Merge pull request AntonKueltz#72 from bbbrumley/bbb_large

[fastecdsa/tests] regression test: multiplication by large scalars

fastecdsa/tests/test_prime_field_curve_math.py

@@ -240,3 +240,31 @@ def test_mul_by_negative(self):
             self.assertEqual(P.x, Q.x)
             self.assertEqual(P.y, Q.y)
 
+    def test_mul_by_large(self):
+        # W25519 test
+        # this is an order h * q point, where ord(G) = q and cofactor h satisfies card(E) = h * q
+        P_25519 = (35096664872667797862139202932949049580901987963171775123990915594423742128033,
+                   22480573877477866270168076032006671893585325258603943218058327520008883368696)
+        # scalar larger than q but smaller than h * q
+        k_25519 = 29372000253601831461196252357151931556312986177449743872632027037220559545805
+        # KAT: Q = k * P
+        Q_25519 = (49706689516442043243945288648738077613576846608357551203998149787039218825283,
+                   39031159953669648926560068238390400180132971507115734045330364888380270413913)
+        P_25519 = Point(P_25519[0], P_25519[1], curve=W25519)
+        R = k_25519 * P_25519
+        expected = Point(Q_25519[0], Q_25519[1], curve=W25519)
+        self.assertEqual(R, expected)
+
+        # W448 test
+        # this is an order h * q point, where ord(G) = q and cofactor h satisfies card(E) = h * q
+        P_448 = (231480979532797508943026590383724571663349496894338686929676625369384864922735088561874582237479033305968563866115522624182905190510908,
+                 386642878578520576902801772187402730328995571185781418728101620741813344331894790606494081334128109534545128357659367878296954820089456)
+        # scalar larger than q but smaller than h * q
+        k_448 = 402277635739946816237642095194112559838556500677282525912537756673080201343619608058123416303707654128973619279630717054942423338738673
+        # KAT: Q = k * P
+        Q_448 = (594031426065062897452711501095164269186787326947787097339623446049485959406429079799671040253813345976305183137288555654745835823926292,
+                 397805400082591898298129134663530334000872412871159149907636409950148029590985263340056678772524289857573459442468777694902850559368658)
+        P_448 = Point(P_448[0], P_448[1], curve=W448)
+        R = k_448 * P_448
+        expected = Point(Q_448[0], Q_448[1], curve=W448)
+        self.assertEqual(R, expected)