import FIREFOX_52_6_0esr_RELEASE from mozilla-esr52 hg repo

python/PyECC/ecc/primes.py

@@ -0,0 +1,82 @@
+'''
+This module implements simple prime generation and primality testing.
+'''
+
+from random import SystemRandom
+random = SystemRandom()
+from os import urandom
+
+def exp(x, n, m):
+    '''Efficiently compute x ** n mod m'''
+    y = 1
+    z = x
+    while n > 0:
+        if n & 1:
+            y = (y * z) % m
+        z = (z * z) % m
+        n //= 2
+    return y
+
+
+# Miller-Rabin-Test
+
+def prime(n, k):
+    '''Checks whether n is probably prime (with probability 1 - 4**(-k)'''
+    
+    if n % 2 == 0:
+        return False
+    
+    d = n - 1
+    s = 0
+    
+    while d % 2 == 0:
+        s += 1
+        d /= 2
+        
+    for i in xrange(k):
+        
+        a = long(2 + random.randint(0, n - 4))
+        x = exp(a, d, n)
+        if (x == 1) or (x == n - 1):
+            continue
+        
+        for r in xrange(1, s):
+            x = (x * x) % n
+            
+            if x == 1:
+                return False
+            
+            if x == n - 1:
+                break
+            
+        else:
+            return False
+    return True
+
+
+# Generate and Test Algorithms
+
+def get_prime(size, accuracy):
+    '''Generate a pseudorandom prime number with the specified size (bytes).'''
+    
+    while 1:
+
+        # read some random data from the operating system
+        rstr = urandom(size - 1)
+        r = 128 | ord(urandom(1))   # MSB = 1 (not less than size)
+        for c in rstr:
+            r = (r << 8) | ord(c)
+        r |= 1                      # LSB = 1 (odd)
+
+        # test whether this results in a prime number
+        if prime(r, accuracy):
+            return r
+
+
+def get_prime_upto(n, accuracy):
+    '''Find largest prime less than n'''
+    n |= 1
+    while n > 0:
+        n -= 2
+        if prime(n, accuracy):
+            return n