fmt

src/fields/extensions.rs

@@ -63,11 +63,11 @@ impl<const D: usize, const N: usize, F: FieldExtensionTrait<D, N>> ConstantTimeE
     }
 }
 impl<'a, 'b, const D: usize, const N: usize, F: FieldExtensionTrait<D, N>>
-Add<&'b FieldExtension<D, N, F>> for &'a FieldExtension<D, N, F>
+    Add<&'b FieldExtension<D, N, F>> for &'a FieldExtension<D, N, F>
 {
     type Output = FieldExtension<D, N, F>;
-    
-    fn add(self, other: &'b FieldExtension<D, N, F>) -> Self::Output  {
+
+    fn add(self, other: &'b FieldExtension<D, N, F>) -> Self::Output {
         let mut i = 0;
         let mut retval = [F::zero(); N];
         while i < N {
@@ -78,7 +78,8 @@ Add<&'b FieldExtension<D, N, F>> for &'a FieldExtension<D, N, F>
     }
 }
 impl<const D: usize, const N: usize, F: FieldExtensionTrait<D, N>> Add<FieldExtension<D, N, F>>
-for FieldExtension<D, N, F> {
+    for FieldExtension<D, N, F>
+{
     type Output = Self;
     fn add(self, other: FieldExtension<D, N, F>) -> Self::Output {
         &self + &other
@@ -92,8 +93,9 @@ impl<const D: usize, const N: usize, F: FieldExtensionTrait<D, N>> AddAssign
     }
 }
 impl<'a, 'b, const D: usize, const N: usize, F: FieldExtensionTrait<D, N>>
-Sub<&'b FieldExtension<D, N, F>> for &'a FieldExtension<D, N, F>{
-    type Output = FieldExtension<D,N,F>;
+    Sub<&'b FieldExtension<D, N, F>> for &'a FieldExtension<D, N, F>
+{
+    type Output = FieldExtension<D, N, F>;
 
     fn sub(self, other: &'b FieldExtension<D, N, F>) -> Self::Output {
         let mut i = 0;
@@ -106,10 +108,11 @@ Sub<&'b FieldExtension<D, N, F>> for &'a FieldExtension<D, N, F>{
     }
 }
 impl<const D: usize, const N: usize, F: FieldExtensionTrait<D, N>> Sub<FieldExtension<D, N, F>>
-for FieldExtension<D, N, F> {
+    for FieldExtension<D, N, F>
+{
     type Output = Self;
     fn sub(self, other: FieldExtension<D, N, F>) -> Self::Output {
-       &self - &other
+        &self - &other
     }
 }
 impl<const D: usize, const N: usize, F: FieldExtensionTrait<D, N>> SubAssign

src/fields/fp.rs

@@ -403,7 +403,7 @@ impl Fp {
         // will require the frobenius transformation
         match exponent {
             1 => self.pow(BN254_FP_MODULUS.value()),
-            _ => *self
+            _ => *self,
         }
     }
     pub fn sqrt(&self) -> CtOption<Self> {
@@ -415,13 +415,9 @@ impl Fp {
         // prime that is congruent to 3 mod 4. In this case, the sqrt only has the
         // possible solution of $\pm pow(n, \frac{p+1}{4})$, which is where this magic
         // number below comes from ;)
-        let arg =
-            ((Self::new(Self::characteristic()) + Self::one()) / Self::from(4)).value();
+        let arg = ((Self::new(Self::characteristic()) + Self::one()) / Self::from(4)).value();
         let sqrt = self.pow(arg);
-        CtOption::new(
-            sqrt,
-            sqrt.square().ct_eq(self),
-        )
+        CtOption::new(sqrt, sqrt.square().ct_eq(self))
     }
     pub fn square(&self) -> Self {
         (*self) * (*self)
@@ -919,10 +915,7 @@ mod tests {
             for _ in 0..100 {
                 let a = <Fp as FieldExtensionTrait<1, 1>>::rand(&mut OsRng);
                 let b = a.square();
-                assert!(
-                    bool::from(b.is_square()),
-                    "Is square failed"
-                );
+                assert!(bool::from(b.is_square()), "Is square failed");
             }
         }
         #[test]

