs.namespace(|| "representation of g_d"))?
);
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"))?
);
note_contents.extend(pk_d.repr(cs.namespace(|| "representation of pk_d"))?);
assert_eq!(
note_contents.len(),
@@ -312,14 +268,14 @@ impl<'a, E: JubjubEngine> Circuit<E> for Spend<'a, E> {
cs.namespace(|| "note content hash"),
pedersen_hash::Personalization::NoteCommitment,
&note_contents,
self.params
self.params,
)?;
{
// Booleanize the randomness for the note commitment
let rcm = boolean::field_into_boolean_vec_le(
cs.namespace(|| "rcm"),
self.commitment_randomness
self.commitment_randomness,
)?;
// Compute the note commitment randomness in the exponent
@@ -327,7 +283,7 @@ impl<'a, E: JubjubEngine> Circuit<E> for Spend<'a, E> {
cs.namespace(|| "computation of commitment randomness"),
FixedGenerators::NoteCommitmentRandomness,
&rcm,
self.params
self.params,
)?;
// Randomize the note commitment. Pedersen hashes are not
@@ -335,7 +291,7 @@ impl<'a, E: JubjubEngine> Circuit<E> for Spend<'a, E> {
cm = cm.add(
cs.namespace(|| "randomization of note commitment"),
&rcm,
self.params
self.params,
)?;
}
@@ -356,7 +312,7 @@ impl<'a, E: JubjubEngine> Circuit<E> for Spend<'a, E> {
// depth of the tree.
let cur_is_right = boolean::Boolean::from(boolean::AllocatedBit::alloc(
cs.namespace(|| "position bit"),
e.map(|e| e.1)
e.map(|e| e.1),
)?);
// Push this boolean for nullifier computation later
@@ -364,19 +320,15 @@ impl<'a, E: JubjubEngine> Circuit<E> for Spend<'a, E> {
// Witness the authentication path element adjacent
// at this depth.
let path_element = num::AllocatedNum::alloc(
cs.namespace(|| "path element"),
|| {
Ok(e.get()?.0)
}
)?;
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 (xl, xr) = num::AllocatedNum::conditionally_reverse(
cs.namespace(|| "conditional reversal of preimage"),
&cur,
&path_element,
&cur_is_right
&cur_is_right,
)?;
// We don't need to be strict, because the function is
@@ -392,20 +344,19 @@ impl<'a, E: JubjubEngine> Circuit<E> for Spend<'a, E> {
cs.namespace(|| "computation of pedersen hash"),
pedersen_hash::Personalization::MerkleTree(i),
&preimage,
self.params
)?.get_x().clone(); // Injective encoding
self.params,
)?
.get_x()
.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()?)
}
)?;
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
@@ -414,7 +365,7 @@ impl<'a, E: JubjubEngine> Circuit<E> for Spend<'a, E> {
|| "conditionally enforce correct root",
|lc| lc + cur.get_variable() - rt.get_variable(),
|lc| lc + &value_num.lc(E::Fr::one()),
|lc| lc
|lc| lc,
);
// Expose the anchor
@@ -430,29 +381,27 @@ impl<'a, E: JubjubEngine> Circuit<E> for Spend<'a, E> {
cs.namespace(|| "g^position"),
FixedGenerators::NullifierPosition,
&position_bits,
self.params
self.params,
)?;
// Add the position to the commitment
rho = rho.add(
cs.namespace(|| "faerie gold prevention"),
&position,
self.params
self.params,
)?;
}
// Let's compute nf = BLAKE2s(nk || rho)
nf_preimage.extend(
rho.repr(cs.namespace(|| "representation of 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,
constants::PRF_NF_PERSONALIZATION
constants::PRF_NF_PERSONALIZATION,
)?;
multipack::pack_into_inputs(cs.namespace(|| "pack nullifier"), &nf)
@@ -460,8 +409,7 @@ impl<'a, E: JubjubEngine> Circuit<E> for Spend<'a, E> {
}
impl<'a, E: JubjubEngine> Circuit<E> for Output<'a, E> {
fn synthesize<CS: ConstraintSystem<E>>(self, cs: &mut CS) -> Result<(), SynthesisError>
{
fn synthesize<CS: ConstraintSystem<E>>(self, cs: &mut CS) -> Result<(), SynthesisError> {
// Let's start to construct our note, which contains
// value (big endian)
let mut note_contents = vec![];
@@ -471,7 +419,7 @@ impl<'a, E: JubjubEngine> Circuit<E> for Output<'a, E> {
note_contents.extend(expose_value_commitment(
cs.namespace(|| "value commitment"),
self.value_commitment,
self.params
self.params,
)?);
// Let's deal with g_d
@@ -483,7 +431,7 @@ impl<'a, E: JubjubEngine> Circuit<E> for Output<'a, E> {
let g_d = ecc::EdwardsPoint::witness(
cs.namespace(|| "witness g_d"),
self.payment_address.as_ref().and_then(|a| a.g_d(params)),
self.params
self.params,
)?;
// g_d is ensured to be large order. The relationship
@@ -495,29 +443,17 @@ impl<'a, E: JubjubEngine> Circuit<E> for Output<'a, E> {
//
// 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"),
self.params
)?;
g_d.assert_not_small_order(cs.namespace(|| "g_d not small order"), self.params)?;
// Extend our note contents with the representation of
// g_d.
