Added basic Chinese Remainder theorem implementation, not yet used.

1 files changed, 74 insertions, 0 deletions

diff --git a/rsa/common.py b/rsa/common.py
index 5ae92f0..4d7698f 100644
--- a/rsa/common.py
+++ b/rsa/common.py
@@ -69,6 +69,80 @@ def byte_size(number):
 
     return int(math.ceil(bit_size(number) / 8.0))
 
+
+def extended_gcd(a, b):
+    """Returns a tuple (r, i, j) such that r = gcd(a, b) = ia + jb
+    """
+    # r = gcd(a,b) i = multiplicitive inverse of a mod b
+    #      or      j = multiplicitive inverse of b mod a
+    # Neg return values for i or j are made positive mod b or a respectively
+    # Iterateive Version is faster and uses much less stack space
+    x = 0
+    y = 1
+    lx = 1
+    ly = 0
+    oa = a                             #Remember original a/b to remove 
+    ob = b                             #negative values from return results
+    while b != 0:
+        q = a // b
+        (a, b)  = (b, a % b)
+        (x, lx) = ((lx - (q * x)),x)
+        (y, ly) = ((ly - (q * y)),y)
+    if (lx < 0): lx += ob              #If neg wrap modulo orignal b
+    if (ly < 0): ly += oa              #If neg wrap modulo orignal a
+    return (a, lx, ly)                 #Return only positive values
+
+def inverse(x, n):
+    '''Returns x^-1 (mod n)
+    
+    >>> inverse(7, 4)
+    3
+    >>> (inverse(143, 4) * 143) % 4
+    1
+    '''
+
+    (divider, inv, _) = extended_gcd(x, n)
+
+    if divider != 1:
+        raise ValueError("x (%d) and n (%d) are not relatively prime" % (x, n))
+
+    return inv
+
+
+def crt(a_values, modulo_values):
+    '''Chinese Remainder Theorem.
+
+    Calculates x such that x = a[i] (mod m[i]) for each i.
+
+    :param a_values: the a-values of the above equation
+    :param modulo_values: the m-values of the above equation
+    :returns: x such that x = a[i] (mod m[i]) for each i
+    
+
+    >>> crt([2, 3], [3, 5])
+    8
+
+    >>> crt([2, 3, 2], [3, 5, 7])
+    23
+
+    >>> crt([2, 3, 0], [7, 11, 15])
+    135
+    '''
+
+    m = 1
+    x = 0 
+
+    for modulo in modulo_values:
+        m *= modulo
+
+    for (m_i, a_i) in zip(modulo_values, a_values):
+        M_i = m // m_i
+        inv = inverse(M_i, m_i)
+
+        x = (x + a_i * M_i * inv) % m
+
+    return x
+
 if __name__ == '__main__':
     import doctest
     doctest.testmod()