From 718b25c94991895eadbb09d4cf8b5d7e35e0d588 Mon Sep 17 00:00:00 2001
From: Jack Grigg <jack@z.cash>
Date: Mon, 2 Jul 2018 16:43:17 +0100
Subject: [PATCH 1/6] Use ff crate for Field traits

---
 Cargo.toml                        |  6 +++++-
 src/domain.rs                     |  3 +--
 src/groth16/generator.rs          |  3 +--
 src/groth16/mod.rs                |  2 +-
 src/groth16/prover.rs             |  3 +--
 src/groth16/tests/dummy_engine.rs | 14 +++++++-------
 src/groth16/tests/mod.rs          |  7 ++-----
 src/groth16/verifier.rs           |  2 +-
 src/lib.rs                        |  4 +++-
 src/multiexp.rs                   | 19 ++++++++-----------
 tests/mimc.rs                     |  7 +++----
 11 files changed, 33 insertions(+), 37 deletions(-)

diff --git a/Cargo.toml b/Cargo.toml
index 3a9105f7c..86914bb4f 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -11,12 +11,16 @@ version = "0.1.0"
 [dependencies]
 rand = "0.4"
 bit-vec = "0.4.4"
+ff = "0.4"
 futures = "0.1"
 futures-cpupool = "0.1"
 num_cpus = "1"
 crossbeam = "0.3"
-pairing = "0.14"
 byteorder = "1"
 
+[dependencies.pairing]
+git = "https://github.com/ebfull/pairing"
+rev = "183a64b08e9dc7067f78624ec161371f1829623e"
+
 [features]
 default = []
diff --git a/src/domain.rs b/src/domain.rs
index ff626e5d0..886b4644f 100644
--- a/src/domain.rs
+++ b/src/domain.rs
@@ -10,10 +10,9 @@
 //! This allows us to perform polynomial operations in O(n)
 //! by performing an O(n log n) FFT over such a domain.
 
+use ff::{Field, PrimeField};
 use pairing::{
     Engine,
-    Field,
-    PrimeField,
     CurveProjective
 };
 
diff --git a/src/groth16/generator.rs b/src/groth16/generator.rs
index 1eed62db0..2b319ea46 100644
--- a/src/groth16/generator.rs
+++ b/src/groth16/generator.rs
@@ -2,10 +2,9 @@ use rand::Rng;
 
 use std::sync::Arc;
 
+use ff::{Field, PrimeField};
 use pairing::{
     Engine,
-    PrimeField,
-    Field,
     Wnaf,
     CurveProjective,
     CurveAffine
diff --git a/src/groth16/mod.rs b/src/groth16/mod.rs
index 3b8d67148..a55b6c838 100644
--- a/src/groth16/mod.rs
+++ b/src/groth16/mod.rs
@@ -486,8 +486,8 @@ mod test_with_bls12_381 {
     use super::*;
     use {Circuit, SynthesisError, ConstraintSystem};
 
+    use ff::Field;
     use rand::{Rand, thread_rng};
-    use pairing::{Field};
     use pairing::bls12_381::{Bls12, Fr};
 
     #[test]
diff --git a/src/groth16/prover.rs b/src/groth16/prover.rs
index f21fcce90..7e53120e6 100644
--- a/src/groth16/prover.rs
+++ b/src/groth16/prover.rs
@@ -4,10 +4,9 @@ use std::sync::Arc;
 
 use futures::Future;
 
+use ff::{Field, PrimeField};
 use pairing::{
     Engine,
-    PrimeField,
-    Field,
     CurveProjective,
     CurveAffine
 };
diff --git a/src/groth16/tests/dummy_engine.rs b/src/groth16/tests/dummy_engine.rs
index 26c899650..c739f34d5 100644
--- a/src/groth16/tests/dummy_engine.rs
+++ b/src/groth16/tests/dummy_engine.rs
@@ -1,13 +1,10 @@
+use ff::{
+    Field, LegendreSymbol, PrimeField, PrimeFieldDecodingError,
+    PrimeFieldRepr, ScalarEngine, SqrtField};
 use pairing::{
     Engine,
-    PrimeField,
-    PrimeFieldRepr,
-    Field,
-    SqrtField,
-    LegendreSymbol,
     CurveProjective,
     CurveAffine,
-    PrimeFieldDecodingError,
     GroupDecodingError,
     EncodedPoint
 };
@@ -263,8 +260,11 @@ impl PrimeField for Fr {
 #[derive(Clone)]
 pub struct DummyEngine;
 
