diff --git a/Cargo.toml b/Cargo.toml
index 677fe6ad3..a19bc0038 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -1,6 +1,6 @@
 [package]
 name = "pairing"
-version = "0.10.1"
+version = "0.10.2"
 authors = ["Sean Bowe <ewillbefull@gmail.com>"]
 license = "MIT/Apache-2.0"
 
@@ -12,7 +12,7 @@ repository = "https://github.com/ebfull/pairing"
 [dependencies]
 rand = "0.3"
 byteorder = "1.1.0"
-clippy = { version = "0.0.145", optional = true }
+clippy = { version = "0.0.148", optional = true }
 
 [features]
 unstable-wnaf = []
diff --git a/src/bls12_381/ec.rs b/src/bls12_381/ec.rs
index a4eaa1a7f..16deca520 100644
--- a/src/bls12_381/ec.rs
+++ b/src/bls12_381/ec.rs
@@ -108,6 +108,7 @@ macro_rules! curve_impl {
         }
 
         impl CurveAffine for $affine {
+            type Engine = Bls12;
             type Scalar = $scalarfield;
             type Base = $basefield;
             type Prepared = $prepared;
@@ -174,6 +175,7 @@ macro_rules! curve_impl {
         }
 
         impl CurveProjective for $projective {
+            type Engine = Bls12;
             type Scalar = $scalarfield;
             type Base = $basefield;
             type Affine = $affine;
@@ -582,7 +584,7 @@ macro_rules! curve_impl {
 pub mod g1 {
     use rand::{Rand, Rng};
     use super::g2::G2Affine;
-    use super::super::{Fq, Fr, FrRepr, FqRepr, Fq12};
+    use super::super::{Bls12, Fq, Fr, FrRepr, FqRepr, Fq12};
     use ::{CurveProjective, CurveAffine, PrimeField, SqrtField, PrimeFieldRepr, Field, BitIterator, EncodedPoint, GroupDecodingError, Engine};
 
     curve_impl!("G1", G1, G1Affine, G1Prepared, Fq, Fr, G1Uncompressed, G1Compressed, G2Affine);
@@ -1134,7 +1136,7 @@ pub mod g1 {
 
 pub mod g2 {
     use rand::{Rand, Rng};
-    use super::super::{Fq2, Fr, Fq, FrRepr, FqRepr, Fq12};
+    use super::super::{Bls12, Fq2, Fr, Fq, FrRepr, FqRepr, Fq12};
     use super::g1::G1Affine;
     use ::{CurveProjective, CurveAffine, PrimeField, SqrtField, PrimeFieldRepr, Field, BitIterator, EncodedPoint, GroupDecodingError, Engine};
 
diff --git a/src/bls12_381/fq.rs b/src/bls12_381/fq.rs
index e7be0ec59..edfe1500c 100644
--- a/src/bls12_381/fq.rs
+++ b/src/bls12_381/fq.rs
@@ -10,7 +10,7 @@ const MODULUS_BITS: u32 = 381;
 
 // The number of bits that must be shaved from the beginning of
 // the representation when randomly sampling.
-const REPR_SHAVE_BITS: usize = 3;
+const REPR_SHAVE_BITS: u32 = 3;
 
 // R = 2**384 % q
 const R: FqRepr = FqRepr([0x760900000002fffd, 0xebf4000bc40c0002, 0x5f48985753c758ba, 0x77ce585370525745, 0x5c071a97a256ec6d, 0x15f65ec3fa80e493]);
@@ -25,7 +25,7 @@ const INV: u64 = 0x89f3fffcfffcfffd;
 const GENERATOR: FqRepr = FqRepr([0x321300000006554f, 0xb93c0018d6c40005, 0x57605e0db0ddbb51, 0x8b256521ed1f9bcb, 0x6cf28d7901622c03, 0x11ebab9dbb81e28c]);
 
 // 2^s * t = MODULUS - 1 with t odd
-const S: usize = 1;
+const S: u32 = 1;
 
 // 2^s root of unity computed by GENERATOR^t
 const ROOT_OF_UNITY: FqRepr = FqRepr([0x43f5fffffffcaaae, 0x32b7fff2ed47fffd, 0x7e83a49a2e99d69, 0xeca8f3318332bb7a, 0xef148d1ea0f4c069, 0x40ab3263eff0206]);
@@ -278,7 +278,7 @@ impl PrimeFieldRepr for FqRepr {
     }
 