src/fields/fp12.rs

@@ -207,7 +207,7 @@ impl<'a, 'b> Mul<&'b Fp12> for &'a Fp12 {
         ])
     }
 }
-impl Mul for Fp12{
+impl Mul for Fp12 {
     type Output = Self;
     fn mul(self, other: Self) -> Self::Output {
         (&self).mul(&other)
@@ -221,9 +221,7 @@ impl MulAssign for Fp12 {
 impl Inv for Fp12 {
     type Output = Self;
     fn inv(self) -> Self::Output {
-        let tmp = (self.0[0].square()
-            - (self.0[1].square().residue_mul()))
-        .inv();
+        let tmp = (self.0[0].square() - (self.0[1].square().residue_mul())).inv();
         Self([self.0[0] * tmp, -(self.0[1] * tmp)])
     }
 }
@@ -367,12 +365,13 @@ impl Fp12 {
     pub fn frobenius(&self, exponent: usize) -> Self {
         Self::new(&[
             self.0[0].frobenius(exponent),
-            self.0[1].frobenius(exponent)
+            self.0[1]
+                .frobenius(exponent)
                 .scale(FROBENIUS_COEFF_FP12_C1[exponent % 12]),
         ])
     }
     pub fn square(&self) -> Self {
-        // For F_{p^{12}} = F_{p^6}(w)/(w^2-\gamma), and A=a_0 + a_1*w \in F_{p^{12}}, 
+        // For F_{p^{12}} = F_{p^6}(w)/(w^2-\gamma), and A=a_0 + a_1*w \in F_{p^{12}},
         // we determine C=c_0+c_1*w = A^2\in F_{p^{12}}
         // Alg 22 from <https://eprint.iacr.org/2010/354.pdf>
         let c0 = self.0[0] - self.0[1];

src/fields/fp2.rs

@@ -95,17 +95,11 @@ impl Fp2 {
         if alpha == -Fp2::one() {
             let i = Fp2::new(&[Fp::ZERO, Fp::ONE]);
             let sqrt = i * a1 * (*self);
-            CtOption::new(
-                sqrt,
-                sqrt.square().ct_eq(self),
-            )
+            CtOption::new(sqrt, sqrt.square().ct_eq(self))
         } else {
             let b = (alpha + Fp2::one()).pow(&P_MINUS_1_OVER_2);
             let sqrt = b * a1 * (*self);
-            CtOption::new(
-                sqrt,
-                sqrt.square().ct_eq(self),
-            )
+            CtOption::new(sqrt, sqrt.square().ct_eq(self))
         }
     }
     pub fn square(&self) -> Self {
@@ -131,8 +125,7 @@ impl Fp2 {
             }
         };
         let sum = self.0[0].square()
-            + <Fp as FieldExtensionTrait<1, 1>>::quadratic_non_residue()
-            * (-self.0[0]).square();
+            + <Fp as FieldExtensionTrait<1, 1>>::quadratic_non_residue() * (-self.0[0]).square();
         Choice::from((legendre(&sum) != -1) as u8)
     }
     pub fn sgn0(&self) -> Choice {
@@ -158,8 +151,7 @@ impl FieldExtensionTrait<2, 2> for Fp2 {
         FP2_TWIST_CURVE_CONSTANT
     }
 }
-impl<'a, 'b> Mul<&'b Fp2> for &'a Fp2
-{
+impl<'a, 'b> Mul<&'b Fp2> for &'a Fp2 {
     type Output = Fp2;
     fn mul(self, other: &'b Fp2) -> Self::Output {
         // This requires a bit more consideration. In Fp2,
@@ -176,11 +168,10 @@ impl<'a, 'b> Mul<&'b Fp2> for &'a Fp2
         ])
     }
 }
-impl Mul<Fp2> for Fp2
-{
+impl Mul<Fp2> for Fp2 {
     type Output = Self;
     fn mul(self, other: Fp2) -> Self::Output {
-        // TODO linter complains about this being a needless reference if I do &a * &b, so this 
+        // TODO linter complains about this being a needless reference if I do &a * &b, so this
         // gets around it
         (&self).mul(&other)
     }
@@ -416,11 +407,7 @@ mod tests {
                 ],
             );
             for i in [a, b, c] {
-                assert_eq!(
-                    i.square(),
-                    i * i,
-                    "Squaring failed"
-                );
+                assert_eq!(i.square(), i * i, "Squaring failed");
             }
         }
         #[test]
@@ -512,10 +499,7 @@ mod tests {
             for _ in 0..100 {
                 let a = <Fp2 as FieldExtensionTrait<2, 2>>::rand(&mut OsRng);
                 let b = a.square();
-                assert!(
-                    bool::from(b.is_square()),
-                    "Is square failed"
-                );
+                assert!(bool::from(b.is_square()), "Is square failed");
             }
         }
     }