-impl Engine for DummyEngine {
+impl ScalarEngine for DummyEngine {
     type Fr = Fr;
+}
+
+impl Engine for DummyEngine {
     type G1 = Fr;
     type G1Affine = Fr;
     type G2 = Fr;
diff --git a/src/groth16/tests/mod.rs b/src/groth16/tests/mod.rs
index a8e291477..0e05c36ab 100644
--- a/src/groth16/tests/mod.rs
+++ b/src/groth16/tests/mod.rs
@@ -1,8 +1,5 @@
-use pairing::{
-    Engine,
-    Field,
-    PrimeField
-};
+use ff::{Field, PrimeField};
+use pairing::Engine;
 
 mod dummy_engine;
 use self::dummy_engine::*;
diff --git a/src/groth16/verifier.rs b/src/groth16/verifier.rs
index 083e1d025..a4e914bc3 100644
--- a/src/groth16/verifier.rs
+++ b/src/groth16/verifier.rs
@@ -1,8 +1,8 @@
+use ff::PrimeField;
 use pairing::{
     Engine,
     CurveProjective,
     CurveAffine,
-    PrimeField
 };
 
 use super::{
diff --git a/src/lib.rs b/src/lib.rs
index fb8d0431b..2ddb4ac3b 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -1,3 +1,4 @@
+extern crate ff;
 extern crate pairing;
 extern crate rand;
 extern crate num_cpus;
@@ -12,7 +13,8 @@ mod multiexp;
 pub mod domain;
 pub mod groth16;
 
-use pairing::{Engine, Field};
+use ff::Field;
+use pairing::Engine;
 
 use std::ops::{Add, Sub};
 use std::fmt;
diff --git a/src/multiexp.rs b/src/multiexp.rs
index b1dc1f1fc..2481d863e 100644
--- a/src/multiexp.rs
+++ b/src/multiexp.rs
@@ -1,10 +1,7 @@
+use ff::{Field, PrimeField, PrimeFieldRepr, ScalarEngine};
 use pairing::{
     CurveAffine,
     CurveProjective,
-    Engine,
-    PrimeField,
-    Field,
-    PrimeFieldRepr
 };
 use std::sync::Arc;
 use std::io;
@@ -141,7 +138,7 @@ fn multiexp_inner<Q, D, G, S>(
     pool: &Worker,
     bases: S,
     density_map: D,
-    exponents: Arc<Vec<<<G::Engine as Engine>::Fr as PrimeField>::Repr>>,
+    exponents: Arc<Vec<<<G::Engine as ScalarEngine>::Fr as PrimeField>::Repr>>,
     mut skip: u32,
     c: u32,
     handle_trivial: bool
@@ -167,8 +164,8 @@ fn multiexp_inner<Q, D, G, S>(
             // Create space for the buckets
             let mut buckets = vec![<G as CurveAffine>::Projective::zero(); (1 << c) - 1];
 
-            let zero = <G::Engine as Engine>::Fr::zero().into_repr();
-            let one = <G::Engine as Engine>::Fr::one().into_repr();
+            let zero = <G::Engine as ScalarEngine>::Fr::zero().into_repr();
+            let one = <G::Engine as ScalarEngine>::Fr::one().into_repr();
 
             // Sort the bases into buckets
             for (&exp, density) in exponents.iter().zip(density_map.as_ref().iter()) {
@@ -211,7 +208,7 @@ fn multiexp_inner<Q, D, G, S>(
 
     skip += c;
 
-    if skip >= <G::Engine as Engine>::Fr::NUM_BITS {
+    if skip >= <G::Engine as ScalarEngine>::Fr::NUM_BITS {
         // There isn't another region.
         Box::new(this)
     } else {
@@ -238,7 +235,7 @@ pub fn multiexp<Q, D, G, S>(
     pool: &Worker,
     bases: S,
     density_map: D,
-    exponents: Arc<Vec<<<G::Engine as Engine>::Fr as PrimeField>::Repr>>
+    exponents: Arc<Vec<<<G::Engine as ScalarEngine>::Fr as PrimeField>::Repr>>
 ) -> Box<Future<Item=<G as CurveAffine>::Projective, Error=SynthesisError>>
     where for<'a> &'a Q: QueryDensity,
           D: Send + Sync + 'static + Clone + AsRef<Q>,
@@ -280,12 +277,12 @@ fn test_with_bls12() {
     }
 
     use rand::{self, Rand};
-    use pairing::bls12_381::Bls12;
+    use pairing::{bls12_381::Bls12, Engine};
 
     const SAMPLES: usize = 1 << 14;
 
     let rng = &mut rand::thread_rng();
-    let v = Arc::new((0..SAMPLES).map(|_| <Bls12 as Engine>::Fr::rand(rng).into_repr()).collect::<Vec<_>>());
+    let v = Arc::new((0..SAMPLES).map(|_| <Bls12 as ScalarEngine>::Fr::rand(rng).into_repr()).collect::<Vec<_>>());
     let g = Arc::new((0..SAMPLES).map(|_| <Bls12 as Engine>::G1::rand(rng).into_affine()).collect::<Vec<_>>());
 
     let naive = naive_multiexp(g.clone(), v.clone());
diff --git a/tests/mimc.rs b/tests/mimc.rs
index d6ff72b7b..1d554a57d 100644
--- a/tests/mimc.rs
+++ b/tests/mimc.rs
@@ -1,4 +1,5 @@
 extern crate bellman;
+extern crate ff;
 extern crate pairing;
 extern crate rand;
 