     #[inline(always)]
-    fn divn(&mut self, mut n: usize) {
+    fn divn(&mut self, mut n: u32) {
         if n >= 64 * 6 {
             *self = Self::from(0);
             return;
@@ -325,6 +325,32 @@ impl PrimeFieldRepr for FqRepr {
         }
     }
 
+    #[inline(always)]
+    fn muln(&mut self, mut n: u32) {
+        if n >= 64 * 6 {
+            *self = Self::from(0);
+            return;
+        }
+
+        while n >= 64 {
+            let mut t = 0;
+            for i in &mut self.0 {
+                ::std::mem::swap(&mut t, i);
+            }
+            n -= 64;
+        }
+
+        if n > 0 {
+            let mut t = 0;
+            for i in &mut self.0 {
+                let t2 = *i >> (64 - n);
+                *i <<= n;
+                *i |= t;
+                t = t2;
+            }
+        }
+    }
+
     #[inline(always)]
     fn num_bits(&self) -> u32 {
         let mut ret = (6 as u32) * 64;
@@ -444,7 +470,7 @@ impl PrimeField for Fq {
         Fq(GENERATOR)
     }
 
-    fn s() -> usize {
+    fn s() -> u32 {
         S
     }
 
@@ -1740,6 +1766,7 @@ fn fq_field_tests() {
     ::tests::field::random_field_tests::<Fq>();
     ::tests::field::random_sqrt_tests::<Fq>();
     ::tests::field::random_frobenius_tests::<Fq, _>(Fq::char(), 13);
+    ::tests::field::from_str_tests::<Fq>();
 }
 
 #[test]
diff --git a/src/bls12_381/fr.rs b/src/bls12_381/fr.rs
index 63cc26476..9fc90ee0a 100644
--- a/src/bls12_381/fr.rs
+++ b/src/bls12_381/fr.rs
@@ -8,7 +8,7 @@ const MODULUS_BITS: u32 = 255;
 
 // The number of bits that must be shaved from the beginning of
 // the representation when randomly sampling.
-const REPR_SHAVE_BITS: usize = 1;
+const REPR_SHAVE_BITS: u32 = 1;
 
 // R = 2**256 % r
 const R: FrRepr = FrRepr([0x1fffffffe, 0x5884b7fa00034802, 0x998c4fefecbc4ff5, 0x1824b159acc5056f]);
@@ -23,7 +23,7 @@ const INV: u64 = 0xfffffffeffffffff;
 const GENERATOR: FrRepr = FrRepr([0xefffffff1, 0x17e363d300189c0f, 0xff9c57876f8457b0, 0x351332208fc5a8c4]);
 
 // 2^s * t = MODULUS - 1 with t odd
-const S: usize = 32;
+const S: u32 = 32;
 
 // 2^s root of unity computed by GENERATOR^t
 const ROOT_OF_UNITY: FrRepr = FrRepr([0xb9b58d8c5f0e466a, 0x5b1b4c801819d7ec, 0xaf53ae352a31e64, 0x5bf3adda19e9b27b]);
@@ -114,7 +114,7 @@ impl PrimeFieldRepr for FrRepr {
     }
 
     #[inline(always)]
-    fn divn(&mut self, mut n: usize) {
+    fn divn(&mut self, mut n: u32) {
         if n >= 64 * 4 {
             *self = Self::from(0);
             return;
@@ -161,6 +161,32 @@ impl PrimeFieldRepr for FrRepr {
         }
     }
 
+    #[inline(always)]
+    fn muln(&mut self, mut n: u32) {
+        if n >= 64 * 4 {
+            *self = Self::from(0);
+            return;
+        }
+
+        while n >= 64 {
+            let mut t = 0;
+            for i in &mut self.0 {
+                ::std::mem::swap(&mut t, i);
+            }
+            n -= 64;
+        }
+
+        if n > 0 {
+            let mut t = 0;
+            for i in &mut self.0 {
+                let t2 = *i >> (64 - n);
+                *i <<= n;
+                *i |= t;
+                t = t2;
+            }
+        }
+    }
+
     #[inline(always)]
     fn num_bits(&self) -> u32 {
         let mut ret = (4 as u32) * 64;
@@ -264,7 +290,7 @@ impl PrimeField for Fr {
         Fr(GENERATOR)
     }
 
