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Filename : randnum.py
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#  Copyright 2011 Sybren A. Stüvel <sybren@stuvel.eu>
#
#  Licensed under the Apache License, Version 2.0 (the "License");
#  you may not use this file except in compliance with the License.
#  You may obtain a copy of the License at
#
#      https://www.apache.org/licenses/LICENSE-2.0
#
#  Unless required by applicable law or agreed to in writing, software
#  distributed under the License is distributed on an "AS IS" BASIS,
#  WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
#  See the License for the specific language governing permissions and
#  limitations under the License.

"""Functions for generating random numbers."""

# Source inspired by code by Yesudeep Mangalapilly <yesudeep@gmail.com>

import os
import struct

from rsa import common, transform


def read_random_bits(nbits: int) -> bytes:
    """Reads 'nbits' random bits.

    If nbits isn't a whole number of bytes, an extra byte will be appended with
    only the lower bits set.
    """

    nbytes, rbits = divmod(nbits, 8)

    # Get the random bytes
    randomdata = os.urandom(nbytes)

    # Add the remaining random bits
    if rbits > 0:
        randomvalue = ord(os.urandom(1))
        randomvalue >>= 8 - rbits
        randomdata = struct.pack("B", randomvalue) + randomdata

    return randomdata


def read_random_int(nbits: int) -> int:
    """Reads a random integer of approximately nbits bits."""

    randomdata = read_random_bits(nbits)
    value = transform.bytes2int(randomdata)

    # Ensure that the number is large enough to just fill out the required
    # number of bits.
    value |= 1 << (nbits - 1)

    return value


def read_random_odd_int(nbits: int) -> int:
    """Reads a random odd integer of approximately nbits bits.

    >>> read_random_odd_int(512) & 1
    1
    """

    value = read_random_int(nbits)

    # Make sure it's odd
    return value | 1


def randint(maxvalue: int) -> int:
    """Returns a random integer x with 1 <= x <= maxvalue

    May take a very long time in specific situations. If maxvalue needs N bits
    to store, the closer maxvalue is to (2 ** N) - 1, the faster this function
    is.
    """

    bit_size = common.bit_size(maxvalue)

    tries = 0
    while True:
        value = read_random_int(bit_size)
        if value <= maxvalue:
            break

        if tries % 10 == 0 and tries:
            # After a lot of tries to get the right number of bits but still
            # smaller than maxvalue, decrease the number of bits by 1. That'll
            # dramatically increase the chances to get a large enough number.
            bit_size -= 1
        tries += 1

    return value