Use ff crate for Field traits

Cargo.toml

@@ -15,6 +15,7 @@ repository = "https://github.com/ebfull/pairing"
 rand = "0.4"
 byteorder = "1"
 clippy = { version = "0.0.200", optional = true }
+ff = "0.3"
 
 [features]
 unstable-features = ["expose-arith"]

benches/bls12_381/fq.rs

@@ -1,7 +1,7 @@
 use rand::{Rand, SeedableRng, XorShiftRng};
 
+use ff::{Field, PrimeField, PrimeFieldRepr, SqrtField};
 use pairing::bls12_381::*;
-use pairing::{Field, PrimeField, PrimeFieldRepr, SqrtField};
 
 #[bench]
 fn bench_fq_repr_add_nocarry(b: &mut ::test::Bencher) {

benches/bls12_381/fq12.rs

@@ -1,7 +1,7 @@
 use rand::{Rand, SeedableRng, XorShiftRng};
 
+use ff::Field;
 use pairing::bls12_381::*;
-use pairing::Field;
 
 #[bench]
 fn bench_fq12_add_assign(b: &mut ::test::Bencher) {

benches/bls12_381/fq2.rs

@@ -1,7 +1,7 @@
 use rand::{Rand, SeedableRng, XorShiftRng};
 
+use ff::{Field, SqrtField};
 use pairing::bls12_381::*;
-use pairing::{Field, SqrtField};
 
 #[bench]
 fn bench_fq2_add_assign(b: &mut ::test::Bencher) {

benches/bls12_381/fr.rs

@@ -1,7 +1,7 @@
 use rand::{Rand, SeedableRng, XorShiftRng};
 
+use ff::{Field, PrimeField, PrimeFieldRepr, SqrtField};
 use pairing::bls12_381::*;
-use pairing::{Field, PrimeField, PrimeFieldRepr, SqrtField};
 
 #[bench]
 fn bench_fr_repr_add_nocarry(b: &mut ::test::Bencher) {

benches/pairing_benches.rs

@@ -1,5 +1,6 @@
 #![feature(test)]
 
+extern crate ff;
 extern crate pairing;
 extern crate rand;
 extern crate test;

src/lib.rs

@@ -14,6 +14,7 @@
 #![deny(missing_debug_implementations)]
 
 extern crate byteorder;
+extern crate ff;
 extern crate rand;
 
 #[cfg(test)]
@@ -24,9 +25,9 @@ pub mod bls12_381;
 mod wnaf;
 pub use self::wnaf::Wnaf;
 
+use ff::*;
 use std::error::Error;
 use std::fmt;
-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
@@ -263,208 +264,6 @@ pub trait EncodedPoint:
     fn from_affine(affine: Self::Affine) -> Self;
 }
 