src/fields/fp6.rs

@@ -180,10 +180,8 @@ impl Fp6 {
     pub fn frobenius(&self, exponent: usize) -> Self {
         Self::new(&[
             self.0[0].frobenius(exponent),
-            self.0[1].frobenius(exponent)
-                * FROBENIUS_COEFF_FP6_C1[exponent % 6],
-            self.0[2].frobenius(exponent)
-                * FROBENIUS_COEFF_FP6_C2[exponent % 6],
+            self.0[1].frobenius(exponent) * FROBENIUS_COEFF_FP6_C1[exponent % 6],
+            self.0[2].frobenius(exponent) * FROBENIUS_COEFF_FP6_C2[exponent % 6],
         ])
     }
 
@@ -260,10 +258,8 @@ impl MulAssign for Fp6 {
 impl Inv for Fp6 {
     type Output = Self;
     fn inv(self) -> Self::Output {
-        let t0 = self.0[0].square()
-            - self.0[1] * self.0[2].residue_mul();
-        let t1 = self.0[2].square().residue_mul()
-            - self.0[0] * self.0[1];
+        let t0 = self.0[0].square() - self.0[1] * self.0[2].residue_mul();
+        let t1 = self.0[2].square().residue_mul() - self.0[0] * self.0[1];
         let t2 = self.0[1].square() - self.0[0] * self.0[2];
 
         let inverse = ((self.0[2] * t1 + self.0[1] * t2).residue_mul() + self.0[0] * t0).inv();
@@ -570,12 +566,12 @@ mod tests {
             );
             assert_eq!(
                 a,
-                a.frobenius(1).
-                    frobenius(1).
-                    frobenius(1).
-                    frobenius(1).
-                    frobenius(1).
-                    frobenius(1),
+                a.frobenius(1)
+                    .frobenius(1)
+                    .frobenius(1)
+                    .frobenius(1)
+                    .frobenius(1)
+                    .frobenius(1),
                 "Frobenius failed at cycle order 6"
             );
         }

src/fields/utils.rs

@@ -10,4 +10,4 @@ pub fn to_larger_uint<const N: usize, const M: usize>(smaller_bytes: &[u8; N]) -
 // Specific conversion functions
 pub fn u256_to_u512(u256: &U256) -> U512 {
     U512::from_be_bytes(to_larger_uint::<32, 64>(&u256.to_be_bytes()))
-}
+}

src/groups/g2.rs

@@ -23,7 +23,7 @@ use crypto_bigint::U256;
 use num_traits::{One, Zero};
 use subtle::{Choice, ConstantTimeEq};
 
-/// This is the X coordinate of the generator for the r-torsion of the twist curve, generated 
+/// This is the X coordinate of the generator for the r-torsion of the twist curve, generated
 /// directly from sage
 const G2_X: Fp2 = Fp2::new(&[
     Fp::new(U256::from_words([

src/groups/mod.rs

@@ -462,8 +462,10 @@ mod tests {
             fn test_svdw() {
                 load_g1_reference_data!(g1_points);
 