-    fn s() -> usize {
+    fn s() -> u32 {
         S
     }
 
@@ -1452,6 +1478,7 @@ fn fr_field_tests() {
     ::tests::field::random_field_tests::<Fr>();
     ::tests::field::random_sqrt_tests::<Fr>();
     ::tests::field::random_frobenius_tests::<Fr, _>(Fr::char(), 13);
+    ::tests::field::from_str_tests::<Fr>();
 }
 
 #[test]
diff --git a/src/bls12_381/mod.rs b/src/bls12_381/mod.rs
index 6454877e9..28af9d8a0 100644
--- a/src/bls12_381/mod.rs
+++ b/src/bls12_381/mod.rs
@@ -11,6 +11,7 @@ mod tests;
 pub use self::fr::{Fr, FrRepr};
 pub use self::fq::{Fq, FqRepr};
 pub use self::fq2::Fq2;
+pub use self::fq6::Fq6;
 pub use self::fq12::Fq12;
 pub use self::ec::{G1, G2, G1Affine, G2Affine, G1Prepared, G2Prepared, G1Uncompressed, G2Uncompressed, G1Compressed, G2Compressed};
 
diff --git a/src/lib.rs b/src/lib.rs
index 6e98aa6ec..62abed95f 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -9,6 +9,7 @@
 #![cfg_attr(feature = "clippy", plugin(clippy))]
 #![cfg_attr(feature = "clippy", allow(inline_always))]
 #![cfg_attr(feature = "clippy", allow(too_many_arguments))]
+#![cfg_attr(feature = "clippy", allow(unreadable_literal))]
 
 // The compiler provides `test` (on nightly) for benchmarking tools, but
 // it's hidden behind a feature flag. Enable it if we're testing.
@@ -34,21 +35,21 @@ use std::io::{self, Read, Write};
 /// An "engine" is a collection of types (fields, elliptic curve groups, etc.)
 /// with well-defined relationships. In particular, the G1/G2 curve groups are
 /// of prime order `r`, and are equipped with a bilinear pairing function.
-pub trait Engine {
+pub trait Engine: Sized {
     /// This is the scalar field of the G1/G2 groups.
     type Fr: PrimeField;
 
     /// The projective representation of an element in G1.
-    type G1: CurveProjective<Base=Self::Fq, Scalar=Self::Fr, Affine=Self::G1Affine> + From<Self::G1Affine>;
+    type G1: CurveProjective<Engine=Self, Base=Self::Fq, Scalar=Self::Fr, Affine=Self::G1Affine> + From<Self::G1Affine>;
 
     /// The affine representation of an element in G1.
-    type G1Affine: CurveAffine<Base=Self::Fq, Scalar=Self::Fr, Projective=Self::G1, Pair=Self::G2Affine, PairingResult=Self::Fqk> + From<Self::G1>;
+    type G1Affine: CurveAffine<Engine=Self, Base=Self::Fq, Scalar=Self::Fr, Projective=Self::G1, Pair=Self::G2Affine, PairingResult=Self::Fqk> + From<Self::G1>;
 
     /// The projective representation of an element in G2.
-    type G2: CurveProjective<Base=Self::Fqe, Scalar=Self::Fr, Affine=Self::G2Affine> + From<Self::G2Affine>;
+    type G2: CurveProjective<Engine=Self, Base=Self::Fqe, Scalar=Self::Fr, Affine=Self::G2Affine> + From<Self::G2Affine>;
 
     /// The affine representation of an element in G2.
-    type G2Affine: CurveAffine<Base=Self::Fqe, Scalar=Self::Fr, Projective=Self::G2, Pair=Self::G1Affine, PairingResult=Self::Fqk> + From<Self::G2>;
+    type G2Affine: CurveAffine<Engine=Self, Base=Self::Fqe, Scalar=Self::Fr, Projective=Self::G2, Pair=Self::G1Affine, PairingResult=Self::Fqk> + From<Self::G2>;
 