-/// This trait represents an element of a field.
-pub trait Field:
-    Sized + Eq + Copy + Clone + Send + Sync + fmt::Debug + fmt::Display + 'static + rand::Rand
-{
-    /// Returns the zero element of the field, the additive identity.
-    fn zero() -> Self;
-
-    /// Returns the one element of the field, the multiplicative identity.
-    fn one() -> Self;
-
-    /// Returns true iff this element is zero.
-    fn is_zero(&self) -> bool;
-
-    /// Squares this element.
-    fn square(&mut self);
-
-    /// Doubles this element.
-    fn double(&mut self);
-
-    /// Negates this element.
-    fn negate(&mut self);
-
-    /// Adds another element to this element.
-    fn add_assign(&mut self, other: &Self);
-
-    /// Subtracts another element from this element.
-    fn sub_assign(&mut self, other: &Self);
-
-    /// Multiplies another element by this element.
-    fn mul_assign(&mut self, other: &Self);
-
-    /// Computes the multiplicative inverse of this element, if nonzero.
-    fn inverse(&self) -> Option<Self>;
-
-    /// Exponentiates this element by a power of the base prime modulus via
-    /// the Frobenius automorphism.
-    fn frobenius_map(&mut self, power: usize);
-
-    /// Exponentiates this element by a number represented with `u64` limbs,
-    /// least significant digit first.
-    fn pow<S: AsRef<[u64]>>(&self, exp: S) -> Self {
-        let mut res = Self::one();
-
-        let mut found_one = false;
-
-        for i in BitIterator::new(exp) {
-            if found_one {
-                res.square();
-            } else {
-                found_one = i;
-            }
-
-            if i {
-                res.mul_assign(self);
-            }
-        }
-
-        res
-    }
-}
-
-/// This trait represents an element of a field that has a square root operation described for it.
-pub trait SqrtField: Field {
-    /// Returns the Legendre symbol of the field element.
-    fn legendre(&self) -> LegendreSymbol;
-
-    /// Returns the square root of the field element, if it is
-    /// quadratic residue.
-    fn sqrt(&self) -> Option<Self>;
-}
-
-/// This trait represents a wrapper around a biginteger which can encode any element of a particular
-/// prime field. It is a smart wrapper around a sequence of `u64` limbs, least-significant digit
-/// first.
-pub trait PrimeFieldRepr:
-    Sized
-    + Copy
-    + Clone
-    + Eq
-    + Ord
-    + Send
-    + Sync
-    + Default
-    + fmt::Debug
-    + fmt::Display
-    + 'static
-    + rand::Rand
-    + AsRef<[u64]>
-    + AsMut<[u64]>
-    + From<u64>
-{
-    /// Subtract another represetation from this one.
-    fn sub_noborrow(&mut self, other: &Self);
-
-    /// Add another representation to this one.
-    fn add_nocarry(&mut self, other: &Self);
-
-    /// 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.
-    fn is_zero(&self) -> bool;
-
-    /// Returns true iff this number is odd.
-    fn is_odd(&self) -> bool;
-
-    /// Returns true iff this number is even.
-    fn is_even(&self) -> bool;
-
-    /// Performs a rightwise bitshift of this number, effectively dividing
-    /// it by 2.
-    fn div2(&mut self);
-
-    /// Performs a rightwise bitshift of this number by some amount.
-    fn shr(&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 shl(&mut self, amt: u32);
-
-    /// Writes this `PrimeFieldRepr` as a big endian integer.
-    fn write_be<W: Write>(&self, mut writer: W) -> io::Result<()> {
-        use byteorder::{BigEndian, WriteBytesExt};
-
-        for digit in self.as_ref().iter().rev() {
-            writer.write_u64::<BigEndian>(*digit)?;
-        }
-
-        Ok(())
-    }
-
-    /// Reads a big endian integer into this representation.
-    fn read_be<R: Read>(&mut self, mut reader: R) -> io::Result<()> {
-        use byteorder::{BigEndian, ReadBytesExt};
-
-        for digit in self.as_mut().iter_mut().rev() {
-            *digit = reader.read_u64::<BigEndian>()?;
-        }
-
-        Ok(())
-    }
-
-    /// Writes this `PrimeFieldRepr` as a little endian integer.
-    fn write_le<W: Write>(&self, mut writer: W) -> io::Result<()> {
-        use byteorder::{LittleEndian, WriteBytesExt};
-
-        for digit in self.as_ref().iter() {
-            writer.write_u64::<LittleEndian>(*digit)?;
