Make all module_utils and plugin_utils private (#887)

* Add leading underscore. Remove deprecated module utils.

* Document module and plugin utils as private. Add changelog fragment.

* Convert relative to absolute imports.

* Remove unnecessary imports.

plugins/module_utils/_crypto/math.py

@@ -0,0 +1,158 @@
+# Copyright (c) 2019, Felix Fontein <felix@fontein.de>
+# GNU General Public License v3.0+ (see LICENSES/GPL-3.0-or-later.txt or https://www.gnu.org/licenses/gpl-3.0.txt)
+# SPDX-License-Identifier: GPL-3.0-or-later
+
+# Note that this module util is **PRIVATE** to the collection. It can have breaking changes at any time.
+# Do not use this from other collections or standalone plugins/modules!
+
+from __future__ import annotations
+
+
+def binary_exp_mod(f: int, e: int, m: int) -> int:
+    """Computes f^e mod m in O(log e) multiplications modulo m."""
+    # Compute len_e = floor(log_2(e))
+    len_e = -1
+    x = e
+    while x > 0:
+        x >>= 1
+        len_e += 1
+    # Compute f**e mod m
+    result = 1
+    for k in range(len_e, -1, -1):
+        result = (result * result) % m
+        if ((e >> k) & 1) != 0:
+            result = (result * f) % m
+    return result
+
+
+def simple_gcd(a: int, b: int) -> int:
+    """Compute GCD of its two inputs."""
+    while b != 0:
+        a, b = b, a % b
+    return a
+
+
+def quick_is_not_prime(n: int) -> bool:
+    """Does some quick checks to see if we can poke a hole into the primality of n.
+
+    A result of `False` does **not** mean that the number is prime; it just means
+    that we could not detect quickly whether it is not prime.
+    """
+    if n <= 2:
+        return n < 2
+    # The constant in the next line is the product of all primes < 200
+    prime_product = 7799922041683461553249199106329813876687996789903550945093032474868511536164700810
+    gcd = simple_gcd(n, prime_product)
+    if gcd > 1:
+        if n < 200 and gcd == n:
+            # Explicitly check for all primes < 200
+            return n not in (
+                2,
+                3,
+                5,
+                7,
+                11,
+                13,
+                17,
+                19,
+                23,
+                29,
+                31,
+                37,
+                41,
+                43,
+                47,
+                53,
+                59,
+                61,
+                67,
+                71,
+                73,
+                79,
+                83,
+                89,
+                97,
+                101,
+                103,
+                107,
+                109,
+                113,
+                127,
+                131,
+                137,
+                139,
+                149,
+                151,
+                157,
+                163,
+                167,
+                173,
+                179,
+                181,
+                191,
+                193,
+                197,
+                199,
+            )
+        return True
+    # TODO: maybe do some iterations of Miller-Rabin to increase confidence
+    # (https://en.wikipedia.org/wiki/Miller%E2%80%93Rabin_primality_test)
+    return False
+
+
+def count_bytes(no: int) -> int:
+    """
+    Given an integer, compute the number of bytes necessary to store its absolute value.
+    """
+    no = abs(no)
+    if no == 0:
+        return 0
+    return (no.bit_length() + 7) // 8
+
+
+def count_bits(no: int) -> int:
+    """
+    Given an integer, compute the number of bits necessary to store its absolute value.
+    """
+    no = abs(no)
+    if no == 0:
+        return 0
+    return no.bit_length()
+
+
+def convert_int_to_bytes(no: int, count: int | None = None) -> bytes:
+    """
+    Convert the absolute value of an integer to a byte string in network byte order.
+
+    If ``count`` is provided, it must be sufficiently large so that the integer's
+    absolute value can be represented with these number of bytes. The resulting byte
+    string will have length exactly ``count``.
+
+    The value zero will be converted to an empty byte string if ``count`` is provided.
+    """
+    no = abs(no)
+    if count is None:
+        count = count_bytes(no)
+    return no.to_bytes(count, byteorder="big")
+
+
+def convert_int_to_hex(no: int, digits: int | None = None) -> str:
+    """
+    Convert the absolute value of an integer to a string of hexadecimal digits.
+
+    If ``digits`` is provided, the string will be padded on the left with ``0``s so
+    that the returned value has length ``digits``. If ``digits`` is not sufficient,
+    the string will be longer.
+    """
+    no = abs(no)
+    value = f"{no:x}"
+    if digits is not None and len(value) < digits:
+        value = "0" * (digits - len(value)) + value
+    return value
+
+
+def convert_bytes_to_int(data: bytes) -> int:
+    """
+    Convert a byte string to an unsigned integer in network byte order.
+    """
+    return int.from_bytes(data, byteorder="big", signed=False)