Jacobi symbol not defined for negative n, add more test vectors

Author: Legrandin

lib/Crypto/Math/_Numbers_int.py

@@ -390,6 +390,9 @@ def jacobi_symbol(a, n):
         a = int(a)
         n = int(n)
 
+        if n <= 0:
+            raise ValueError("n must be a positive integer")
+
         if (n & 1) == 0:
             raise ValueError("n must be even for the Jacobi symbol")
 

lib/Crypto/SelfTest/Math/test_Numbers.py

@@ -618,12 +618,53 @@ def test_jacobi_symbol(self):
 
         js = self.Integer.jacobi_symbol
 
+        # Jacobi symbol is always 1 for k==1 or n==1
+        for k in range(1, 30):
+            self.assertEqual(js(k, 1), 1)
+        for n in range(1, 30, 2):
+            self.assertEqual(js(1, n), 1)
+
+        # Fail if n is not positive odd
+        self.assertRaises(ValueError, js, 6, -2)
+        self.assertRaises(ValueError, js, 6, -1)
+        self.assertRaises(ValueError, js, 6, 0)
+        self.assertRaises(ValueError, js, 0, 0)
+        self.assertRaises(ValueError, js, 6, 2)
+        self.assertRaises(ValueError, js, 6, 4)
+        self.assertRaises(ValueError, js, 6, 6)
+        self.assertRaises(ValueError, js, 6, 8)
+
         for tv in data:
             self.assertEqual(js(tv[0], tv[1]), tv[2])
             self.assertEqual(js(self.Integer(tv[0]), tv[1]), tv[2])
             self.assertEqual(js(tv[0], self.Integer(tv[1])), tv[2])
 
