ff: Move pow_vartime back into Field trait

The only places we don't use constant u64 limbs, we use PrimeField::char
instead (except in a single test where we use a field element).

pairing/src/bls12_381/fq.rs

@@ -2,8 +2,6 @@ use super::fq2::Fq2;
 use ff::{Field, PrimeField};
 use std::ops::{AddAssign, MulAssign, SubAssign};
 
-#[cfg(test)]
-use ff::PowVartime;
 #[cfg(test)]
 use std::ops::Neg;
 
@@ -1644,11 +1642,15 @@ fn test_fq_pow() {
         assert_eq!(c, target);
     }
 
+    use byteorder::ByteOrder;
+    let mut char_limbs = [0; 6];
+    byteorder::LittleEndian::read_u64_into(Fq::char().as_ref(), &mut char_limbs);
+
     for _ in 0..1000 {
         // Exponentiating by the modulus should have no effect in a prime field.
         let a = Fq::random(&mut rng);
 
-        assert_eq!(a, a.pow_vartime(Fq::char()));
+        assert_eq!(a, a.pow_vartime(char_limbs));
     }
 }
 

pairing/src/bls12_381/fq2.rs

@@ -1,5 +1,5 @@
 use super::fq::{Fq, FROBENIUS_COEFF_FQ2_C1, NEGATIVE_ONE};
-use ff::{Field, PowVartime};
+use ff::Field;
 use rand_core::RngCore;
 use std::cmp::Ordering;
 use std::ops::{Add, AddAssign, Mul, MulAssign, Neg, Sub, SubAssign};

pairing/src/bls12_381/fr.rs

@@ -7,8 +7,6 @@ use std::ops::{AddAssign, MulAssign, SubAssign};
 #[PrimeFieldReprEndianness = "little"]
 pub struct Fr([u64; 4]);
 
-#[cfg(test)]
-use ff::PowVartime;
 #[cfg(test)]
 use rand_core::SeedableRng;
 #[cfg(test)]
@@ -430,11 +428,15 @@ fn test_fr_pow() {
         assert_eq!(c, target);
     }
 
+    use byteorder::ByteOrder;
+    let mut char_limbs = [0; 4];
+    byteorder::LittleEndian::read_u64_into(Fr::char().as_ref(), &mut char_limbs);
+
     for _ in 0..1000 {
         // Exponentiating by the modulus should have no effect in a prime field.
         let a = Fr::random(&mut rng);
 
-        assert_eq!(a, a.pow_vartime(Fr::char()));
+        assert_eq!(a, a.pow_vartime(char_limbs));
     }
 }
 

pairing/src/bls12_381/mod.rs

@@ -23,7 +23,7 @@ pub use self::fr::{Fr, FrRepr};
 
 use super::{Engine, PairingCurveAffine};
 
-use ff::{BitIterator, Field, PowVartime, ScalarEngine};
+use ff::{BitIterator, Field, ScalarEngine};
 use group::CurveAffine;
 use std::ops::{AddAssign, MulAssign, Neg, SubAssign};
 use subtle::CtOption;

pairing/src/tests/engine.rs

@@ -1,10 +1,10 @@
-use ff::PowVartime;
+use ff::{Endianness, Field, PrimeField};
 use group::{CurveAffine, CurveProjective};
 use rand_core::SeedableRng;
 use rand_xorshift::XorShiftRng;
 use std::ops::MulAssign;
 
-use crate::{Engine, Field, PairingCurveAffine, PrimeField};
+use crate::{Engine, PairingCurveAffine};
 
 pub fn engine_tests<E: Engine>() {
     let mut rng = XorShiftRng::from_seed([
@@ -130,8 +130,14 @@ fn random_bilinearity_tests<E: Engine>() {
 
         let mut cd = c;
         cd.mul_assign(&d);
+        let mut cd = cd.into_repr();
+        <E::Fr as PrimeField>::ReprEndianness::toggle_little_endian(&mut cd);
 
-        let abcd = E::pairing(a, b).pow_vartime(cd.into_repr());
+        use byteorder::ByteOrder;
+        let mut cd_limbs = [0; 4];
+        byteorder::LittleEndian::read_u64_into(cd.as_ref(), &mut cd_limbs);
+
+        let abcd = E::pairing(a, b).pow_vartime(cd_limbs);
 
         assert_eq!(acbd, adbc);
         assert_eq!(acbd, abcd);