@@ -9,10 +10,8 @@ use rand::{thread_rng, Rng};
 use std::time::{Duration, Instant};
 
 // Bring in some tools for using pairing-friendly curves
-use pairing::{
-    Engine,
-    Field
-};
+use ff::Field;
+use pairing::Engine;
 
 // We're going to use the BLS12-381 pairing-friendly elliptic curve.
 use pairing::bls12_381::{

From 3e8f2f820253392415f61347d3435086732986a2 Mon Sep 17 00:00:00 2001
From: Jack Grigg <jack@z.cash>
Date: Fri, 6 Jul 2018 21:24:03 +0100
Subject: [PATCH 2/6] Use group crate for curve traits and wNAF

---
 Cargo.toml                        |  5 +++--
 src/domain.rs                     | 10 ++++------
 src/groth16/generator.rs          |  8 ++------
 src/groth16/mod.rs                |  8 ++++----
 src/groth16/prover.rs             |  7 ++-----
 src/groth16/tests/dummy_engine.rs | 30 ++++++++++++++----------------
 src/groth16/verifier.rs           |  7 ++-----
 src/lib.rs                        |  1 +
 src/multiexp.rs                   |  5 +----
 9 files changed, 33 insertions(+), 48 deletions(-)

diff --git a/Cargo.toml b/Cargo.toml
index 86914bb4f..8abf83ee1 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -14,13 +14,14 @@ bit-vec = "0.4.4"
 ff = "0.4"
 futures = "0.1"
 futures-cpupool = "0.1"
+group = "0.1"
 num_cpus = "1"
 crossbeam = "0.3"
 byteorder = "1"
 
 [dependencies.pairing]
-git = "https://github.com/ebfull/pairing"
-rev = "183a64b08e9dc7067f78624ec161371f1829623e"
+git = "https://github.com/str4d/pairing"
+rev = "3d41ee5abaa4888ff3607689aba007be8856816d"
 
 [features]
 default = []
diff --git a/src/domain.rs b/src/domain.rs
index 886b4644f..26cb4f948 100644
--- a/src/domain.rs
+++ b/src/domain.rs
@@ -10,11 +10,9 @@
 //! This allows us to perform polynomial operations in O(n)
 //! by performing an O(n log n) FFT over such a domain.
 
-use ff::{Field, PrimeField};
-use pairing::{
-    Engine,
-    CurveProjective
-};
+use ff::{Field, PrimeField, ScalarEngine};
+use group::CurveProjective;
+use pairing::Engine;
 
 use super::{
     SynthesisError
@@ -188,7 +186,7 @@ impl<E: Engine, G: Group<E>> EvaluationDomain<E, G> {
     }
 }
 
-pub trait Group<E: Engine>: Sized + Copy + Clone + Send + Sync {
+pub trait Group<E: ScalarEngine>: Sized + Copy + Clone + Send + Sync {
     fn group_zero() -> Self;
     fn group_mul_assign(&mut self, by: &E::Fr);
     fn group_add_assign(&mut self, other: &Self);
diff --git a/src/groth16/generator.rs b/src/groth16/generator.rs
index 2b319ea46..f3f3d3afd 100644
--- a/src/groth16/generator.rs
+++ b/src/groth16/generator.rs
@@ -3,12 +3,8 @@ use rand::Rng;
 use std::sync::Arc;
 
 use ff::{Field, PrimeField};
-use pairing::{
-    Engine,
-    Wnaf,
-    CurveProjective,
-    CurveAffine
-};
+use group::{CurveAffine, CurveProjective, Wnaf};
+use pairing::Engine;
 
 use super::{
     Parameters,
diff --git a/src/groth16/mod.rs b/src/groth16/mod.rs
index a55b6c838..620f32edb 100644
--- a/src/groth16/mod.rs
+++ b/src/groth16/mod.rs
@@ -1,7 +1,7 @@
+use group::{CurveAffine, EncodedPoint};
 use pairing::{
     Engine,
-    CurveAffine,
-    EncodedPoint
+    PairingCurveAffine,
 };
 
