Increase testing for primality

Author: Legrandin

lib/Crypto/Math/Primality.py

@@ -63,6 +63,9 @@ def miller_rabin_test(candidate, iterations, randfunc=None):
     if not isinstance(candidate, Integer):
         candidate = Integer(candidate)
 
+    if candidate in (1, 2, 3, 5):
+        return PROBABLY_PRIME
+    
     if candidate.is_even():
         return COMPOSITE
 
@@ -129,6 +132,8 @@ def lucas_test(candidate):
         candidate = Integer(candidate)
 
     # Step 1
+    if candidate in (1, 2, 3, 5):
+        return PROBABLY_PRIME
     if candidate.is_even() or candidate.is_perfect_square():
         return COMPOSITE
 
@@ -144,6 +149,8 @@ def alternate():
             value = -value
 
     for D in alternate():
+        if candidate in (D, -D):
+            continue
         js = Integer.jacobi_symbol(D, candidate)
         if js == 0:
             return COMPOSITE
@@ -206,7 +213,7 @@ def alternate():
 from Crypto.Util.number import sieve_base as _sieve_base
 ## The optimal number of small primes to use for the sieve
 ## is probably dependent on the platform and the candidate size
-_sieve_base = _sieve_base[:100]
+_sieve_base = set(_sieve_base[:100])
 
 
 def test_probable_prime(candidate, randfunc=None):
@@ -237,11 +244,13 @@ def test_probable_prime(candidate, randfunc=None):
     if not isinstance(candidate, Integer):
         candidate = Integer(candidate)
 
-    # First,  check trial division by the smallest primes
+    # First, check trial division by the smallest primes
+    if int(candidate) in _sieve_base:
+        return PROBABLY_PRIME
     try:
         map(candidate.fail_if_divisible_by, _sieve_base)
     except ValueError:
-        return False
+        return COMPOSITE
 
     # These are the number of Miller-Rabin iterations s.t. p(k, t) < 1E-30,
     # with p(k, t) being the probability that a randomly chosen k-bit number

lib/Crypto/SelfTest/Math/test_Primality.py

@@ -51,20 +51,24 @@
 
 class TestPrimality(unittest.TestCase):
 
-    primes = (13, 17, 19, 23, 2**127-1, 175637383534939453397801320455508570374088202376942372758907369518414308188137781042871856139027160010343454418881888953150175357127346872102307696660678617989191485418582475696230580407111841072614783095326672517315988762029036079794994990250662362650625650262324085116467511357592728695033227611029693067539)
-    composites = (12, 7*23, (2**19-1)*(2**67-1), 9746347772161,)
+    primes = (1, 2, 3, 5, 7, 11, 13, 17, 19, 23, 2**127-1, 175637383534939453397801320455508570374088202376942372758907369518414308188137781042871856139027160010343454418881888953150175357127346872102307696660678617989191485418582475696230580407111841072614783095326672517315988762029036079794994990250662362650625650262324085116467511357592728695033227611029693067539)
+    composites = (0, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 7*23, (2**19-1)*(2**67-1), 9746347772161,)
 
     def test_miller_rabin(self):
         for prime in self.primes:
             self.assertEqual(miller_rabin_test(prime, 3), PROBABLY_PRIME)
         for composite in self.composites:
             self.assertEqual(miller_rabin_test(composite, 3), COMPOSITE)
+        self.assertRaises(ValueError, miller_rabin_test, -1, 3)
 
     def test_lucas(self):
         for prime in self.primes:
-            self.assertEqual(lucas_test(prime), PROBABLY_PRIME)
+            res = lucas_test(prime)
+            self.assertEqual(res, PROBABLY_PRIME)
         for composite in self.composites:
-            self.assertEqual(lucas_test(composite), COMPOSITE)
+            res = lucas_test(composite)
+            self.assertEqual(res, COMPOSITE)
+        self.assertRaises(ValueError, lucas_test, -1)
 
     def test_is_prime(self):
         primes = (170141183460469231731687303715884105727,
@@ -82,6 +86,11 @@ def test_is_prime(self):
         for np in not_primes:
             self.assertEqual(test_probable_prime(np), COMPOSITE)
 
+        from Crypto.Util.number import sieve_base
+        for p in sieve_base[:100]:
+            res = test_probable_prime(p)
+            self.assertEqual(res, PROBABLY_PRIME)
+
     def test_generate_prime_bit_size(self):
         p = generate_probable_prime(exact_bits=512)
         self.assertEqual(p.size_in_bits(), 512)