move numeric code out of __add__

don't treat the universal code for point addition specially

Author: tomato42

src/ecdsa/ellipticcurve.py

@@ -333,6 +333,33 @@ def _add_with_z2_1(self, X1, Y1, Z1, X2, Y2):
           return INFINITY
       return PointJacobi(self.__curve, X3, Y3, Z3, self.__order)
 
+  def _add_with_z_ne(self, X1, Y1, Z1, X2, Y2, Z2):
+      """add points with arbitrary z"""
+      # after:
+      # http://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian.html#addition-add-2007-bl
+      p = self.__curve.p()
+      Z1Z1 = Z1 * Z1 % p
+      Z2Z2 = Z2 * Z2 % p
+      U1 = X1 * Z2Z2 % p
+      U2 = X2 * Z1Z1 % p
+      S1 = Y1 * Z2 * Z2Z2 % p
+      S2 = Y2 * Z1 * Z1Z1 % p
+      H = U2 - U1
+      I = 4 * H * H % p
+      J = H * I % p
+      r = 2 * (S2 - S1) % p
+      if not H and not r:
+          return self.double()
+      V = U1 * I
+      X3 = (r * r - J - 2 * V) % p
+      Y3 = (r * (V - X3) - 2 * S1 * J) % p
+      Z3 = ((Z1 + Z2)**2 - Z1Z1 - Z2Z2) * H % p
+
+      if not Y3 or not Z3:
+          return INFINITY
+
+      return PointJacobi(self.__curve, X3, Y3, Z3, self.__order)
+
   def __radd__(self, other):
       """Add other to self."""
       return self + other
@@ -348,7 +375,6 @@ def __add__(self, other):
       if self.__curve != other.__curve:
           raise ValueError("The other point is on different curve")
 
-      p = self.__curve.p()
       X1, Y1, Z1 = self.__x, self.__y, self.__z
       X2, Y2, Z2 = other.__x, other.__y, other.__z
       if Z1 == Z2:
@@ -359,30 +385,7 @@ def __add__(self, other):
           return self._add_with_z2_1(X2, Y2, Z2, X1, Y1)
       if Z2 == 1:
           return self._add_with_z2_1(X1, Y1, Z1, X2, Y2)
-
-      # after:
-      # http://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian.html#addition-add-2007-bl
-      Z1Z1 = Z1 * Z1 % p
-      Z2Z2 = Z2 * Z2 % p
-      U1 = X1 * Z2Z2 % p
-      U2 = X2 * Z1Z1 % p
-      S1 = Y1 * Z2 * Z2Z2 % p
-      S2 = Y2 * Z1 * Z1Z1 % p
-      H = U2 - U1
-      I = 4 * H * H % p
-      J = H * I % p
-      r = 2 * (S2 - S1) % p
-      if not H and not r:
-          return self.double()
-      V = U1 * I
-      X3 = (r * r - J - 2 * V) % p
-      Y3 = (r * (V - X3) - 2 * S1 * J) % p
-      Z3 = ((Z1 + Z2)**2 - Z1Z1 - Z2Z2) * H % p
-
-      if not Y3 or not Z3:
-          return INFINITY
-
-      return PointJacobi(self.__curve, X3, Y3, Z3, self.__order)
+      return self._add_with_z_ne(X1, Y1, Z1, X2, Y2, Z2)
 
   def __rmul__(self, other):
       """Multiply point by an integer."""