[arith]: isSquare on 𝔽r (#576)

Author: mratsim

constantine/math/arithmetic/finite_fields_square_root.nim

@@ -361,13 +361,13 @@ func invsqrt_if_square_vartime*[Name](r: var Fp[Name], a: Fp[Name]): SecretBool
 # Legendre symbol / Euler's Criterion / Kronecker's symbol
 # ------------------------------------------------------------
 
-func isSquare*(a: Fp): SecretBool =
-  ## Returns true if ``a`` is a square (quadratic residue) in 𝔽p
+func isSquare*(a: FF): SecretBool =
+  ## Returns true if ``a`` is a square (quadratic residue) in 𝔽p or 𝔽r
   ##
-  ## Assumes that the prime modulus ``p`` is public.
-  var aa {.noInit.}: Fp.getBigInt()
+  ## Assumes that the prime modulus ``p`` (or ``r``) is public.
+  var aa {.noInit.}: FF.getBigInt()
   aa.fromField(a)
-  let symbol = legendre(aa.limbs, Fp.getModulus().limbs, aa.bits)
+  let symbol = legendre(aa.limbs, FF.getModulus().limbs, aa.bits)
   return not(symbol == MaxWord)
 
 {.pop.} # inline

tests/math_fields/t_finite_fields_sqrt.nim

@@ -199,4 +199,18 @@ proc main() =
       a.fromHex"0x7ff7ffffffffffff1dfb7fafc0000000"
       testSqrtImpl(a)
 
+  suite "isSquare on 𝔽r" & " [" & $WordBitWidth & "-bit words]":
+    test "𝔽r[BW6_761] is consistent with 𝔽p[BLS12_381]":
+      block:
+        var a: Fr[BW6_761]
+        a.fromHex"0x184d02ce4f24d5e59b4150a57a31b202fd40a4b41d7518c22b84bee475fbcb7763100448ef6b17a6ea603cf062e5db51"
+        check:
+          bool(not a.isSquare())
+
+      block:
+        var a: Fr[BW6_761]
+        a.fromHex"0x0f16d7854229d8804bcadd889f70411d6a482bde840d238033bf868e89558d39d52f9df60b2d745e02584375f16c34a3"
+        check:
+          bool(not a.isSquare())
+
 main()