 use ::{
@@ -385,9 +385,9 @@ pub struct PreparedVerifyingKey<E: Engine> {
     /// Pairing result of alpha*beta
     alpha_g1_beta_g2: E::Fqk,
     /// -gamma in G2
-    neg_gamma_g2: <E::G2Affine as CurveAffine>::Prepared,
+    neg_gamma_g2: <E::G2Affine as PairingCurveAffine>::Prepared,
     /// -delta in G2
-    neg_delta_g2: <E::G2Affine as CurveAffine>::Prepared,
+    neg_delta_g2: <E::G2Affine as PairingCurveAffine>::Prepared,
     /// Copy of IC from `VerifiyingKey`.
     ic: Vec<E::G1Affine>
 }
diff --git a/src/groth16/prover.rs b/src/groth16/prover.rs
index 7e53120e6..c674622cf 100644
--- a/src/groth16/prover.rs
+++ b/src/groth16/prover.rs
@@ -5,11 +5,8 @@ use std::sync::Arc;
 use futures::Future;
 
 use ff::{Field, PrimeField};
-use pairing::{
-    Engine,
-    CurveProjective,
-    CurveAffine
-};
+use group::{CurveAffine, CurveProjective};
+use pairing::Engine;
 
 use super::{
     ParameterSource,
diff --git a/src/groth16/tests/dummy_engine.rs b/src/groth16/tests/dummy_engine.rs
index c739f34d5..d5f37a971 100644
--- a/src/groth16/tests/dummy_engine.rs
+++ b/src/groth16/tests/dummy_engine.rs
@@ -1,13 +1,8 @@
 use ff::{
     Field, LegendreSymbol, PrimeField, PrimeFieldDecodingError,
     PrimeFieldRepr, ScalarEngine, SqrtField};
-use pairing::{
-    Engine,
-    CurveProjective,
-    CurveAffine,
-    GroupDecodingError,
-    EncodedPoint
-};
+use group::{CurveAffine, CurveProjective, EncodedPoint, GroupDecodingError};
+use pairing::{Engine, PairingCurveAffine};
 
 use std::cmp::Ordering;
 use std::fmt;
@@ -277,8 +272,8 @@ impl Engine for DummyEngine {
 
     fn miller_loop<'a, I>(i: I) -> Self::Fqk
         where I: IntoIterator<Item=&'a (
-                                    &'a <Self::G1Affine as CurveAffine>::Prepared,
-                                    &'a <Self::G2Affine as CurveAffine>::Prepared
+                                    &'a <Self::G1Affine as PairingCurveAffine>::Prepared,
+                                    &'a <Self::G2Affine as PairingCurveAffine>::Prepared
                                )>
     {
         let mut acc = <Fr as Field>::zero();
@@ -401,11 +396,8 @@ impl EncodedPoint for FakePoint {
 }
 
 impl CurveAffine for Fr {
-    type Pair = Fr;
-    type PairingResult = Fr;
     type Compressed = FakePoint;
     type Uncompressed = FakePoint;
-    type Prepared = Fr;
     type Projective = Fr;
     type Base = Fr;
     type Scalar = Fr;
@@ -437,6 +429,16 @@ impl CurveAffine for Fr {
         res
     }
 
+    fn into_projective(&self) -> Self::Projective {
+        *self
+    }
+}
+
+impl PairingCurveAffine for Fr {
+    type Prepared = Fr;
+    type Pair = Fr;
+    type PairingResult = Fr;
+
     fn prepare(&self) -> Self::Prepared {
         *self
     }
@@ -444,8 +446,4 @@ impl CurveAffine for Fr {
     fn pairing_with(&self, other: &Self::Pair) -> Self::PairingResult {
         self.mul(*other)
     }
-
-    fn into_projective(&self) -> Self::Projective {
-        *self
-    }
 }
diff --git a/src/groth16/verifier.rs b/src/groth16/verifier.rs
index a4e914bc3..71c747837 100644
--- a/src/groth16/verifier.rs
+++ b/src/groth16/verifier.rs
@@ -1,9 +1,6 @@
 use ff::PrimeField;
-use pairing::{
-    Engine,
-    CurveProjective,
-    CurveAffine,
-};
+use group::{CurveAffine, CurveProjective};
+use pairing::{Engine, PairingCurveAffine};
 
 use super::{
     Proof,
diff --git a/src/lib.rs b/src/lib.rs
index 2ddb4ac3b..6beaddd7f 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -1,4 +1,5 @@
 extern crate ff;
+extern crate group;
 extern crate pairing;
 extern crate rand;
 extern crate num_cpus;
diff --git a/src/multiexp.rs b/src/multiexp.rs
index 2481d863e..cea13f342 100644
--- a/src/multiexp.rs
+++ b/src/multiexp.rs
@@ -1,8 +1,5 @@
 use ff::{Field, PrimeField, PrimeFieldRepr, ScalarEngine};
-use pairing::{
-    CurveAffine,
-    CurveProjective,
-};
+use group::{CurveAffine, CurveProjective};
 use std::sync::Arc;
 use std::io;
 use bit_vec::{self, BitVec};

