Create enum for LegendreSymbol, fix test.

src/bls12_381/ec.rs

@@ -1480,7 +1480,7 @@ pub mod g2 {
             if let Some(y) = rhs.sqrt() {
                 let mut negy = y;
                 negy.negate();
-                
+
                 let p = G2Affine {
                     x: x,
                     y: if y < negy { y } else { negy },

src/bls12_381/fq.rs

@@ -833,19 +833,14 @@ impl SqrtField for Fq {
 }
 
 impl LegendreField for Fq {
-    fn legendre(&self) -> i32 {
-        // (q - 1) / 2 =
-        // 2001204777610833696708894912867952078278441409969503942666029068062015825245418932221343814564507832018947136279893
-        let x = self.pow([0xcff7fffffffd555, 0xf55ffff58a9ffffd,
-                          0x39869507b587b120, 0x23ba5c279c2895fb,
-                          0x58dd3db21a5d66bb, 0xd0088f51cbff34d2]);
-        if x == Self::one() {
-            1
-        } else if x == Self::zero() {
-            0
-        } else {
-            -1
-        }
+    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 }
     }
 }
 
@@ -1320,12 +1315,12 @@ fn test_fq_sub_assign() {
         let mut tmp = Fq(FqRepr([0x531221a410efc95b, 0x72819306027e9717, 0x5ecefb937068b746, 0x97de59cd6feaefd7, 0xdc35c51158644588, 0xb2d176c04f2100]));
         tmp.sub_assign(&Fq(FqRepr([0x98910d20877e4ada, 0x940c983013f4b8ba, 0xf677dc9b8345ba33, 0xbef2ce6b7f577eba, 0xe1ae288ac3222c44, 0x5968bb602790806])));
         assert_eq!(tmp, Fq(FqRepr([0x748014838971292c, 0xfd20fad49fddde5c, 0xcf87f198e3d3f336, 0x3d62d6e6e41883db, 0x45a3443cd88dc61b, 0x151d57aaf755ff94])));
-        
+
         // Test the opposite subtraction which doesn't test reduction.
         tmp = Fq(FqRepr([0x98910d20877e4ada, 0x940c983013f4b8ba, 0xf677dc9b8345ba33, 0xbef2ce6b7f577eba, 0xe1ae288ac3222c44, 0x5968bb602790806]));
         tmp.sub_assign(&Fq(FqRepr([0x531221a410efc95b, 0x72819306027e9717, 0x5ecefb937068b746, 0x97de59cd6feaefd7, 0xdc35c51158644588, 0xb2d176c04f2100])));
         assert_eq!(tmp, Fq(FqRepr([0x457eeb7c768e817f, 0x218b052a117621a3, 0x97a8e10812dd02ed, 0x2714749e0f6c8ee3, 0x57863796abde6bc, 0x4e3ba3f4229e706])));
-        
+
         // Test for sensible results with zero
         tmp = Fq(FqRepr::from(0));
         tmp.sub_assign(&Fq(FqRepr::from(0)));
@@ -1796,29 +1791,21 @@ fn test_fq_ordering() {
 fn fq_repr_tests() {
     ::tests::repr::random_repr_tests::<FqRepr>();
 }
+
 #[test]
 fn test_fq_legendre() {
-    assert_eq!(1, Fq::one().legendre());
-    assert_eq!(0, Fq::zero().legendre());
+    use ::LegendreSymbol::*;
 
-    let e = Fq(FqRepr([0x914577fdcc41112, 0x1a6c20f3392c28e2, 0xd53f75da0c40fd21,
-                       0xb747c10d13caf0d0, 0x0de1adc19c24d8d2, 0x2103f924191033d2]));
-    assert_eq!(-1, e.legendre());
+    assert_eq!(QResidue, Fq::one().legendre());
+    assert_eq!(Zero, Fq::zero().legendre());
 
