Merge traits SqrtField and LegendreField into SqrtField.

src/bls12_381/fq.rs

@@ -1,4 +1,4 @@
-use ::{Field, LegendreField, PrimeField, SqrtField, PrimeFieldRepr, PrimeFieldDecodingError};
+use ::{Field, PrimeField, SqrtField, PrimeFieldRepr, PrimeFieldDecodingError};
 use std::cmp::Ordering;
 use super::fq2::Fq2;
 
@@ -810,6 +810,17 @@ impl Fq {
 }
 
 impl SqrtField for Fq {
+
+    fn legendre(&self) -> ::LegendreSymbol {
+        use ::LegendreSymbol::*;
+
+        let s = self.pow([0xdcff7fffffffd555, 0xf55ffff58a9ffff, 0xb39869507b587b12,
+                          0xb23ba5c279c2895f, 0x258dd3db21a5d66b, 0xd0088f51cbff34d]);
+        if s == Fq::zero() { Zero }
+        else if s == Fq::one() { QResidue }
+        else { QNonResidue }
+    }
+
     fn sqrt(&self) -> Option<Self> {
         // Shank's algorithm for q mod 4 = 3
         // https://eprint.iacr.org/2012/685.pdf (page 9, algorithm 2)
@@ -832,17 +843,6 @@ impl SqrtField for Fq {
     }
 }
 
-impl LegendreField for Fq {
-    fn legendre(&self) -> ::LegendreSymbol {
-        use ::LegendreSymbol::*;
-
-        let s = self.pow([0xdcff7fffffffd555, 0xf55ffff58a9ffff, 0xb39869507b587b12,
-                          0xb23ba5c279c2895f, 0x258dd3db21a5d66b, 0xd0088f51cbff34d]);
-        if s == Fq::zero() { Zero }
-        else if s == Fq::one() { QResidue }
-        else { QNonResidue }
-    }
-}
 
 #[test]
 fn test_b_coeff() {

src/bls12_381/fq2.rs

@@ -1,5 +1,5 @@
 use rand::{Rng, Rand};
-use ::{Field, LegendreField, SqrtField};
+use ::{Field, SqrtField};
 use super::fq::{Fq, FROBENIUS_COEFF_FQ2_C1, NEGATIVE_ONE};
 
 use std::cmp::Ordering;
@@ -156,6 +156,11 @@ impl Field for Fq2 {
 }
 
 impl SqrtField for Fq2 {
+
+    fn legendre(&self) -> ::LegendreSymbol {
+        Fq2::norm(&self).legendre()
+    }
+
     fn sqrt(&self) -> Option<Self> {
         // Algorithm 9, https://eprint.iacr.org/2012/685.pdf
 
@@ -196,12 +201,6 @@ impl SqrtField for Fq2 {
     }
 }
 
-impl LegendreField for Fq2 {
-    fn legendre(&self) -> ::LegendreSymbol {
-        Fq2::norm(&self).legendre()
-    }
-}
-
 #[test]
 fn test_fq2_ordering() {
     let mut a = Fq2 {

src/bls12_381/fr.rs

@@ -1,4 +1,4 @@
-use ::{Field, LegendreField, PrimeField, SqrtField, PrimeFieldRepr, PrimeFieldDecodingError};
+use ::{Field, PrimeField, SqrtField, PrimeFieldRepr, PrimeFieldDecodingError};
 use ::LegendreSymbol::*;
 
 // r = 52435875175126190479447740508185965837690552500527637822603658699938581184513
@@ -552,6 +552,14 @@ impl Fr {
 }
 
 impl SqrtField for Fr {
+
+    fn legendre(&self) -> ::LegendreSymbol {
+        let s = self.pow([0x7fffffff80000000, 0xa9ded2017fff2dff, 0x199cec0404d0ec02, 0x39f6d3a994cebea4]);
+        if s == Self::zero() { Zero }
+        else if s == Self::one() { QResidue }
+        else { QNonResidue }
+    }
+
     fn sqrt(&self) -> Option<Self> {
         // Tonelli-Shank's algorithm for q mod 16 = 1
         // https://eprint.iacr.org/2012/685.pdf (page 12, algorithm 5)
@@ -595,15 +603,6 @@ impl SqrtField for Fr {
     }
 }
 
-impl LegendreField for Fr {
-    fn legendre(&self) -> ::LegendreSymbol {
-        let s = self.pow([0x7fffffff80000000, 0xa9ded2017fff2dff, 0x199cec0404d0ec02, 0x39f6d3a994cebea4]);
-        if s == Self::zero() { Zero }
-        else if s == Self::one() { QResidue }
-        else { QNonResidue }
-    }
-}
-
 #[cfg(test)]
 use rand::{SeedableRng, XorShiftRng, Rand};
 

src/lib.rs

@@ -327,18 +327,14 @@ pub trait Field: Sized +
 /// 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 an element of a field that has a Legendre symbol described for it.
-pub trait LegendreField: Field
-{
-    /// Returns the legendre symbol of the field element.
-    fn legendre(&self) -> LegendreSymbol;
-}
-
 
 /// 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