From 276e09f1fb6c11598a799b815702046de82e5e9f Mon Sep 17 00:00:00 2001
From: Jack Grigg <jack@z.cash>
Date: Fri, 6 Jul 2018 21:37:18 +0100
Subject: [PATCH 3/6] Use ff:ScalarEngine instead of pairing::Engine in bellman
 core

---
 src/domain.rs | 27 +++++++++++++--------------
 src/lib.rs    | 37 ++++++++++++++++++-------------------
 2 files changed, 31 insertions(+), 33 deletions(-)

diff --git a/src/domain.rs b/src/domain.rs
index 26cb4f948..87a824084 100644
--- a/src/domain.rs
+++ b/src/domain.rs
@@ -12,7 +12,6 @@
 
 use ff::{Field, PrimeField, ScalarEngine};
 use group::CurveProjective;
-use pairing::Engine;
 
 use super::{
     SynthesisError
@@ -20,7 +19,7 @@ use super::{
 
 use super::multicore::Worker;
 
-pub struct EvaluationDomain<E: Engine, G: Group<E>> {
+pub struct EvaluationDomain<E: ScalarEngine, G: Group<E>> {
     coeffs: Vec<G>,
     exp: u32,
     omega: E::Fr,
@@ -29,7 +28,7 @@ pub struct EvaluationDomain<E: Engine, G: Group<E>> {
     minv: E::Fr
 }
 
-impl<E: Engine, G: Group<E>> EvaluationDomain<E, G> {
+impl<E: ScalarEngine, G: Group<E>> EvaluationDomain<E, G> {
     pub fn as_ref(&self) -> &[G] {
         &self.coeffs
     }
@@ -224,23 +223,23 @@ impl<G: CurveProjective> Group<G::Engine> for Point<G> {
     }
 }
 
-pub struct Scalar<E: Engine>(pub E::Fr);
+pub struct Scalar<E: ScalarEngine>(pub E::Fr);
 
-impl<E: Engine> PartialEq for Scalar<E> {
+impl<E: ScalarEngine> PartialEq for Scalar<E> {
     fn eq(&self, other: &Scalar<E>) -> bool {
         self.0 == other.0
     }
 }
 
-impl<E: Engine> Copy for Scalar<E> { }
+impl<E: ScalarEngine> Copy for Scalar<E> { }
 
-impl<E: Engine> Clone for Scalar<E> {
+impl<E: ScalarEngine> Clone for Scalar<E> {
     fn clone(&self) -> Scalar<E> {
         *self
     }
 }
 
-impl<E: Engine> Group<E> for Scalar<E> {
+impl<E: ScalarEngine> Group<E> for Scalar<E> {
     fn group_zero() -> Self {
         Scalar(E::Fr::zero())
     }
@@ -255,7 +254,7 @@ impl<E: Engine> Group<E> for Scalar<E> {
     }
 }
 
-fn best_fft<E: Engine, T: Group<E>>(a: &mut [T], worker: &Worker, omega: &E::Fr, log_n: u32)
+fn best_fft<E: ScalarEngine, T: Group<E>>(a: &mut [T], worker: &Worker, omega: &E::Fr, log_n: u32)
 {
     let log_cpus = worker.log_num_cpus();
 
@@ -266,7 +265,7 @@ fn best_fft<E: Engine, T: Group<E>>(a: &mut [T], worker: &Worker, omega: &E::Fr,
     }
 }
 
-fn serial_fft<E: Engine, T: Group<E>>(a: &mut [T], omega: &E::Fr, log_n: u32)
+fn serial_fft<E: ScalarEngine, T: Group<E>>(a: &mut [T], omega: &E::Fr, log_n: u32)
 {
     fn bitreverse(mut n: u32, l: u32) -> u32 {
         let mut r = 0;
@@ -311,7 +310,7 @@ fn serial_fft<E: Engine, T: Group<E>>(a: &mut [T], omega: &E::Fr, log_n: u32)
     }
 }
 
-fn parallel_fft<E: Engine, T: Group<E>>(
+fn parallel_fft<E: ScalarEngine, T: Group<E>>(
     a: &mut [T],
     worker: &Worker,
     omega: &E::Fr,
@@ -377,7 +376,7 @@ fn polynomial_arith() {
     use pairing::bls12_381::Bls12;
     use rand::{self, Rand};
 
