#

#   number.py : Number-theoretic functions

#

#  Part of the Python Cryptography Toolkit

#

#  Written by Andrew M. Kuchling, Barry A. Warsaw, and others

#

# ===================================================================

# The contents of this file are dedicated to the public domain.  To

# the extent that dedication to the public domain is not available,

# everyone is granted a worldwide, perpetual, royalty-free,

# non-exclusive license to exercise all rights associated with the

# contents of this file for any purpose whatsoever.

# No rights are reserved.

#

# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,

# EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF

# MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND

# NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS

# BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN

# ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN

# CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE

# SOFTWARE.

# ===================================================================

#

​

__revision__ = "$Id$"

​

from Crypto.pct_warnings import GetRandomNumber_DeprecationWarning, PowmInsecureWarning

from warnings import warn as _warn

import math

import sys

from Crypto.Util.py3compat import *

​

bignum = long

try:

    from Crypto.PublicKey import _fastmath

except ImportError:

    # For production, we are going to let import issues due to gmp/mpir shared

    # libraries not loading slide silently and use slowmath. If you'd rather

    # see an exception raised if _fastmath exists but cannot be imported,

    # uncomment the below

    #