+    assert_eq!(QNonResidue, Fq::from_repr(FqRepr::from(2)).unwrap().legendre());
+    assert_eq!(QResidue, Fq::from_repr(FqRepr::from(4)).unwrap().legendre());
 
-    // f
-    let e = Fq(FqRepr([0xe51d5292ae8126f, 0x382d60874f48db82, 0xb0dde25abc614254,
-                       0x34f4456bd18813df, 0x2c668010247ee04c, 0x44cb8bbdd7c4f1b0]));
-    assert_eq!(-1, e.legendre());
-
-    // f ** 9
-    let e = Fq(FqRepr([0x69fc8eb1b590c712, 0xd73f4fb6fd34042e, 0xb5677ef2ed0eede7,
-                       0x367d831c592848c8, 0xb60615cc44e533f5, 0x127da624461b200e]));
-
-    assert_eq!(-1, e.legendre());
-
-    let e = Fq(FqRepr([0x83c7ad9e29b7facc, 0x97b3c8fbdb50cc39, 0x9e2ccd0eb5db5e72,
-                       0xc74a00d90e1b247d, 0x90e38ef46c8d7eb7, 0x16882d6aa70bb469]));
-    assert_eq!(1, e.legendre());
-
+    let e = FqRepr([0x52a112f249778642, 0xd0bedb989b7991f, 0xdad3b6681aa63c05,
+                    0xf2efc0bb4721b283, 0x6057a98f18c24733, 0x1022c2fd122889e4]);
+    assert_eq!(QNonResidue, Fq::from_repr(e).unwrap().legendre());
+    let e = FqRepr([0x6dae594e53a96c74, 0x19b16ca9ba64b37b, 0x5c764661a59bfc68,
+                    0xaa346e9b31c60a, 0x346059f9d87a9fa9, 0x1d61ac6bfd5c88b]);
+    assert_eq!(QResidue, Fq::from_repr(e).unwrap().legendre());
 }

src/bls12_381/fq2.rs

@@ -197,7 +197,7 @@ impl SqrtField for Fq2 {
 }
 
 impl LegendreField for Fq2 {
-    fn legendre(&self) -> i32 {
+    fn legendre(&self) -> ::LegendreSymbol {
         Fq2::norm(&self).legendre()
     }
 }
@@ -431,13 +431,14 @@ fn test_fq2_sqrt() {
 
 #[test]
 fn test_fq2_legendre() {
+    use ::LegendreSymbol::*;
+
     // i^2 = -1
     let mut m1 = Fq2::one();
     m1.negate();
-    assert_eq!(1, m1.legendre());
-
+    assert_eq!(QResidue, m1.legendre());
     m1.mul_by_nonresidue();
-    assert_eq!(-1, m1.legendre());
+    assert_eq!(QNonResidue, m1.legendre());
 }
 
 #[cfg(test)]

src/bls12_381/fr.rs

@@ -1,4 +1,5 @@
 use ::{Field, LegendreField, PrimeField, SqrtField, PrimeFieldRepr, PrimeFieldDecodingError};
+use ::LegendreSymbol::*;
 
 // r = 52435875175126190479447740508185965837690552500527637822603658699938581184513
 const MODULUS: FrRepr = FrRepr([0xffffffff00000001, 0x53bda402fffe5bfe, 0x3339d80809a1d805, 0x73eda753299d7d48]);
@@ -559,7 +560,7 @@ impl SqrtField for Fr {
             return Some(*self);
         }
 
-        if self.legendre() != 1 {
+        if let QNonResidue = self.legendre() {
             None
         } else {
             let mut c = Fr(ROOT_OF_UNITY);
@@ -598,16 +599,11 @@ impl SqrtField for Fr {
 }
 
 impl LegendreField for Fr {
-        fn legendre(&self) -> i32 {
-        // (q - 1) / 2 = 26217937587563095239723870254092982918845276250263818911301829349969290592256
-        let x = self.pow([0x7fffffff80000000, 0xa9ded2017fff2dff, 0x199cec0404d0ec02, 0x39f6d3a994cebea4]);
-        if x == Self::one() {
-            1
-        } else if x == Self::zero() {
-            0
-        } else {
-            -1
-        }
+    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)]
@@ -792,13 +788,13 @@ fn test_fr_repr_sub_noborrow() {
 