-    fn test_mul<E: Engine, R: rand::Rng>(rng: &mut R)
+    fn test_mul<E: ScalarEngine, R: rand::Rng>(rng: &mut R)
     {
         let worker = Worker::new();
 
@@ -424,7 +423,7 @@ fn fft_composition() {
     use pairing::bls12_381::Bls12;
     use rand;
 
-    fn test_comp<E: Engine, R: rand::Rng>(rng: &mut R)
+    fn test_comp<E: ScalarEngine, R: rand::Rng>(rng: &mut R)
     {
         let worker = Worker::new();
 
@@ -463,7 +462,7 @@ fn parallel_fft_consistency() {
     use rand::{self, Rand};
     use std::cmp::min;
 
-    fn test_consistency<E: Engine, R: rand::Rng>(rng: &mut R)
+    fn test_consistency<E: ScalarEngine, R: rand::Rng>(rng: &mut R)
     {
         let worker = Worker::new();
 
diff --git a/src/lib.rs b/src/lib.rs
index 6beaddd7f..42eccea07 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -14,8 +14,7 @@ mod multiexp;
 pub mod domain;
 pub mod groth16;
 
-use ff::Field;
-use pairing::Engine;
+use ff::{Field, ScalarEngine};
 
 use std::ops::{Add, Sub};
 use std::fmt;
@@ -27,7 +26,7 @@ use std::marker::PhantomData;
 /// rank-1 quadratic constraint systems. The `Circuit` trait represents a
 /// circuit that can be synthesized. The `synthesize` method is called during
 /// CRS generation and during proving.
-pub trait Circuit<E: Engine> {
+pub trait Circuit<E: ScalarEngine> {
     /// Synthesize the circuit into a rank-1 quadratic constraint system
     fn synthesize<CS: ConstraintSystem<E>>(
         self,
@@ -64,21 +63,21 @@ pub enum Index {
 /// This represents a linear combination of some variables, with coefficients
 /// in the scalar field of a pairing-friendly elliptic curve group.
 #[derive(Clone)]
-pub struct LinearCombination<E: Engine>(Vec<(Variable, E::Fr)>);
+pub struct LinearCombination<E: ScalarEngine>(Vec<(Variable, E::Fr)>);
 
-impl<E: Engine> AsRef<[(Variable, E::Fr)]> for LinearCombination<E> {
+impl<E: ScalarEngine> AsRef<[(Variable, E::Fr)]> for LinearCombination<E> {
     fn as_ref(&self) -> &[(Variable, E::Fr)] {
         &self.0
     }
 }
 
-impl<E: Engine> LinearCombination<E> {
+impl<E: ScalarEngine> LinearCombination<E> {
     pub fn zero() -> LinearCombination<E> {
         LinearCombination(vec![])
     }
 }
 
-impl<E: Engine> Add<(E::Fr, Variable)> for LinearCombination<E> {
+impl<E: ScalarEngine> Add<(E::Fr, Variable)> for LinearCombination<E> {
     type Output = LinearCombination<E>;
 
     fn add(mut self, (coeff, var): (E::Fr, Variable)) -> LinearCombination<E> {
@@ -88,7 +87,7 @@ impl<E: Engine> Add<(E::Fr, Variable)> for LinearCombination<E> {
     }
 }
 
-impl<E: Engine> Sub<(E::Fr, Variable)> for LinearCombination<E> {
+impl<E: ScalarEngine> Sub<(E::Fr, Variable)> for LinearCombination<E> {
     type Output = LinearCombination<E>;
 
     fn sub(self, (mut coeff, var): (E::Fr, Variable)) -> LinearCombination<E> {
@@ -98,7 +97,7 @@ impl<E: Engine> Sub<(E::Fr, Variable)> for LinearCombination<E> {
     }
 }
 
-impl<E: Engine> Add<Variable> for LinearCombination<E> {
+impl<E: ScalarEngine> Add<Variable> for LinearCombination<E> {
     type Output = LinearCombination<E>;
 
     fn add(self, other: Variable) -> LinearCombination<E> {
@@ -106,7 +105,7 @@ impl<E: Engine> Add<Variable> for LinearCombination<E> {
     }
 }
 
-impl<E: Engine> Sub<Variable> for LinearCombination<E> {
+impl<E: ScalarEngine> Sub<Variable> for LinearCombination<E> {
     type Output = LinearCombination<E>;
 
     fn sub(self, other: Variable) -> LinearCombination<E> {
@@ -114,7 +113,7 @@ impl<E: Engine> Sub<Variable> for LinearCombination<E> {
     }
 }
 
