1 files changed, 10 insertions, 7 deletions
diff --git a/bip-schnorr/reference.py b/bip-schnorr/reference.py
index e5d9557..7de37c2 100644
--- a/bip-schnorr/reference.py
+++ b/bip-schnorr/reference.py
@@ -11,6 +11,9 @@ def tagged_hash(tag, msg):
     tag_hash = hashlib.sha256(tag.encode()).digest()
     return hashlib.sha256(tag_hash + tag_hash + msg).digest()
 
+def is_infinity(P):
+    return P is None
+
 def x(P):
     return P[0]
 
@@ -59,11 +62,11 @@ def int_from_bytes(b):
 def hash_sha256(b):
     return hashlib.sha256(b).digest()
 
-def jacobi(x):
-    return pow(x, (p - 1) // 2, p)
+def is_square(x):
+    return pow(x, (p - 1) // 2, p) == 1
 
-def is_quad(x):
-    return jacobi(x) == 1
+def has_square_y(P):
+    return not is_infinity(P) and is_square(y(P))
 
 def pubkey_gen(seckey):
     x = int_from_bytes(seckey)
@@ -79,12 +82,12 @@ def schnorr_sign(msg, seckey0):
     if not (1 <= seckey0 <= n - 1):
         raise ValueError('The secret key must be an integer in the range 1..n-1.')
     P = point_mul(G, seckey0)
-    seckey = seckey0 if is_quad(y(P)) else n - seckey0
+    seckey = seckey0 if has_square_y(P) else n - seckey0
     k0 = int_from_bytes(tagged_hash("BIPSchnorrDerive", bytes_from_int(seckey) + msg)) % n
     if k0 == 0:
         raise RuntimeError('Failure. This happens only with negligible probability.')
     R = point_mul(G, k0)
-    k = n - k0 if not is_quad(y(R)) else k0
+    k = n - k0 if not has_square_y(R) else k0
     e = int_from_bytes(tagged_hash("BIPSchnorr", bytes_from_point(R) + bytes_from_point(P) + msg)) % n
     return bytes_from_point(R) + bytes_from_int((k + e * seckey) % n)
 
@@ -104,7 +107,7 @@ def schnorr_verify(msg, pubkey, sig):
         return False
     e = int_from_bytes(tagged_hash("BIPSchnorr", sig[0:32] + pubkey + msg)) % n
     R = point_add(point_mul(G, s), point_mul(P, n - e))
-    if R is None or not is_quad(y(R)) or x(R) != r:
+    if R is None or not has_square_y(R) or x(R) != r:
         return False
     return True