How MD5 Works

def to_little_endian(string_32: bytes) -> bytes:
    """
    Converts the given string to little-endian in groups of 8 chars.

    Arguments:
        string_32 {[string]} -- [32-char string]

    Raises:
        ValueError -- [input is not 32 char]

    Returns:
        32-char little-endian string
    >>> to_little_endian(b'1234567890abcdfghijklmnopqrstuvw')
    b'pqrstuvwhijklmno90abcdfg12345678'
    >>> to_little_endian(b'1234567890')
    Traceback (most recent call last):
    ...
    ValueError: Input must be of length 32
    """
    if len(string_32) != 32:
        raise ValueError("Input must be of length 32")

    little_endian = b""
    for i in [3, 2, 1, 0]:
        little_endian += string_32[8 * i : 8 * i + 8]
    return little_endian

def preprocess(message: bytes) -> bytes:
    """
    Preprocesses the message string:
    - Convert message to bit string
    - Pad bit string to a multiple of 512 chars:
        - Append a 1
        - Append 0's until length = 448 (mod 512)
        - Append length of original message (64 chars)

    Example: Suppose the input is the following:
        message = "a"

        The message bit string is "01100001", which is 8 bits long. Thus, the
        bit string needs 439 bits of padding so that
        (bit_string + "1" + padding) = 448 (mod 512).
        The message length is "000010000...0" in 64-bit little-endian binary.
        The combined bit string is then 512 bits long.

    Arguments:
        message {[string]} -- [message string]

    Returns:
        processed bit string padded to a multiple of 512 chars

    >>> preprocess(b"a") == (b"01100001" + b"1" +
    ...                     (b"0" * 439) + b"00001000" + (b"0" * 56))
    True
    >>> preprocess(b"") == b"1" + (b"0" * 447) + (b"0" * 64)
    True
    """
    bit_string = b""
    for char in message:
        bit_string += format(char, "08b").encode("utf-8")
    start_len = format(len(bit_string), "064b").encode("utf-8")

    # Pad bit_string to a multiple of 512 chars
    bit_string += b"1"
    while len(bit_string) % 512 != 448:
        bit_string += b"0"
    bit_string += to_little_endian(start_len[32:]) + to_little_endian(start_len[:32])

    return bit_string

    # Convert to bit string, add padding and append message length
    bit_string = preprocess(message)

    added_consts = [int(2**32 * abs(sin(i + 1))) for i in range(64)]

    # Starting states
    a0 = 0x67452301
    b0 = 0xEFCDAB89
    c0 = 0x98BADCFE
    d0 = 0x10325476

        for i in range(64):
            if i <= 15:
                # f = (b & c) | (not_32(b) & d)     # Alternate definition for f
                f = d ^ (b & (c ^ d))
                g = i
            elif i <= 31:
                # f = (d & b) | (not_32(d) & c)     # Alternate definition for f
                f = c ^ (d & (b ^ c))
                g = (5 * i + 1) % 16
            elif i <= 47:
                f = b ^ c ^ d
                g = (3 * i + 5) % 16
            else:
                f = c ^ (b | not_32(d))
                g = (7 * i) % 16
            f = (f + a + added_consts[i] + block_words[g]) % 2**32
            a = d
            d = c
            c = b
            b = sum_32(b, left_rotate_32(f, shift_amounts[i]))

def md5_me(message: bytes) -> bytes:
    """
    Returns the 32-char MD5 hash of a given message.

    Reference: https://en.wikipedia.org/wiki/MD5#Algorithm

    Arguments:
        message {[string]} -- [message]

    Returns:
        32-char MD5 hash string

    >>> md5_me(b"")
    b'd41d8cd98f00b204e9800998ecf8427e'
    >>> md5_me(b"The quick brown fox jumps over the lazy dog")
    b'9e107d9d372bb6826bd81d3542a419d6'
    >>> md5_me(b"The quick brown fox jumps over the lazy dog.")
    b'e4d909c290d0fb1ca068ffaddf22cbd0'

    >>> import hashlib
    >>> from string import ascii_letters
    >>> msgs = [b"", ascii_letters.encode("utf-8"), "Üñîçø∂é".encode("utf-8"),
    ...         b"The quick brown fox jumps over the lazy dog."]
    >>> all(md5_me(msg) == hashlib.md5(msg).hexdigest().encode("utf-8") for msg in msgs)
    True
    """