-impl<'a, E: Engine> Add<&'a LinearCombination<E>> for LinearCombination<E> {
+impl<'a, E: ScalarEngine> Add<&'a LinearCombination<E>> for LinearCombination<E> {
     type Output = LinearCombination<E>;
 
     fn add(mut self, other: &'a LinearCombination<E>) -> LinearCombination<E> {
@@ -126,7 +125,7 @@ impl<'a, E: Engine> Add<&'a LinearCombination<E>> for LinearCombination<E> {
     }
 }
 
-impl<'a, E: Engine> Sub<&'a LinearCombination<E>> for LinearCombination<E> {
+impl<'a, E: ScalarEngine> Sub<&'a LinearCombination<E>> for LinearCombination<E> {
     type Output = LinearCombination<E>;
 
     fn sub(mut self, other: &'a LinearCombination<E>) -> LinearCombination<E> {
@@ -138,7 +137,7 @@ impl<'a, E: Engine> Sub<&'a LinearCombination<E>> for LinearCombination<E> {
     }
 }
 
-impl<'a, E: Engine> Add<(E::Fr, &'a LinearCombination<E>)> for LinearCombination<E> {
+impl<'a, E: ScalarEngine> Add<(E::Fr, &'a LinearCombination<E>)> for LinearCombination<E> {
     type Output = LinearCombination<E>;
 
     fn add(mut self, (coeff, other): (E::Fr, &'a LinearCombination<E>)) -> LinearCombination<E> {
@@ -152,7 +151,7 @@ impl<'a, E: Engine> Add<(E::Fr, &'a LinearCombination<E>)> for LinearCombination
     }
 }
 
-impl<'a, E: Engine> Sub<(E::Fr, &'a LinearCombination<E>)> for LinearCombination<E> {
+impl<'a, E: ScalarEngine> Sub<(E::Fr, &'a LinearCombination<E>)> for LinearCombination<E> {
     type Output = LinearCombination<E>;
 
     fn sub(mut self, (coeff, other): (E::Fr, &'a LinearCombination<E>)) -> LinearCombination<E> {
@@ -222,7 +221,7 @@ impl fmt::Display for SynthesisError {
 
 /// Represents a constraint system which can have new variables
 /// allocated and constrains between them formed.
-pub trait ConstraintSystem<E: Engine>: Sized {
+pub trait ConstraintSystem<E: ScalarEngine>: Sized {
     /// Represents the type of the "root" of this constraint system
     /// so that nested namespaces can minimize indirection.
     type Root: ConstraintSystem<E>;
@@ -294,9 +293,9 @@ pub trait ConstraintSystem<E: Engine>: Sized {
 
 /// This is a "namespaced" constraint system which borrows a constraint system (pushing
 /// a namespace context) and, when dropped, pops out of the namespace context.
-pub struct Namespace<'a, E: Engine, CS: ConstraintSystem<E> + 'a>(&'a mut CS, PhantomData<E>);
+pub struct Namespace<'a, E: ScalarEngine, CS: ConstraintSystem<E> + 'a>(&'a mut CS, PhantomData<E>);
 
-impl<'cs, E: Engine, CS: ConstraintSystem<E>> ConstraintSystem<E> for Namespace<'cs, E, CS> {
+impl<'cs, E: ScalarEngine, CS: ConstraintSystem<E>> ConstraintSystem<E> for Namespace<'cs, E, CS> {
     type Root = CS::Root;
 
     fn one() -> Variable {
@@ -359,7 +358,7 @@ impl<'cs, E: Engine, CS: ConstraintSystem<E>> ConstraintSystem<E> for Namespace<
     }
 }
 
-impl<'a, E: Engine, CS: ConstraintSystem<E>> Drop for Namespace<'a, E, CS> {
+impl<'a, E: ScalarEngine, CS: ConstraintSystem<E>> Drop for Namespace<'a, E, CS> {
     fn drop(&mut self) {
         self.get_root().pop_namespace()
     }
@@ -367,7 +366,7 @@ impl<'a, E: Engine, CS: ConstraintSystem<E>> Drop for Namespace<'a, E, CS> {
 
 /// Convenience implementation of ConstraintSystem<E> for mutable references to
 /// constraint systems.
-impl<'cs, E: Engine, CS: ConstraintSystem<E>> ConstraintSystem<E> for &'cs mut CS {
+impl<'cs, E: ScalarEngine, CS: ConstraintSystem<E>> ConstraintSystem<E> for &'cs mut CS {
     type Root = CS::Root;
 
     fn one() -> Variable {

From 4272cfa5b0dceac471bef115955e1534be84a018 Mon Sep 17 00:00:00 2001
From: Jack Grigg <jack@z.cash>
Date: Fri, 6 Jul 2018 21:51:22 +0100
Subject: [PATCH 4/6] =?UTF-8?q?Make=20pairing=20and=20groth16=20optional?=
 =?UTF-8?q?=20=F0=9F=8E=89?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