note_contents.extend(
g_d.repr(cs.namespace(|| "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
)?;
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,
self.params
)?;
let epk = g_d.mul(cs.namespace(|| "epk computation"), &esk, self.params)?;
// Expose epk publicly.
epk.inputize(cs.namespace(|| "epk"))?;
@@ -534,13 +470,13 @@ impl<'a, E: JubjubEngine> Circuit<E> for Output<'a, E> {
// endian bits (to match the representation)
let y_contents = boolean::field_into_boolean_vec_le(
cs.namespace(|| "pk_d bits of y"),
pk_d.map(|e| e.1)
pk_d.map(|e| e.1),
)?;
// Witness the sign bit
let sign_bit = boolean::Boolean::from(boolean::AllocatedBit::alloc(
cs.namespace(|| "pk_d bit of x"),
pk_d.map(|e| e.0.into_repr().is_odd())
pk_d.map(|e| e.0.into_repr().is_odd()),
)?);
// Extend the note with pk_d representation
@@ -560,14 +496,14 @@ impl<'a, E: JubjubEngine> Circuit<E> for Output<'a, E> {
cs.namespace(|| "note content hash"),
pedersen_hash::Personalization::NoteCommitment,
&note_contents,
self.params
self.params,
)?;
{
// Booleanize the randomness
let rcm = boolean::field_into_boolean_vec_le(
cs.namespace(|| "rcm"),
self.commitment_randomness
self.commitment_randomness,
)?;
// Compute the note commitment randomness in the exponent
@@ -575,14 +511,14 @@ impl<'a, E: JubjubEngine> Circuit<E> for Output<'a, E> {
cs.namespace(|| "computation of commitment randomness"),
FixedGenerators::NoteCommitmentRandomness,
&rcm,
self.params
self.params,
)?;
// Randomize our note commitment
cm = cm.add(
cs.namespace(|| "randomization of note commitment"),
&rcm,
self.params
self.params,
)?;
}
@@ -604,7 +540,7 @@ fn test_input_circuit_with_bls12_381() {
use rand_core::{RngCore, SeedableRng};
use rand_xorshift::XorShiftRng;
use zcash_primitives::{
jubjub::{JubjubBls12, fs, edwards},
jubjub::{edwards, fs, JubjubBls12},
pedersen_hash,
primitives::{Diversifier, Note, ProofGenerationKey},
};
@@ -628,7 +564,7 @@ fn test_input_circuit_with_bls12_381() {
let proof_generation_key = ProofGenerationKey {
ak: ak.clone(),
nsk: nsk.clone()
nsk: nsk.clone(),
};
let viewing_key = proof_generation_key.into_viewing_key(params);
@@ -642,11 +578,7 @@ fn test_input_circuit_with_bls12_381() {
Diversifier(d)
};
if let Some(p) = viewing_key.into_payment_address(
diversifier,
params
)
{
if let Some(p) = viewing_key.into_payment_address(diversifier, params) {
payment_address = p;
break;
}
@@ -664,15 +596,14 @@ fn test_input_circuit_with_bls12_381() {
value: value_commitment.value,
g_d: g_d.clone(),
pk_d: payment_address.pk_d.clone(),
r: commitment_randomness.clone()
r: commitment_randomness.clone(),
};
let mut position = 0u64;
let cm: Fr = note.cm(params);
let mut cur = cm.clone();
for (i, val) in auth_path.clone().into_iter().enumerate()
{
for (i, val) in auth_path.clone().into_iter().enumerate() {
let (uncle, b) = val.unwrap();
let mut lhs = cur;
@@ -691,10 +622,12 @@ fn test_input_circuit_with_bls12_381() {
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;
.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;
@@ -716,14 +649,17 @@ fn test_input_circuit_with_bls12_381() {
commitment_randomness: Some(commitment_randomness),
ar: Some(ar),
auth_path: auth_path.clone(),
anchor: Some(cur)
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.hash(),
"d37c738e83df5d9b0bb6495ac96abf21bcb2697477e2c15c2c7916ff7a3b6a89"
);
assert_eq!(cs.get("randomization of note commitment/x3/num"), cm);
