Initial commit

venv/Lib/site-packages/rsa/common.py

@@ -0,0 +1,184 @@
+#  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.
+
+"""Common functionality shared by several modules."""
+
+import typing
+
+
+class NotRelativePrimeError(ValueError):
+    def __init__(self, a: int, b: int, d: int, msg: str = "") -> None:
+        super().__init__(msg or "%d and %d are not relatively prime, divider=%i" % (a, b, d))
+        self.a = a
+        self.b = b
+        self.d = d
+
+
+def bit_size(num: int) -> int:
+    """
+    Number of bits needed to represent a integer excluding any prefix
+    0 bits.
+
+    Usage::
+
+        >>> bit_size(1023)
+        10
+        >>> bit_size(1024)
+        11
+        >>> bit_size(1025)
+        11
+
+    :param num:
+        Integer value. If num is 0, returns 0. Only the absolute value of the
+        number is considered. Therefore, signed integers will be abs(num)
+        before the number's bit length is determined.
+    :returns:
+        Returns the number of bits in the integer.
+    """
+
+    try:
+        return num.bit_length()
+    except AttributeError as ex:
+        raise TypeError("bit_size(num) only supports integers, not %r" % type(num)) from ex
+
+
+def byte_size(number: int) -> int:
+    """
+    Returns the number of bytes required to hold a specific long number.
+
+    The number of bytes is rounded up.
+
+    Usage::
+
+        >>> byte_size(1 << 1023)
+        128
+        >>> byte_size((1 << 1024) - 1)
+        128
+        >>> byte_size(1 << 1024)
+        129
+
+    :param number:
+        An unsigned integer
+    :returns:
+        The number of bytes required to hold a specific long number.
+    """
+    if number == 0:
+        return 1
+    return ceil_div(bit_size(number), 8)
+
+
+def ceil_div(num: int, div: int) -> int:
+    """
+    Returns the ceiling function of a division between `num` and `div`.
+
+    Usage::
+
+        >>> ceil_div(100, 7)
+        15
+        >>> ceil_div(100, 10)
+        10
+        >>> ceil_div(1, 4)
+        1
+
+    :param num: Division's numerator, a number
+    :param div: Division's divisor, a number
+
+    :return: Rounded up result of the division between the parameters.
+    """
+    quanta, mod = divmod(num, div)
+    if mod:
+        quanta += 1
+    return quanta
+
+
+def extended_gcd(a: int, b: int) -> typing.Tuple[int, int, int]:
+    """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 original b
+    if ly < 0:
+        ly += oa  # If neg wrap modulo original a
+    return a, lx, ly  # Return only positive values
+
+
+def inverse(x: int, n: int) -> int:
+    """Returns the inverse of x % n under multiplication, a.k.a x^-1 (mod n)
+
+    >>> inverse(7, 4)
+    3
+    >>> (inverse(143, 4) * 143) % 4
+    1
+    """
+
+    (divider, inv, _) = extended_gcd(x, n)
+
+    if divider != 1:
+        raise NotRelativePrimeError(x, n, divider)
+
+    return inv
+
+
+def crt(a_values: typing.Iterable[int], modulo_values: typing.Iterable[int]) -> int:
+    """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()