     /// The base field that hosts G1.
     type Fq: PrimeField + SqrtField;
@@ -97,6 +98,7 @@ pub trait CurveProjective: PartialEq +
                            rand::Rand +
                            'static
 {
+    type Engine: Engine;
     type Scalar: PrimeField;
     type Base: SqrtField;
     type Affine: CurveAffine<Projective=Self, Scalar=Self::Scalar>;
@@ -166,6 +168,7 @@ pub trait CurveAffine: Copy +
                        Eq +
                        'static
 {
+    type Engine: Engine;
     type Scalar: PrimeField;
     type Base: SqrtField;
     type Projective: CurveProjective<Affine=Self, Scalar=Self::Scalar>;
@@ -352,7 +355,8 @@ pub trait PrimeFieldRepr: Sized +
     /// Add another representation to this one, returning the carry bit.
     fn add_nocarry(&mut self, other: &Self) -> bool;
 
-    /// Compute the number of bits needed to encode this number.
+    /// Compute the number of bits needed to encode this number. Always a
+    /// multiple of 64.
     fn num_bits(&self) -> u32;
 
     /// Returns true iff this number is zero.
@@ -369,12 +373,15 @@ pub trait PrimeFieldRepr: Sized +
     fn div2(&mut self);
 
     /// Performs a rightwise bitshift of this number by some amount.
-    fn divn(&mut self, amt: usize);
+    fn divn(&mut self, amt: u32);
 
     /// Performs a leftwise bitshift of this number, effectively multiplying
     /// it by 2. Overflow is ignored.
     fn mul2(&mut self);
 
+    /// Performs a leftwise bitshift of this number by some amount.
+    fn muln(&mut self, amt: u32);
+
     /// Writes this `PrimeFieldRepr` as a big endian integer. Always writes
     /// `(num_bits` / 8) bytes.
     fn write_be<W: Write>(&self, mut writer: W) -> io::Result<()> {
@@ -473,6 +480,46 @@ pub trait PrimeField: Field
     /// representation.
     type Repr: PrimeFieldRepr + From<Self>;
 
+    /// Interpret a string of numbers as a (congruent) prime field element.
+    /// Does not accept unnecessary leading zeroes or a blank string.
+    fn from_str(s: &str) -> Option<Self> {
+        if s.is_empty() {
+            return None;
+        }
+
+        if s == "0" {
+            return Some(Self::zero());
+        }
+
+        let mut res = Self::zero();
+
+        let ten = Self::from_repr(Self::Repr::from(10)).unwrap();
+
+        let mut first_digit = true;
+
+        for c in s.chars() {
+            match c.to_digit(10) {
+                Some(c) => {
+                    if first_digit {
+                        if c == 0 {
+                            return None;
+                        }
+
+                        first_digit = false;
+                    }
+
+                    res.mul_assign(&ten);
+                    res.add_assign(&Self::from_repr(Self::Repr::from(c as u64)).unwrap());
+                },
+                None => {
+                    return None;
+                }
+            }
+        }
+
+        Some(res)
+    }
+
     /// Convert this prime field element into a biginteger representation.
     fn from_repr(Self::Repr) -> Result<Self, PrimeFieldDecodingError>;
 
@@ -496,7 +543,7 @@ pub trait PrimeField: Field
     fn multiplicative_generator() -> Self;
 
     /// Returns s such that 2^s * t = `char()` - 1 with t odd.
-    fn s() -> usize;
+    fn s() -> u32;
 
     /// Returns the 2^s root of unity computed by exponentiating the `multiplicative_generator()`
     /// by t.
diff --git a/src/tests/field.rs b/src/tests/field.rs
index dbc9f8cfc..5f9999296 100644
--- a/src/tests/field.rs
+++ b/src/tests/field.rs
@@ -1,5 +1,5 @@
 use rand::{Rng, SeedableRng, XorShiftRng};
-use ::{SqrtField, Field};
+use ::{SqrtField, Field, PrimeField};
 
 pub fn random_frobenius_tests<F: Field, C: AsRef<[u64]>>(characteristic: C, maxpower: usize) {
     let mut rng = XorShiftRng::from_seed([0x5dbe6259, 0x8d313d76, 0x3237db17, 0xe5bc0654]);
@@ -87,6 +87,40 @@ pub fn random_field_tests<F: Field>() {
     }
 }
 