-        }
-
-        Ok(())
-    }
-
-    /// Reads a little endian integer into this representation.
-    fn read_le<R: Read>(&mut self, mut reader: R) -> io::Result<()> {
-        use byteorder::{LittleEndian, ReadBytesExt};
-
-        for digit in self.as_mut().iter_mut() {
-            *digit = reader.read_u64::<LittleEndian>()?;
-        }
-
-        Ok(())
-    }
-}
-
-#[derive(Debug, PartialEq)]
-pub enum LegendreSymbol {
-    Zero = 0,
-    QuadraticResidue = 1,
-    QuadraticNonResidue = -1,
-}
-
-/// An error that may occur when trying to interpret a `PrimeFieldRepr` as a
-/// `PrimeField` element.
-#[derive(Debug)]
-pub enum PrimeFieldDecodingError {
-    /// The encoded value is not in the field
-    NotInField(String),
-}
-
-impl Error for PrimeFieldDecodingError {
-    fn description(&self) -> &str {
-        match *self {
-            PrimeFieldDecodingError::NotInField(..) => "not an element of the field",
-        }
-    }
-}
-
-impl fmt::Display for PrimeFieldDecodingError {
-    fn fmt(&self, f: &mut fmt::Formatter) -> Result<(), fmt::Error> {
-        match *self {
-            PrimeFieldDecodingError::NotInField(ref repr) => {
-                write!(f, "{} is not an element of the field", repr)
-            }
-        }
-    }
-}
-
 /// An error that may occur when trying to decode an `EncodedPoint`.
 #[derive(Debug)]
 pub enum GroupDecodingError {
@@ -504,255 +303,3 @@ impl fmt::Display for GroupDecodingError {
         }
     }
 }
-
-/// This represents an element of a prime field.
-pub trait PrimeField: Field {
-    /// The prime field can be converted back and forth into this biginteger
-    /// 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(u64::from(c))).unwrap());
-                }
-                None => {
-                    return None;
-                }
-            }
-        }
-
-        Some(res)
-    }
-
-    /// Convert this prime field element into a biginteger representation.
-    fn from_repr(Self::Repr) -> Result<Self, PrimeFieldDecodingError>;
-
-    /// Convert a biginteger representation into a prime field element, if
-    /// the number is an element of the field.
-    fn into_repr(&self) -> Self::Repr;
-
-    /// Returns the field characteristic; the modulus.
-    fn char() -> Self::Repr;
-
-    /// How many bits are needed to represent an element of this field.
-    const NUM_BITS: u32;
-
-    /// How many bits of information can be reliably stored in the field element.
-    const CAPACITY: u32;
-
-    /// Returns the multiplicative generator of `char()` - 1 order. This element
-    /// must also be quadratic nonresidue.
-    fn multiplicative_generator() -> Self;
-
-    /// 2^s * t = `char()` - 1 with t odd.
-    const S: u32;
-
-    /// Returns the 2^s root of unity computed by exponentiating the `multiplicative_generator()`
-    /// by t.
-    fn root_of_unity() -> Self;
-}
-
-#[derive(Debug)]
-pub struct BitIterator<E> {
-    t: E,
-    n: usize,
-}
-
-impl<E: AsRef<[u64]>> BitIterator<E> {
-    pub fn new(t: E) -> Self {
-        let n = t.as_ref().len() * 64;
-
-        BitIterator { t, n }
-    }
-}
-
-impl<E: AsRef<[u64]>> Iterator for BitIterator<E> {
-    type Item = bool;
-
-    fn next(&mut self) -> Option<bool> {
-        if self.n == 0 {
-            None
-        } else {
-            self.n -= 1;
-            let part = self.n / 64;
-            let bit = self.n - (64 * part);
-
-            Some(self.t.as_ref()[part] & (1 << bit) > 0)
-        }
-    }
-}
-
-#[test]
-fn test_bit_iterator() {
-    let mut a = BitIterator::new([0xa953d79b83f6ab59, 0x6dea2059e200bd39]);
-    let expected = "01101101111010100010000001011001111000100000000010111101001110011010100101010011110101111001101110000011111101101010101101011001";
-
-    for e in expected.chars() {
-        assert!(a.next().unwrap() == (e == '1'));
-    }
-
-    assert!(a.next().is_none());
-
-    let expected = "1010010101111110101010000101101011101000011101110101001000011001100100100011011010001011011011010001011011101100110100111011010010110001000011110100110001100110011101101000101100011100100100100100001010011101010111110011101011000011101000111011011101011001";
-
-    let mut a = BitIterator::new([
