Add x() and y() functions for points to bip-schnorr

1 files changed, 15 insertions, 9 deletions

diff --git a/bip-schnorr/reference.py b/bip-schnorr/reference.py
index 95e9e53..bd12212 100644
--- a/bip-schnorr/reference.py
+++ b/bip-schnorr/reference.py
@@ -11,19 +11,25 @@ def tagged_hash(tag, msg):
     tag_hash = hashlib.sha256(tag.encode()).digest()
     return hashlib.sha256(tag_hash + tag_hash + msg).digest()
 
+def x(P):
+    return P[0]
+
+def y(P):
+    return P[1]
+
 def point_add(P1, P2):
     if (P1 is None):
         return P2
     if (P2 is None):
         return P1
-    if (P1[0] == P2[0] and P1[1] != P2[1]):
+    if (x(P1) == x(P2) and y(P1) != y(P2)):
         return None
     if (P1 == P2):
-        lam = (3 * P1[0] * P1[0] * pow(2 * P1[1], p - 2, p)) % p
+        lam = (3 * x(P1) * x(P1) * pow(2 * y(P1), p - 2, p)) % p
     else:
-        lam = ((P2[1] - P1[1]) * pow(P2[0] - P1[0], p - 2, p)) % p
-    x3 = (lam * lam - P1[0] - P2[0]) % p
-    return (x3, (lam * (P1[0] - x3) - P1[1]) % p)
+        lam = ((y(P2) - y(P1)) * pow(x(P2) - x(P1), p - 2, p)) % p
+    x3 = (lam * lam - x(P1) - x(P2)) % p
+    return (x3, (lam * (x(P1) - x3) - y(P1)) % p)
 
 def point_mul(P, n):
     R = None
@@ -37,7 +43,7 @@ def bytes_from_int(x):
     return x.to_bytes(32, byteorder="big")
 
 def bytes_from_point(P):
-    return bytes_from_int(P[0])
+    return bytes_from_int(x(P))
 
 def point_from_bytes(b):
     x = int_from_bytes(b)
@@ -66,12 +72,12 @@ 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 (jacobi(P[1]) == 1) else n - seckey0
+    seckey = seckey0 if (jacobi(y(P)) == 1) 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 (jacobi(R[1]) != 1) else k0
+    k = n - k0 if (jacobi(y(R)) != 1) 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)
 
@@ -91,7 +97,7 @@ 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 jacobi(R[1]) != 1 or R[0] != r:
+    if R is None or jacobi(y(R)) != 1 or x(R) != r:
         return False
     return True