#### Md 5

I
P
```"""
The MD5 algorithm is a hash function that's commonly used as a checksum to
detect data corruption. The algorithm works by processing a given message in
blocks of 512 bits, padding the message as needed. It uses the blocks to operate
a 128-bit state and performs a total of 64 such operations. Note that all values
are little-endian, so inputs are converted as needed.

Although MD5 was used as a cryptographic hash function in the past, it's since
been cracked, so it shouldn't be used for security purposes.

"""

from collections.abc import Generator
from math import sin

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 reformat_hex(i: int) -> bytes:
"""
Converts the given non-negative integer to hex string.

Example: Suppose the input is the following:
i = 1234

The input is 0x000004d2 in hex, so the little-endian hex string is
"d2040000".

Arguments:
i {[int]} -- [integer]

Raises:
ValueError -- [input is negative]

Returns:
8-char little-endian hex string

>>> reformat_hex(1234)
b'd2040000'
>>> reformat_hex(666)
b'9a020000'
>>> reformat_hex(0)
b'00000000'
>>> reformat_hex(1234567890)
b'd2029649'
>>> reformat_hex(1234567890987654321)
b'b11c6cb1'
>>> reformat_hex(-1)
Traceback (most recent call last):
...
ValueError: Input must be non-negative
"""
if i < 0:
raise ValueError("Input must be non-negative")

hex_rep = format(i, "08x")[-8:]
little_endian_hex = b""
for j in [3, 2, 1, 0]:
little_endian_hex += hex_rep[2 * j : 2 * j + 2].encode("utf-8")
return little_endian_hex

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

def get_block_words(bit_string: bytes) -> Generator[list[int], None, None]:
"""
Splits bit string into blocks of 512 chars and yields each block as a list
of 32-bit words

Example: Suppose the input is the following:
bit_string =
"000000000...0" +  # 0x00 (32 bits, padded to the right)
"000000010...0" +  # 0x01 (32 bits, padded to the right)
"000000100...0" +  # 0x02 (32 bits, padded to the right)
"000000110...0" +  # 0x03 (32 bits, padded to the right)
...
"000011110...0"    # 0x0a (32 bits, padded to the right)

Then len(bit_string) == 512, so there'll be 1 block. The block is split
into 32-bit words, and each word is converted to little endian. The
first word is interpreted as 0 in decimal, the second word is
interpreted as 1 in decimal, etc.

Thus, block_words == [[0, 1, 2, 3, ..., 15]].

Arguments:
bit_string {[string]} -- [bit string with multiple of 512 as length]

Raises:
ValueError -- [length of bit string isn't multiple of 512]

Yields:
a list of 16 32-bit words

>>> test_string = ("".join(format(n << 24, "032b") for n in range(16))
...                  .encode("utf-8"))
>>> list(get_block_words(test_string))
[[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]]
>>> list(get_block_words(test_string * 4)) == [list(range(16))] * 4
True
>>> list(get_block_words(b"1" * 512)) == [[4294967295] * 16]
True
>>> list(get_block_words(b""))
[]
>>> list(get_block_words(b"1111"))
Traceback (most recent call last):
...
ValueError: Input must have length that's a multiple of 512
"""
if len(bit_string) % 512 != 0:
raise ValueError("Input must have length that's a multiple of 512")

for pos in range(0, len(bit_string), 512):
block = bit_string[pos : pos + 512]
block_words = []
for i in range(0, 512, 32):
block_words.append(int(to_little_endian(block[i : i + 32]), 2))
yield block_words

def not_32(i: int) -> int:
"""
Perform bitwise NOT on given int.

Arguments:
i {[int]} -- [given int]

Raises:
ValueError -- [input is negative]

Returns:
Result of bitwise NOT on i

>>> not_32(34)
4294967261
>>> not_32(1234)
4294966061
>>> not_32(4294966061)
1234
>>> not_32(0)
4294967295
>>> not_32(1)
4294967294
>>> not_32(-1)
Traceback (most recent call last):
...
ValueError: Input must be non-negative
"""
if i < 0:
raise ValueError("Input must be non-negative")

i_str = format(i, "032b")
new_str = ""
for c in i_str:
new_str += "1" if c == "0" else "0"
return int(new_str, 2)

def sum_32(a: int, b: int) -> int:
"""
Add two numbers as 32-bit ints.

Arguments:
a {[int]} -- [first given int]
b {[int]} -- [second given int]

Returns:
(a + b) as an unsigned 32-bit int

>>> sum_32(1, 1)
2
>>> sum_32(2, 3)
5
>>> sum_32(0, 0)
0
>>> sum_32(-1, -1)
4294967294
>>> sum_32(4294967295, 1)
0
"""
return (a + b) % 2**32

def left_rotate_32(i: int, shift: int) -> int:
"""
Rotate the bits of a given int left by a given amount.

Arguments:
i {[int]} -- [given int]
shift {[int]} -- [shift amount]

Raises:
ValueError -- [either given int or shift is negative]

Returns:
`i` rotated to the left by `shift` bits

>>> left_rotate_32(1234, 1)
2468
>>> left_rotate_32(1111, 4)
17776
>>> left_rotate_32(2147483648, 1)
1
>>> left_rotate_32(2147483648, 3)
4
>>> left_rotate_32(4294967295, 4)
4294967295
>>> left_rotate_32(1234, 0)
1234
>>> left_rotate_32(0, 0)
0
>>> left_rotate_32(-1, 0)
Traceback (most recent call last):
...
ValueError: Input must be non-negative
>>> left_rotate_32(0, -1)
Traceback (most recent call last):
...
ValueError: Shift must be non-negative
"""
if i < 0:
raise ValueError("Input must be non-negative")
if shift < 0:
raise ValueError("Shift must be non-negative")
return ((i << shift) ^ (i >> (32 - shift))) % 2**32

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.")

>>> 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
"""

bit_string = preprocess(message)

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

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

shift_amounts = [
7,
12,
17,
22,
7,
12,
17,
22,
7,
12,
17,
22,
7,
12,
17,
22,
5,
9,
14,
20,
5,
9,
14,
20,
5,
9,
14,
20,
5,
9,
14,
20,
4,
11,
16,
23,
4,
11,
16,
23,
4,
11,
16,
23,
4,
11,
16,
23,
6,
10,
15,
21,
6,
10,
15,
21,
6,
10,
15,
21,
6,
10,
15,
21,
]

# Process bit string in chunks, each with 16 32-char words
for block_words in get_block_words(bit_string):
a = a0
b = b0
c = c0
d = d0

# Hash current chunk
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]))

# Add hashed chunk to running total
a0 = sum_32(a0, a)
b0 = sum_32(b0, b)
c0 = sum_32(c0, c)
d0 = sum_32(d0, d)

digest = reformat_hex(a0) + reformat_hex(b0) + reformat_hex(c0) + reformat_hex(d0)
return digest

if __name__ == "__main__":
import doctest

doctest.testmod()
```