From 893e96517df6c6a768a9bc6b5ecd7786f11985ad Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Sybren=20A=2E=20St=C3=BCvel?= <sybren@stuvel.eu>
Date: Sun, 19 Jun 2011 23:51:57 +0200
Subject: Split module into several files

---
 rsa/prime.py | 120 +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 120 insertions(+)
 create mode 100644 rsa/prime.py

(limited to 'rsa/prime.py')

diff --git a/rsa/prime.py b/rsa/prime.py
new file mode 100644
index 0000000..7cc06fb
--- /dev/null
+++ b/rsa/prime.py
@@ -0,0 +1,120 @@
+'''Numerical functions related to primes.'''
+
+__all__ = [ 'getprime', 'are_relatively_prime']
+
+import rsa.randnum
+
+def gcd(p, q):
+    """Returns the greatest common divisor of p and q
+
+    >>> gcd(48, 180)
+    12
+    """
+
+    while q != 0:
+        if p < q: (p,q) = (q,p)
+        (p,q) = (q, p % q)
+    return p
+    
+
+def jacobi(a, b):
+    """Calculates the value of the Jacobi symbol (a/b) where both a and b are
+    positive integers, and b is odd
+    """
+
+    if a == 0: return 0
+    result = 1
+    while a > 1:
+        if a & 1:
+            if ((a-1)*(b-1) >> 2) & 1:
+                result = -result
+            a, b = b % a, a
+        else:
+            if (((b * b) - 1) >> 3) & 1:
+                result = -result
+            a >>= 1
+    if a == 0: return 0
+    return result
+
+def jacobi_witness(x, n):
+    """Returns False if n is an Euler pseudo-prime with base x, and
+    True otherwise.
+    """
+
+    j = jacobi(x, n) % n
+    f = pow(x, (n-1)/2, n)
+
+    if j == f: return False
+    return True
+
+def randomized_primality_testing(n, k):
+    """Calculates whether n is composite (which is always correct) or
+    prime (which is incorrect with error probability 2**-k)
+
+    Returns False if the number is composite, and True if it's
+    probably prime.
+    """
+
+    # 50% of Jacobi-witnesses can report compositness of non-prime numbers
+
+    for i in range(k):
+        x = rsa.randnum.randint(1, n-1)
+        if jacobi_witness(x, n): return False
+    
+    return True
+
+def is_prime(number):
+    """Returns True if the number is prime, and False otherwise.
+
+    >>> is_prime(42)
+    0
+    >>> is_prime(41)
+    1
+    """
+
+    if randomized_primality_testing(number, 6):
+        # Prime, according to Jacobi
+        return True
+    
+    # Not prime
+    return False
+
+    
+def getprime(nbits):
+    """Returns a prime number of max. 'math.ceil(nbits/8)*8' bits. In
+    other words: nbits is rounded up to whole bytes.
+
+    >>> p = getprime(8)
+    >>> is_prime(p-1)
+    0
+    >>> is_prime(p)
+    1
+    >>> is_prime(p+1)
+    0
+    """
+
+    while True:
+        integer = rsa.randnum.read_random_int(nbits)
+
+        # Make sure it's odd
+        integer |= 1
+
+        # Test for primeness
+        if is_prime(integer): break
+
+        # Retry if not prime
+
+    return integer
+
+def are_relatively_prime(a, b):
+    """Returns True if a and b are relatively prime, and False if they
+    are not.
+
+    >>> are_relatively_prime(2, 3)
+    1
+    >>> are_relatively_prime(2, 4)
+    0
+    """
+
+    d = gcd(a, b)
+    return (d == 1)
-- 
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