-        0x429d5f3ac3a3b759,
-        0xb10f4c66768b1c92,
-        0x92368b6d16ecd3b4,
-        0xa57ea85ae8775219,
-    ]);
-
-    for e in expected.chars() {
-        assert!(a.next().unwrap() == (e == '1'));
-    }
-
-    assert!(a.next().is_none());
-}
-
-#[cfg(not(feature = "expose-arith"))]
-use self::arith_impl::*;
-
-#[cfg(feature = "expose-arith")]
-pub use self::arith_impl::*;
-
-#[cfg(feature = "u128-support")]
-mod arith_impl {
-    /// Calculate a - b - borrow, returning the result and modifying
-    /// the borrow value.
-    #[inline(always)]
-    pub fn sbb(a: u64, b: u64, borrow: &mut u64) -> u64 {
-        let tmp = (1u128 << 64) + u128::from(a) - u128::from(b) - u128::from(*borrow);
-
-        *borrow = if tmp >> 64 == 0 { 1 } else { 0 };
-
-        tmp as u64
-    }
-
-    /// Calculate a + b + carry, returning the sum and modifying the
-    /// carry value.
-    #[inline(always)]
-    pub fn adc(a: u64, b: u64, carry: &mut u64) -> u64 {
-        let tmp = u128::from(a) + u128::from(b) + u128::from(*carry);
-
-        *carry = (tmp >> 64) as u64;
-
-        tmp as u64
-    }
-
-    /// Calculate a + (b * c) + carry, returning the least significant digit
-    /// and setting carry to the most significant digit.
-    #[inline(always)]
-    pub fn mac_with_carry(a: u64, b: u64, c: u64, carry: &mut u64) -> u64 {
-        let tmp = (u128::from(a)) + u128::from(b) * u128::from(c) + u128::from(*carry);
-
-        *carry = (tmp >> 64) as u64;
-
-        tmp as u64
-    }
-}
-
-#[cfg(not(feature = "u128-support"))]
-mod arith_impl {
-    #[inline(always)]
-    fn split_u64(i: u64) -> (u64, u64) {
-        (i >> 32, i & 0xFFFFFFFF)
-    }
-
-    #[inline(always)]
-    fn combine_u64(hi: u64, lo: u64) -> u64 {
-        (hi << 32) | lo
-    }
-
-    /// Calculate a - b - borrow, returning the result and modifying
-    /// the borrow value.
-    #[inline(always)]
-    pub fn sbb(a: u64, b: u64, borrow: &mut u64) -> u64 {
-        let (a_hi, a_lo) = split_u64(a);
-        let (b_hi, b_lo) = split_u64(b);
-        let (b, r0) = split_u64((1 << 32) + a_lo - b_lo - *borrow);
-        let (b, r1) = split_u64((1 << 32) + a_hi - b_hi - ((b == 0) as u64));
-
-        *borrow = (b == 0) as u64;
-
-        combine_u64(r1, r0)
-    }
-
-    /// Calculate a + b + carry, returning the sum and modifying the
-    /// carry value.
-    #[inline(always)]
-    pub fn adc(a: u64, b: u64, carry: &mut u64) -> u64 {
-        let (a_hi, a_lo) = split_u64(a);
-        let (b_hi, b_lo) = split_u64(b);
-        let (carry_hi, carry_lo) = split_u64(*carry);
-
-        let (t, r0) = split_u64(a_lo + b_lo + carry_lo);
-        let (t, r1) = split_u64(t + a_hi + b_hi + carry_hi);
-
-        *carry = t;
-
-        combine_u64(r1, r0)
-    }
-
-    /// Calculate a + (b * c) + carry, returning the least significant digit
-    /// and setting carry to the most significant digit.
-    #[inline(always)]
-    pub fn mac_with_carry(a: u64, b: u64, c: u64, carry: &mut u64) -> u64 {
-        /*
-                                [  b_hi  |  b_lo  ]
-                                [  c_hi  |  c_lo  ] *
-        -------------------------------------------
-                                [  b_lo  *  c_lo  ] <-- w
-                       [  b_hi  *  c_lo  ]          <-- x
-                       [  b_lo  *  c_hi  ]          <-- y
-             [   b_hi  *  c_lo  ]                   <-- z
-                                [  a_hi  |  a_lo  ]
-                                [  C_hi  |  C_lo  ]
-        */
-
-        let (a_hi, a_lo) = split_u64(a);
-        let (b_hi, b_lo) = split_u64(b);
-        let (c_hi, c_lo) = split_u64(c);
-        let (carry_hi, carry_lo) = split_u64(*carry);
-
-        let (w_hi, w_lo) = split_u64(b_lo * c_lo);
-        let (x_hi, x_lo) = split_u64(b_hi * c_lo);
-        let (y_hi, y_lo) = split_u64(b_lo * c_hi);
-        let (z_hi, z_lo) = split_u64(b_hi * c_hi);
-
-        let (t, r0) = split_u64(w_lo + a_lo + carry_lo);
-        let (t, r1) = split_u64(t + w_hi + x_lo + y_lo + a_hi + carry_hi);
-        let (t, r2) = split_u64(t + x_hi + y_hi + z_lo);
-        let (_, r3) = split_u64(t + z_hi);
-
-        *carry = combine_u64(r3, r2);
-
-        combine_u64(r1, r0)
-    }
-}