fast examples for numbertheory tests

Author: tomato42

src/ecdsa/numbertheory.py

@@ -20,11 +20,11 @@
 except NameError:
     xrange = range
 try:
-    from gmpy2 import powmod
+    from gmpy2 import powmod, mpz
 
     GMPY2 = True
     GMPY = False
-except ImportError:
+except ImportError:  # pragma: no branch
     GMPY2 = False
     try:
         from gmpy import mpz
@@ -33,8 +33,14 @@
     except ImportError:
         GMPY = False
 
+
+if GMPY2 or GMPY:  # pragma: no branch
+    integer_types = tuple(integer_types + (type(mpz(1)),))
+
+
 import math
 import warnings
+from .util import bit_length
 
 
 class Error(Exception):
@@ -555,16 +561,16 @@ def is_prime(n):
             return True
         else:
             return False
-
-    if gcd(n, 2 * 3 * 5 * 7 * 11) != 1:
+    # 2310 = 2 * 3 * 5 * 7 * 11
+    if gcd(n, 2310) != 1:
         return False
 
     # Choose a number of iterations sufficient to reduce the
     # probability of accepting a composite below 2**-80
     # (from Menezes et al. Table 4.4):
 
     t = 40
-    n_bits = 1 + int(math.log(n, 2))
+    n_bits = 1 + bit_length(n)
     for k, tt in (
         (100, 27),
         (150, 18),

src/ecdsa/test_numbertheory.py

@@ -30,6 +30,16 @@
     square_root_mod_prime,
 )
 
+try:
+    from gmpy2 import mpz
+except ImportError:
+    try:
+        from gmpy import mpz
+    except ImportError:
+
+        def mpz(x):
+            return x
+
 
 BIGPRIMES = (
     999671,
@@ -293,7 +303,7 @@ def test_medium_non_trivial_composite(self):
 
     def test_large_prime(self):
         # nextPrime[2^2048]
-        assert is_prime(2**2048 + 0x3D5)
+        assert is_prime(mpz(2) ** 2048 + 0x3D5)
 
 
 class TestNumbertheory(unittest.TestCase):
@@ -309,6 +319,7 @@ def test_gcd(self):
         "case times-out on it",
     )
     @settings(**HYP_SLOW_SETTINGS)
+    @example([877 * 1151, 877 * 1009])
     @given(st_comp_with_com_fac())
     def test_gcd_with_com_factor(self, numbers):
         n = gcd(numbers)
@@ -323,6 +334,7 @@ def test_gcd_with_com_factor(self, numbers):
         "case times-out on it",
     )
     @settings(**HYP_SLOW_SETTINGS)
+    @example([1151, 1069, 1009])
     @given(st_comp_no_com_fac())
     def test_gcd_with_uncom_factor(self, numbers):
         n = gcd(numbers)
@@ -415,13 +427,16 @@ def test_jacobi_with_one(self):
     @settings(**HYP_SLOW_SETTINGS)
     @given(st.integers(min_value=3, max_value=1000).filter(lambda x: x % 2))
     def test_jacobi(self, mod):
+        mod = mpz(mod)
         if is_prime(mod):
             squares = set()
             for root in range(1, mod):
+                root = mpz(root)
                 assert jacobi(root * root, mod) == 1
                 squares.add(root * root % mod)
             for i in range(1, mod):
                 if i not in squares:
+                    i = mpz(i)
                     assert jacobi(i, mod) == -1
         else:
             factors = factorization(mod)