@@ -731,8 +667,14 @@ fn test_input_circuit_with_bls12_381() {
assert_eq!(cs.get_input(0, "ONE"), Fr::one());
assert_eq!(cs.get_input(1, "rk/x/input variable"), rk.0);
assert_eq!(cs.get_input(2, "rk/y/input variable"), rk.1);
assert_eq!(cs.get_input(3, "value commitment/commitment point/x/input variable"), expected_value_cm.0);
assert_eq!(cs.get_input(4, "value commitment/commitment point/y/input variable"), expected_value_cm.1);
assert_eq!(
cs.get_input(3, "value commitment/commitment point/x/input variable"),
expected_value_cm.0
);
assert_eq!(
cs.get_input(4, "value commitment/commitment point/y/input variable"),
expected_value_cm.1
);
assert_eq!(cs.get_input(5, "anchor/input variable"), cur);
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]);
@@ -748,7 +690,7 @@ fn test_output_circuit_with_bls12_381() {
use rand_core::{RngCore, SeedableRng};
use rand_xorshift::XorShiftRng;
use zcash_primitives::{
jubjub::{JubjubBls12, fs, edwards},
jubjub::{edwards, fs, JubjubBls12},
primitives::{Diversifier, ProofGenerationKey},
};
@@ -769,7 +711,7 @@ fn test_output_circuit_with_bls12_381() {
let proof_generation_key = ProofGenerationKey {
ak: ak.clone(),
nsk: nsk.clone()
nsk: nsk.clone(),
};
let viewing_key = proof_generation_key.into_viewing_key(params);
@@ -783,11 +725,7 @@ fn test_output_circuit_with_bls12_381() {
Diversifier(d)
};
if let Some(p) = viewing_key.into_payment_address(
diversifier,
params
)
{
if let Some(p) = viewing_key.into_payment_address(diversifier, params) {
payment_address = p;
break;
}
@@ -804,30 +742,41 @@ fn test_output_circuit_with_bls12_381() {
value_commitment: Some(value_commitment.clone()),
payment_address: Some(payment_address.clone()),
commitment_randomness: Some(commitment_randomness),
esk: Some(esk.clone())
esk: Some(esk.clone()),
};
instance.synthesize(&mut cs).unwrap();
assert!(cs.is_satisfied());
assert_eq!(cs.num_constraints(), 7827);
assert_eq!(cs.hash(), "c26d5cdfe6ccd65c03390902c02e11393ea6bb96aae32a7f2ecb12eb9103faee");
assert_eq!(
cs.hash(),
"c26d5cdfe6ccd65c03390902c02e11393ea6bb96aae32a7f2ecb12eb9103faee"
);
let expected_cm = payment_address.create_note(
value_commitment.value,
commitment_randomness,
params
).expect("should be valid").cm(params);
let expected_cm = payment_address
.create_note(value_commitment.value, commitment_randomness, params)
.expect("should be valid")
.cm(params);
let expected_value_cm = value_commitment.cm(params).into_xy();
let expected_epk = payment_address.g_d(params).expect("should be valid").mul(esk, params);
let expected_epk = payment_address
.g_d(params)
.expect("should be valid")
.mul(esk, params);
let expected_epk_xy = expected_epk.into_xy();
assert_eq!(cs.num_inputs(), 6);
assert_eq!(cs.get_input(0, "ONE"), Fr::one());
assert_eq!(cs.get_input(1, "value commitment/commitment point/x/input variable"), expected_value_cm.0);
assert_eq!(cs.get_input(2, "value commitment/commitment point/y/input variable"), expected_value_cm.1);
assert_eq!(
cs.get_input(1, "value commitment/commitment point/x/input variable"),
expected_value_cm.0
);
assert_eq!(
cs.get_input(2, "value commitment/commitment point/y/input variable"),
expected_value_cm.1
);
assert_eq!(cs.get_input(3, "epk/x/input variable"), expected_epk_xy.0);
assert_eq!(cs.get_input(4, "epk/y/input variable"), expected_epk_xy.1);
assert_eq!(cs.get_input(5, "commitment/input variable"), expected_cm);