---
 Cargo.toml      | 9 ++++++++-
 src/domain.rs   | 3 +++
 src/lib.rs      | 2 ++
 src/multiexp.rs | 1 +
 4 files changed, 14 insertions(+), 1 deletion(-)

diff --git a/Cargo.toml b/Cargo.toml
index 8abf83ee1..3a77feabc 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -22,6 +22,13 @@ byteorder = "1"
 [dependencies.pairing]
 git = "https://github.com/str4d/pairing"
 rev = "3d41ee5abaa4888ff3607689aba007be8856816d"
+optional = true
 
 [features]
-default = []
+groth16 = ["pairing"]
+default = ["groth16"]
+
+[[test]]
+name = "mimc"
+path = "tests/mimc.rs"
+required-features = ["groth16"]
diff --git a/src/domain.rs b/src/domain.rs
index 87a824084..4606ce5a2 100644
--- a/src/domain.rs
+++ b/src/domain.rs
@@ -371,6 +371,7 @@ fn parallel_fft<E: ScalarEngine, T: Group<E>>(
 
 // Test multiplying various (low degree) polynomials together and
 // comparing with naive evaluations.
+#[cfg(feature = "pairing")]
 #[test]
 fn polynomial_arith() {
     use pairing::bls12_381::Bls12;
@@ -418,6 +419,7 @@ fn polynomial_arith() {
     test_mul::<Bls12, _>(rng);
 }
 
+#[cfg(feature = "pairing")]
 #[test]
 fn fft_composition() {
     use pairing::bls12_381::Bls12;
@@ -456,6 +458,7 @@ fn fft_composition() {
     test_comp::<Bls12, _>(rng);
 }
 
+#[cfg(feature = "pairing")]
 #[test]
 fn parallel_fft_consistency() {
     use pairing::bls12_381::Bls12;
diff --git a/src/lib.rs b/src/lib.rs
index 42eccea07..f6d716399 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -1,5 +1,6 @@
 extern crate ff;
 extern crate group;
+#[cfg(feature = "pairing")]
 extern crate pairing;
 extern crate rand;
 extern crate num_cpus;
@@ -12,6 +13,7 @@ extern crate byteorder;
 pub mod multicore;
 mod multiexp;
 pub mod domain;
+#[cfg(feature = "groth16")]
 pub mod groth16;
 
 use ff::{Field, ScalarEngine};
diff --git a/src/multiexp.rs b/src/multiexp.rs
index cea13f342..d24572bf6 100644
--- a/src/multiexp.rs
+++ b/src/multiexp.rs
@@ -255,6 +255,7 @@ pub fn multiexp<Q, D, G, S>(
     multiexp_inner(pool, bases, density_map, exponents, 0, c, true)
 }
 
+#[cfg(feature = "pairing")]
 #[test]
 fn test_with_bls12() {
     fn naive_multiexp<G: CurveAffine>(

From 2e35a322d5080d372283a164b617e3af93b15ee0 Mon Sep 17 00:00:00 2001
From: Jack Grigg <jack@z.cash>
Date: Sun, 11 Nov 2018 10:52:08 +1300
Subject: [PATCH 5/6] Update sapling-crypto crate to use ff crate

---
 Cargo.toml | 6 +-----
 1 file changed, 1 insertion(+), 5 deletions(-)

diff --git a/Cargo.toml b/Cargo.toml
index 3a77feabc..6812a7fe3 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -17,13 +17,9 @@ futures-cpupool = "0.1"
 group = "0.1"
 num_cpus = "1"
 crossbeam = "0.3"
+pairing = { path = "../pairing", optional = true }
 byteorder = "1"
 
-[dependencies.pairing]
-git = "https://github.com/str4d/pairing"
-rev = "3d41ee5abaa4888ff3607689aba007be8856816d"
-optional = true
-
 [features]
 groth16 = ["pairing"]
 default = ["groth16"]

From 12f93f2fc25d79ca65e587305ff2547e1160452e Mon Sep 17 00:00:00 2001
From: Jack Grigg <jack@z.cash>
Date: Sun, 6 Jan 2019 09:50:07 +0000
Subject: [PATCH 6/6] Add ff and group crates to Cargo workspace

---
 Cargo.toml | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Cargo.toml b/Cargo.toml
index 6812a7fe3..9ba6de490 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -11,10 +11,10 @@ version = "0.1.0"
 [dependencies]
 rand = "0.4"
 bit-vec = "0.4.4"
-ff = "0.4"
+ff = { path = "../ff" }
 futures = "0.1"
 futures-cpupool = "0.1"
-group = "0.1"
+group = { path = "../group" }
 num_cpus = "1"
 crossbeam = "0.3"
 pairing = { path = "../pairing", optional = true }