 #[test]
 fn test_fr_legendre() {
-    assert_eq!(1, Fr::one().legendre());
-    assert_eq!(0, Fr::zero().legendre());
+    assert_eq!(QResidue, Fr::one().legendre());
+    assert_eq!(Zero, Fr::zero().legendre());
 
-    let e = Fr(FrRepr([0x0dbc5349cd5664da, 0x8ac5b6296e3ae29d, 0x127cb819feceaa3b, 0x3a6b21fb03867191]));
-    assert_eq!(1, e.legendre());
-    let e = Fr(FrRepr([0x96341aefd047c045, 0x9b5f4254500a4d65, 0x1ee08223b68ac240, 0x31d9cd545c0ec7c6]));
-    assert_eq!(-1, e.legendre());
+    let e = FrRepr([0x0dbc5349cd5664da, 0x8ac5b6296e3ae29d, 0x127cb819feceaa3b, 0x3a6b21fb03867191]);
+    assert_eq!(QResidue, Fr::from_repr(e).unwrap().legendre());
+    let e = FrRepr([0x96341aefd047c045, 0x9b5f4254500a4d65, 0x1ee08223b68ac240, 0x31d9cd545c0ec7c6]);
+    assert_eq!(QNonResidue, Fr::from_repr(e).unwrap().legendre());
 }
 
 #[test]
@@ -1038,12 +1034,12 @@ fn test_fr_sub_assign() {
         let mut tmp = Fr(FrRepr([0x6a68c64b6f735a2b, 0xd5f4d143fe0a1972, 0x37c17f3829267c62, 0xa2f37391f30915c]));
         tmp.sub_assign(&Fr(FrRepr([0xade5adacdccb6190, 0xaa21ee0f27db3ccd, 0x2550f4704ae39086, 0x591d1902e7c5ba27])));
         assert_eq!(tmp, Fr(FrRepr([0xbc83189d92a7f89c, 0x7f908737d62d38a3, 0x45aa62cfe7e4c3e1, 0x24ffc5896108547d])));
-        
+
         // Test the opposite subtraction which doesn't test reduction.
         tmp = Fr(FrRepr([0xade5adacdccb6190, 0xaa21ee0f27db3ccd, 0x2550f4704ae39086, 0x591d1902e7c5ba27]));
         tmp.sub_assign(&Fr(FrRepr([0x6a68c64b6f735a2b, 0xd5f4d143fe0a1972, 0x37c17f3829267c62, 0xa2f37391f30915c])));
         assert_eq!(tmp, Fr(FrRepr([0x437ce7616d580765, 0xd42d1ccb29d1235b, 0xed8f753821bd1423, 0x4eede1c9c89528ca])));
-        
+
         // Test for sensible results with zero
         tmp = Fr(FrRepr::from(0));
         tmp.sub_assign(&Fr(FrRepr::from(0)));

src/lib.rs

@@ -336,7 +336,7 @@ pub trait SqrtField: Field
 pub trait LegendreField: Field
 {
     /// Returns the legendre symbol of the field element.
-    fn legendre(&self) -> i32;
+    fn legendre(&self) -> LegendreSymbol;
 }
 
 
@@ -417,6 +417,13 @@ pub trait PrimeFieldRepr: Sized +
     }
 }
 
+#[derive(Debug, PartialEq)]
+pub enum LegendreSymbol {
+    Zero = 0,
+    QResidue = 1,
+    QNonResidue = -1
+}
+
 /// An error that may occur when trying to interpret a `PrimeFieldRepr` as a
 /// `PrimeField` element.
 #[derive(Debug)]