-                if let Ok(d) = SvdW::precompute_constants(Fp::ZERO, <Fp as 
-                    FieldExtensionTrait<1,1>>::curve_constant()) {
+                if let Ok(d) = SvdW::precompute_constants(
+                    Fp::ZERO,
+                    <Fp as FieldExtensionTrait<1, 1>>::curve_constant(),
+                ) {
                     for s in g1_points.svdw.iter() {
                         let r = s.i;
                         let p = s.p;

src/pairing.rs

@@ -219,9 +219,9 @@ impl MillerLoopResult {
 /// time. Again, because of the sparse nature of the returned Fp12 from the doubling and addition
 /// steps, we store only the 3 non-zero coefficients in an arr of EllCoeffs
 ///
-/// There's two components to this struct. First, is the original value at which we are 
-/// computing the line. Second, is an array of the coefficients we determine by the generation 
-/// of the line, stored as an array. But an array of 87 elements is very specific, no?  
+/// There's two components to this struct. First, is the original value at which we are
+/// computing the line. Second, is an array of the coefficients we determine by the generation
+/// of the line, stored as an array. But an array of 87 elements is very specific, no?
 /// There's 64 total iterations through the NAF representation, each one incurring a
 /// doubling step. Further, there are 9 `1` digits (each with an addition step), and 12 `3`
 /// digits, each also with an addition step. After the loop, there are 2 more addition steps, so
@@ -334,7 +334,7 @@ impl G2Projective {
         let g = (b + f).scale(TWO_INV);
         let h = (self.y + self.z).square() - (b + c);
         let i = e - b;
-        let j =self.x.square();
+        let j = self.x.square();
         let e_sq = e.square();
 
         self.x = a * (b - f);

src/svdw.rs

@@ -13,8 +13,8 @@
 //! ----------
 //! 1. <https://link.springer.com/chapter/10.1007/11792086_36>
 
-use num_traits::{Inv, Zero};
 use crate::fields::fp::Fp;
+use num_traits::{Inv, Zero};
 use subtle::Choice;
 
 #[derive(Debug)]
@@ -39,8 +39,7 @@ pub trait SvdWTrait: Sized {
 
     fn find_z_svdw(a: Fp, b: Fp) -> Fp {
         let g = |x: &Fp| -> Fp { (*x) * (*x) * (*x) + a * (*x) + b };
-        let h = |x: &Fp| -> Fp { -(Fp::THREE * (*x) * (*x) + Fp::FOUR * a) / (Fp::FOUR * g(x)
-        ) };
+        let h = |x: &Fp| -> Fp { -(Fp::THREE * (*x) * (*x) + Fp::FOUR * a) / (Fp::FOUR * g(x)) };
         let mut ctr = 1;
         loop {
             for z_cand in [Fp::from(ctr), -Fp::from(ctr)] {
@@ -96,8 +95,7 @@ pub trait SvdWTrait: Sized {
     }
     fn unchecked_map_to_point(&self, u: Fp) -> Result<[Fp; 2], MapError>;
 }
-impl SvdWTrait for SvdW
-{
+impl SvdWTrait for SvdW {
     fn unchecked_map_to_point(&self, u: Fp) -> Result<[Fp; 2], MapError> {
         // Implements the SvdW algorithm for a single scalar point
         let cmov = |x: &Fp, y: &Fp, b: &Choice| -> Fp {
@@ -158,7 +156,10 @@ mod tests {
 
         #[test]
         fn test_z_svdw() {
-            let z = SvdW::find_z_svdw(Fp::ZERO, <Fp as FieldExtensionTrait<1,1>>::curve_constant());
+            let z = SvdW::find_z_svdw(
+                Fp::ZERO,
+                <Fp as FieldExtensionTrait<1, 1>>::curve_constant(),
+            );
             assert_eq!(z, Fp::ONE, "Finding Z failed for BN254");
         }
         #[test]