+pub fn from_str_tests<F: PrimeField>() {
+    {
+        let a = "84395729384759238745923745892374598234705297301958723458712394587103249587213984572934750213947582345792304758273458972349582734958273495872304598234";
+        let b = "38495729084572938457298347502349857029384609283450692834058293405982304598230458230495820394850293845098234059823049582309485203948502938452093482039";
+        let c = "3248875134290623212325429203829831876024364170316860259933542844758450336418538569901990710701240661702808867062612075657861768196242274635305077449545396068598317421057721935408562373834079015873933065667961469731886739181625866970316226171512545167081793907058686908697431878454091011239990119126";
+
+        let mut a = F::from_str(a).unwrap();
+        let b = F::from_str(b).unwrap();
+        let c = F::from_str(c).unwrap();
+
+        a.mul_assign(&b);
+
+        assert_eq!(a, c);
+    }
+
+    {
+        let mut rng = XorShiftRng::from_seed([0x5dbe6259, 0x8d313d76, 0x3237db17, 0xe5bc0654]);
+
+        for _ in 0..1000 {
+            let n: u64 = rng.gen();
+
+            let a = F::from_str(&format!("{}", n)).unwrap();
+            let b = F::from_repr(n.into()).unwrap();
+
+            assert_eq!(a, b);
+        }
+    }
+
+    assert!(F::from_str("").is_none());
+    assert!(F::from_str("0").unwrap().is_zero());
+    assert!(F::from_str("00").is_none());
+    assert!(F::from_str("00000000000").is_none());
+}
+
 fn random_multiplication_tests<F: Field, R: Rng>(rng: &mut R) {
     for _ in 0..10000 {
         let a = F::rand(rng);
diff --git a/src/tests/repr.rs b/src/tests/repr.rs
index b0c119cf3..9403df085 100644
--- a/src/tests/repr.rs
+++ b/src/tests/repr.rs
@@ -2,20 +2,64 @@ use rand::{SeedableRng, XorShiftRng};
 use ::{PrimeFieldRepr};
 
 pub fn random_repr_tests<R: PrimeFieldRepr>() {
-	random_encoding_tests::<R>();
+    random_encoding_tests::<R>();
+    random_muln_tests::<R>();
+    random_divn_tests::<R>();
 }
 
 fn random_encoding_tests<R: PrimeFieldRepr>() {
-	let mut rng = XorShiftRng::from_seed([0x5dbe6259, 0x8d313d76, 0x3237db17, 0xe5bc0654]);
+    let mut rng = XorShiftRng::from_seed([0x5dbe6259, 0x8d313d76, 0x3237db17, 0xe5bc0654]);
 
-	for _ in 0..1000 {
-		let r = R::rand(&mut rng);
-		let mut rdecoded = R::default();
+    for _ in 0..1000 {
+        let r = R::rand(&mut rng);
+        let mut rdecoded = R::default();
 
-		let mut v: Vec<u8> = vec![];
-		r.write_be(&mut v).unwrap();
-		rdecoded.read_be(&v[0..]).unwrap();
+        let mut v: Vec<u8> = vec![];
+        r.write_be(&mut v).unwrap();
+        rdecoded.read_be(&v[0..]).unwrap();
 
-		assert_eq!(r, rdecoded);
-	}
+        assert_eq!(r, rdecoded);
+    }
+}
+
+fn random_muln_tests<R: PrimeFieldRepr>() {
+    let mut rng = XorShiftRng::from_seed([0x5dbe6259, 0x8d313d76, 0x3237db17, 0xe5bc0654]);
+
+    for _ in 0..100 {
+        let r = R::rand(&mut rng);
+
+        for shift in 0..(r.num_bits()+1) {
+            let mut r1 = r;
+            let mut r2 = r;
+
+            for _ in 0..shift {
+                r1.mul2();
+            }
+
+            r2.muln(shift);
+
+            assert_eq!(r1, r2);
+        }
+    }
+}
+
+fn random_divn_tests<R: PrimeFieldRepr>() {
+    let mut rng = XorShiftRng::from_seed([0x5dbe6259, 0x8d313d76, 0x3237db17, 0xe5bc0654]);
+
+    for _ in 0..100 {
+        let r = R::rand(&mut rng);
+
+        for shift in 0..(r.num_bits()+1) {
+            let mut r1 = r;
+            let mut r2 = r;
+
+            for _ in 0..shift {
+                r1.div2();
+            }
+
+            r2.divn(shift);
+
+            assert_eq!(r1, r2);
+        }
+    }
 }