Implement Bulletproofs in Rust (#69)

* Initial attempt at Bulletproofs

I don't know why this doesn't work. The generators and hash_cache lines
up without issue. AFAICT, the inner product proof is valid as well, as
are all included formulas.

* Add yinvpow asserts

* Clean code

* Correct bad imports

* Fix the definition of TWO_N

Bulletproofs work now :D

* Tidy up a bit

* fmt + clippy

* Compile a variety of XMR dependencies with optimizations, even under dev

The Rust bulletproof implementation is 8% slower than C right now, under 
release. This is acceptable, even if suboptimal. Under debug, they take 
a quarter of a second to two seconds though, depending on the amount of 
outputs, which justifies this move.

* Remove unnecessary deref in BPs

coins/monero/src/ringct/bulletproofs/scalar_vector.rs

@@ -0,0 +1,106 @@
+use core::ops::{Add, Sub, Mul, Index};
+
+use group::ff::Field;
+use dalek_ff_group::{Scalar, EdwardsPoint};
+
+use multiexp::multiexp;
+
+#[derive(Clone, PartialEq, Eq, Debug)]
+pub(crate) struct ScalarVector(pub(crate) Vec<Scalar>);
+macro_rules! math_op {
+  ($Op: ident, $op: ident, $f: expr) => {
+    impl $Op<Scalar> for ScalarVector {
+      type Output = ScalarVector;
+      fn $op(self, b: Scalar) -> ScalarVector {
+        ScalarVector(self.0.iter().map(|a| $f((a, &b))).collect())
+      }
+    }
+
+    impl $Op<Scalar> for &ScalarVector {
+      type Output = ScalarVector;
+      fn $op(self, b: Scalar) -> ScalarVector {
+        ScalarVector(self.0.iter().map(|a| $f((a, &b))).collect())
+      }
+    }
+
+    impl $Op<ScalarVector> for ScalarVector {
+      type Output = ScalarVector;
+      fn $op(self, b: ScalarVector) -> ScalarVector {
+        assert_eq!(self.len(), b.len());
+        ScalarVector(self.0.iter().zip(b.0.iter()).map($f).collect())
+      }
+    }
+
+    impl $Op<&ScalarVector> for &ScalarVector {
+      type Output = ScalarVector;
+      fn $op(self, b: &ScalarVector) -> ScalarVector {
+        assert_eq!(self.len(), b.len());
+        ScalarVector(self.0.iter().zip(b.0.iter()).map($f).collect())
+      }
+    }
+  };
+}
+math_op!(Add, add, |(a, b): (&Scalar, &Scalar)| *a + *b);
+math_op!(Sub, sub, |(a, b): (&Scalar, &Scalar)| *a - *b);
+math_op!(Mul, mul, |(a, b): (&Scalar, &Scalar)| *a * *b);
+
+impl ScalarVector {
+  pub(crate) fn new(len: usize) -> ScalarVector {
+    ScalarVector(vec![Scalar::zero(); len])
+  }
+
+  pub(crate) fn powers(x: Scalar, len: usize) -> ScalarVector {
+    let mut res = Vec::with_capacity(len);
+    if len == 0 {
+      return ScalarVector(res);
+    }
+
+    res.push(Scalar::one());
+    for i in 1 .. len {
+      res.push(res[i - 1] * x);
+    }
+
+    ScalarVector(res)
+  }
+
+  pub(crate) fn len(&self) -> usize {
+    self.0.len()
+  }
+
+  pub(crate) fn split(self) -> (ScalarVector, ScalarVector) {
+    let (l, r) = self.0.split_at(self.0.len() / 2);
+    (ScalarVector(l.to_vec()), ScalarVector(r.to_vec()))
+  }
+}
+
+impl Index<usize> for ScalarVector {
+  type Output = Scalar;
+  fn index(&self, index: usize) -> &Scalar {
+    &self.0[index]
+  }
+}
+
+pub(crate) fn inner_product(a: &ScalarVector, b: &ScalarVector) -> Scalar {
+  (a * b).0.drain(..).sum()
+}
+
+impl Mul<&[EdwardsPoint]> for &ScalarVector {
+  type Output = EdwardsPoint;
+  fn mul(self, b: &[EdwardsPoint]) -> EdwardsPoint {
+    assert_eq!(self.len(), b.len());
+    multiexp(&self.0.iter().cloned().zip(b.iter().cloned()).collect::<Vec<_>>())
+  }
+}
+
+pub(crate) fn hadamard_fold(
+  l: &[EdwardsPoint],
+  r: &[EdwardsPoint],
+  a: Scalar,
+  b: Scalar,
+) -> Vec<EdwardsPoint> {
+  let mut res = Vec::with_capacity(l.len() / 2);
+  for i in 0 .. l.len() {
+    res.push(multiexp(&[(a, l[i]), (b, r[i])]));
+  }
+  res
+}