-        self.assertRaises(ValueError, js, 6, 8)
+    def test_jacobi_symbol_wikipedia(self):
+
+		# Test vectors from https://en.wikipedia.org/wiki/Jacobi_symbol
+        tv = [
+            (3, [(1, 1), (2, -1), (3, 0), (4, 1), (5, -1), (6, 0), (7, 1), (8, -1), (9, 0), (10, 1), (11, -1), (12, 0), (13, 1), (14, -1), (15, 0), (16, 1), (17, -1), (18, 0), (19, 1), (20, -1), (21, 0), (22, 1), (23, -1), (24, 0), (25, 1), (26, -1), (27, 0), (28, 1), (29, -1), (30, 0)]),
+            (5, [(1, 1), (2, -1), (3, -1), (4, 1), (5, 0), (6, 1), (7, -1), (8, -1), (9, 1), (10, 0), (11, 1), (12, -1), (13, -1), (14, 1), (15, 0), (16, 1), (17, -1), (18, -1), (19, 1), (20, 0), (21, 1), (22, -1), (23, -1), (24, 1), (25, 0), (26, 1), (27, -1), (28, -1), (29, 1), (30, 0)]),
+            (7, [(1, 1), (2, 1), (3, -1), (4, 1), (5, -1), (6, -1), (7, 0), (8, 1), (9, 1), (10, -1), (11, 1), (12, -1), (13, -1), (14, 0), (15, 1), (16, 1), (17, -1), (18, 1), (19, -1), (20, -1), (21, 0), (22, 1), (23, 1), (24, -1), (25, 1), (26, -1), (27, -1), (28, 0), (29, 1), (30, 1)]),
+            (9, [(1, 1), (2, 1), (3, 0), (4, 1), (5, 1), (6, 0), (7, 1), (8, 1), (9, 0), (10, 1), (11, 1), (12, 0), (13, 1), (14, 1), (15, 0), (16, 1), (17, 1), (18, 0), (19, 1), (20, 1), (21, 0), (22, 1), (23, 1), (24, 0), (25, 1), (26, 1), (27, 0), (28, 1), (29, 1), (30, 0)]),
+            (11, [(1, 1), (2, -1), (3, 1), (4, 1), (5, 1), (6, -1), (7, -1), (8, -1), (9, 1), (10, -1), (11, 0), (12, 1), (13, -1), (14, 1), (15, 1), (16, 1), (17, -1), (18, -1), (19, -1), (20, 1), (21, -1), (22, 0), (23, 1), (24, -1), (25, 1), (26, 1), (27, 1), (28, -1), (29, -1), (30, -1)]),
+            (13, [(1, 1), (2, -1), (3, 1), (4, 1), (5, -1), (6, -1), (7, -1), (8, -1), (9, 1), (10, 1), (11, -1), (12, 1), (13, 0), (14, 1), (15, -1), (16, 1), (17, 1), (18, -1), (19, -1), (20, -1), (21, -1), (22, 1), (23, 1), (24, -1), (25, 1), (26, 0), (27, 1), (28, -1), (29, 1), (30, 1)]),
+            (15, [(1, 1), (2, 1), (3, 0), (4, 1), (5, 0), (6, 0), (7, -1), (8, 1), (9, 0), (10, 0), (11, -1), (12, 0), (13, -1), (14, -1), (15, 0), (16, 1), (17, 1), (18, 0), (19, 1), (20, 0), (21, 0), (22, -1), (23, 1), (24, 0), (25, 0), (26, -1), (27, 0), (28, -1), (29, -1), (30, 0)]),
+            (17, [(1, 1), (2, 1), (3, -1), (4, 1), (5, -1), (6, -1), (7, -1), (8, 1), (9, 1), (10, -1), (11, -1), (12, -1), (13, 1), (14, -1), (15, 1), (16, 1), (17, 0), (18, 1), (19, 1), (20, -1), (21, 1), (22, -1), (23, -1), (24, -1), (25, 1), (26, 1), (27, -1), (28, -1), (29, -1), (30, 1)]),
+            (19, [(1, 1), (2, -1), (3, -1), (4, 1), (5, 1), (6, 1), (7, 1), (8, -1), (9, 1), (10, -1), (11, 1), (12, -1), (13, -1), (14, -1), (15, -1), (16, 1), (17, 1), (18, -1), (19, 0), (20, 1), (21, -1), (22, -1), (23, 1), (24, 1), (25, 1), (26, 1), (27, -1), (28, 1), (29, -1), (30, 1)]),
+            (21, [(1, 1), (2, -1), (3, 0), (4, 1), (5, 1), (6, 0), (7, 0), (8, -1), (9, 0), (10, -1), (11, -1), (12, 0), (13, -1), (14, 0), (15, 0), (16, 1), (17, 1), (18, 0), (19, -1), (20, 1), (21, 0), (22, 1), (23, -1), (24, 0), (25, 1), (26, 1), (27, 0), (28, 0), (29, -1), (30, 0)]),
+            (23, [(1, 1), (2, 1), (3, 1), (4, 1), (5, -1), (6, 1), (7, -1), (8, 1), (9, 1), (10, -1), (11, -1), (12, 1), (13, 1), (14, -1), (15, -1), (16, 1), (17, -1), (18, 1), (19, -1), (20, -1), (21, -1), (22, -1), (23, 0), (24, 1), (25, 1), (26, 1), (27, 1), (28, -1), (29, 1), (30, -1)]),
+            (25, [(1, 1), (2, 1), (3, 1), (4, 1), (5, 0), (6, 1), (7, 1), (8, 1), (9, 1), (10, 0), (11, 1), (12, 1), (13, 1), (14, 1), (15, 0), (16, 1), (17, 1), (18, 1), (19, 1), (20, 0), (21, 1), (22, 1), (23, 1), (24, 1), (25, 0), (26, 1), (27, 1), (28, 1), (29, 1), (30, 0)]),
+            (27, [(1, 1), (2, -1), (3, 0), (4, 1), (5, -1), (6, 0), (7, 1), (8, -1), (9, 0), (10, 1), (11, -1), (12, 0), (13, 1), (14, -1), (15, 0), (16, 1), (17, -1), (18, 0), (19, 1), (20, -1), (21, 0), (22, 1), (23, -1), (24, 0), (25, 1), (26, -1), (27, 0), (28, 1), (29, -1), (30, 0)]),
+            (29, [(1, 1), (2, -1), (3, -1), (4, 1), (5, 1), (6, 1), (7, 1), (8, -1), (9, 1), (10, -1), (11, -1), (12, -1), (13, 1), (14, -1), (15, -1), (16, 1), (17, -1), (18, -1), (19, -1), (20, 1), (21, -1), (22, 1), (23, 1), (24, 1), (25, 1), (26, -1), (27, -1), (28, 1), (29, 0), (30, 1)]),
+            ]
+
+        js = self.Integer.jacobi_symbol
+
+        for n, kj in tv:
+            for k, j in kj:
+                self.assertEqual(js(k, n), j)
+
 
 class TestIntegerInt(TestIntegerBase):