Fix point at infinity verification in signature and public key

Author: cdottori-stark

ellipticcurve/curve.py

@@ -3,7 +3,6 @@
 #
 # y^2 = x^3 + A*x + B (mod P)
 #
-
 from .point import Point
 
 
@@ -26,7 +25,13 @@ def contains(self, p):
         :param p: Point p = Point(x, y)
         :return: boolean
         """
-        return (p.y**2 - (p.x**3 + self.A * p.x + self.B)) % self.P == 0
+        if not 0 <= p.x <= self.P - 1:
+            return False
+        if not 0 <= p.y <= self.P - 1:
+            return False
+        if (p.y**2 - (p.x**3 + self.A * p.x + self.B)) % self.P != 0:
+            return False
+        return True
 
     def length(self):
         return (1 + len("%x" % self.N)) // 2
@@ -67,10 +72,8 @@ def length(self):
 
 def getCurveByOid(oid):
     if oid not in _curvesByOid:
-        raise Exception(
-            "Unknown curve with oid %s; The following are registered: %s" % (
-                ".".join(oid),
-                ", ".join([curve.name for curve in supportedCurves])
-            )
-        )
+        raise Exception("Unknown curve with oid {oid}; The following are registered: {names}".format(
+            oid=".".join(oid),
+            names=", ".join([curve.name for curve in supportedCurves]),
+        ))
     return _curvesByOid[oid]

ellipticcurve/ecdsa.py

@@ -40,6 +40,7 @@ def verify(cls, message, signature, publicKey, hashfunc=sha256):
         inv = Math.inv(s, curve.N)
         u1 = Math.multiply(curve.G, n=(numberMessage * inv) % curve.N, N=curve.N, A=curve.A, P=curve.P)
         u2 = Math.multiply(publicKey.point, n=(r * inv) % curve.N, N=curve.N, A=curve.A, P=curve.P)
-        add = Math.add(u1, u2, A=curve.A, P=curve.P)
-        modX = add.x % curve.N
-        return r == modX
+        v = Math.add(u1, u2, A=curve.A, P=curve.P)
+        if v.isAtInfinity():
+            return False
+        return v.x % curve.N == r

ellipticcurve/math.py

@@ -97,7 +97,7 @@ def _jacobianDouble(cls, p, A, P):
         :param A: Coefficient of the first-order term of the equation Y^2 = X^3 + A*X + B (mod p)
         :return: Point that represents the sum of First and Second Point
         """
-        if not p.y:
+        if p.y == 0:
             return Point(0, 0, 0)
 
         ysq = (p.y ** 2) % P
@@ -120,10 +120,9 @@ def _jacobianAdd(cls, p, q, A, P):
         :param A: Coefficient of the first-order term of the equation Y^2 = X^3 + A*X + B (mod p)
         :return: Point that represents the sum of First and Second Point
         """
-        if not p.y:
+        if p.y == 0:
             return q
-
-        if not q.y:
+        if q.y == 0:
             return p
 
         U1 = (p.x * q.z ** 2) % P

ellipticcurve/point.py

@@ -6,3 +6,9 @@ def __init__(self, x=0, y=0, z=0):
         self.x = x
         self.y = y
         self.z = z
+
+    def __str__(self):
+        return "({x}, {y}, {z})".format(x=self.x, y=self.y, z=self.z)
+
+    def isAtInfinity(self):
+        return self.y == 0

ellipticcurve/publicKey.py

@@ -1,8 +1,9 @@
+from .math import Math
 from .point import Point
+from .curve import secp256k1, getCurveByOid
 from .utils.pem import getPemContent, createPem
-from .utils.binary import hexFromByteString, byteStringFromHex, intFromHex, base64FromByteString, byteStringFromBase64
 from .utils.der import hexFromInt, parse, DerFieldType, encodeConstructed, encodePrimitive
-from .curve import secp256k1, getCurveByOid
+from .utils.binary import hexFromByteString, byteStringFromHex, intFromHex, base64FromByteString, byteStringFromBase64
 
 
 class PublicKey:
@@ -65,12 +66,16 @@ def fromString(cls, string, curve=secp256k1, validatePoint=True):
             x=intFromHex(xs),
             y=intFromHex(ys),
         )
-        if validatePoint and not curve.contains(p):
-            raise Exception(
-                "Point ({x},{y}) is not valid for curve {name}".format(x=p.x, y=p.y, name=curve.name)
-            )
-
-        return PublicKey(point=p, curve=curve)
+        publicKey = PublicKey(point=p, curve=curve)
+        if not validatePoint:
+            return publicKey
+        if p.isAtInfinity():
+            raise Exception("Public Key point is at infinity")
+        if not curve.contains(p):
+            raise Exception("Point ({x},{y}) is not valid for curve {name}".format(x=p.x, y=p.y, name=curve.name))
+        if not Math.multiply(p=p, n=curve.N, N=curve.N, A=curve.A, P=curve.P).isAtInfinity():
+            raise Exception("Point ({x},{y}) * {name}.N is not at infinity".format(x=p.x, y=p.y, name=curve.name))
+        return publicKey
 
 
 _ecdsaPublicKeyOid = (1, 2, 840, 10045, 2, 1)

tests/testEcdsa.py

@@ -1,5 +1,5 @@
 from unittest.case import TestCase
-from ellipticcurve import Ecdsa, PrivateKey
+from ellipticcurve import Ecdsa, PrivateKey, Signature
 
 
 class EcdsaTest(TestCase):
@@ -24,3 +24,11 @@ def testVerifyWrongMessage(self):
         signature = Ecdsa.sign(message1, privateKey)
 
         self.assertFalse(Ecdsa.verify(message2, signature, publicKey))
+
+    def testZeroSignature(self):
+        privateKey = PrivateKey()
+        publicKey = privateKey.publicKey()
+
+        message2 = "This is the wrong message"
+
+        self.assertFalse(Ecdsa.verify(message2, Signature(0, 0), publicKey))