added naive SHA256 and RSA implementations

ctf-solutions/bean_counter.py

@@ -0,0 +1,92 @@
+'''
+Solution for https://cryptohack.org/courses/symmetric/bean_counter/
+'''
+
+import os
+import requests
+from math import ceil
+
+from Crypto.Cipher import AES
+
+from imp.math.util import xor_bytes
+
+class StepUpCounter(object):
+    def __init__(self, step_up=False):
+        self.value = os.urandom(16).hex()
+        self.step = 1
+        self.stup = step_up
+
+    def increment(self):
+        if self.stup:
+            self.newIV = hex(int(self.value, 16) + self.step)
+        else:
+            self.newIV = hex(int(self.value, 16) - self.stup)
+        self.value = self.newIV[2:len(self.newIV)]
+        return bytes.fromhex(self.value.zfill(32))
+
+    def __repr__(self):
+        self.increment()
+        return self.value
+
+'''
+NOTE: Since step_up is used ONLY as false, we can simplify:  
+class StepUpCounter(object):
+    def __init__(self):
+        self.value = os.urandom(16).hex()
+
+    # SAME AS DOING NOTHING
+    def increment(self):
+        return self.value()
+
+    def __repr__(self):
+        return self.value
+'''
+
+URL = 'https://aes.cryptohack.org/bean_counter'
+
+def get_encrypted() -> bytes:
+    resp = requests.get(f'{URL}/encrypt/')
+    encrypted = bytes.fromhex(resp.json()['encrypted'])
+    return encrypted
+
+PNG_HEADER = [
+    '89', '50', '4e', '47', 
+    '0d', '0a', '1a', '0a', 
+    '00', '00', '00', '0d', 
+    '49', '48', '44', '52'
+]
+
+def main() -> None:
+    # NOTE: the counter is constant!
+    ctr = StepUpCounter()
+    # init = ctr.increment()
+    # init_val = ctr.value
+    # for i in range(2560000):
+    #     if ctr.increment() != init:
+    #         print('Counter Changed')
+    #         print(i)
+    #         break
+    #     elif ctr.value != init_val:
+    #         print('valued changed')
+    #         print(i)
+    #         break
+            
+    # PNGs *should* have a constant header, we will use the first 16 bytes
+    # to determine what the counter value must be set to
+    encrypted = get_encrypted()
+    png_header = bytes.fromhex(''.join(PNG_HEADER))
+    ctr_value = xor_bytes(encrypted[:16], png_header)
+    # apply the counter value to the entire encrypted image (in blocks of 16 bytes)
+    BLOCK_SIZE = 16
+    with open('bean_flag.png', 'wb') as f:
+        for i in range(ceil(len(encrypted) / BLOCK_SIZE)):
+            block = encrypted[i*BLOCK_SIZE : (i+1)*BLOCK_SIZE]
+            # NOTE: the block we get is not guaranteed to be block size (ie if at end)
+            plaintext_block = xor_bytes(block, ctr_value[:len(block)])
+            f.write(plaintext_block)
+
+if __name__ == '__main__':
+    try:
+        main()
+    except (KeyboardInterrupt, EOFError):
+        print('\n[!] Interrupt')

ctf-solutions/flipping_cookie.py

@@ -0,0 +1,55 @@
+'''
+Solution to https://cryptohack.org/courses/symmetric/flipping_cookie/ 
+'''
+
+import requests
+from datetime import datetime, timedelta
+
+URL = 'https://aes.cryptohack.org/flipping_cookie'
+
+# NOTE: assumes A and B are equal length
+def xor_bytes(A: bytes, B: bytes) -> bytes:
+    return b''.join([(a ^ b).to_bytes() for (a, b) in zip(A, B)])
+def xor_str(A: str, B: str) -> str:
+    return ''.join([chr(ord(a) ^ ord(b)) for (a, b) in zip(A, B)])
+
+def gen_expiry() -> str:
+    return (datetime.today() + timedelta(days=1)).strftime("%s")
+
+def get_cookie() -> tuple[bytes, bytes]:
+    resp = requests.get(f'{URL}/get_cookie/')
+    cookie = resp.json()['cookie']
+    iv = bytes.fromhex(cookie[:32])
+    ciphertext = bytes.fromhex(cookie[32:])
+    return iv, ciphertext
+
+
+def main() -> None:
+    # cookie flipping preprocessing step
+    admin_len = len('admin=')
+    expiry_len = len(';expiry=') + len(gen_expiry())
+    admin_mask = '\x00' * admin_len
+    expiry_mask = '\x00' * expiry_len
+    # we aim to replace "admin=False;" with "admin=True;;"
+    # NOTE: double semicolon ("True;;") is intentional
+    # NOTE: and the server won't ever realise it happened!
+    deletion = admin_mask  + 'False' + expiry_mask
+    insertion = admin_mask + 'True;' + expiry_mask
+    # determine the value that replaces deletion with insertion
+    cookie_flip = xor_str(deletion, insertion)
+
+    # get our new cookie and apply the cookie flip!
+    iv, ciphertext = get_cookie()
+    flipped_iv = xor_bytes(cookie_flip.encode(), iv)
+
+    print('Flipped Cookie:')
+    print('IV:', flipped_iv.hex())
+    print('Body:', ciphertext.hex())
+
+    
+    
+        
+    
+
+if __name__ == '__main__':
+    main()

ctf-solutions/symmetry.py

@@ -0,0 +1,39 @@
+'''
+Solution to https://cryptohack.org/courses/symmetric/symmetry/ 
+'''
+
+import os
+import requests
+
+from imp.math.util import xor_bytes, xor_str
+
+URL = 'https://aes.cryptohack.org/symmetry'
+
+def get_encrypted_flag() -> tuple[bytes, bytes]:
+    resp = requests.get(f'{URL}/encrypt_flag/')
+    ciphertext = resp.json()['ciphertext']
+    iv = bytes.fromhex(ciphertext[:32])
+    flag = bytes.fromhex(ciphertext[32:])
+    return iv, flag
+
+def encrypt(plaintext: bytes, iv: bytes) -> bytes:
+    plaintext, iv = plaintext.hex(), iv.hex()
+    resp = requests.get(f'{URL}/encrypt/{plaintext}/{iv}')
+    return bytes.fromhex(resp.json()['ciphertext'])
+
+def main() -> None:
+    iv, flag = get_encrypted_flag()
+    # generate a random plaintext of equal length to the flag
+    random_plaintext = os.urandom(len(flag))
+    random_ciphertext = encrypt(random_plaintext, iv)
+    # XOR random plaintext with corresponding ciphertext to
+    # get the set generated by IV under the keyed AES permutation
+    aes_orbit = xor_bytes(random_plaintext, random_ciphertext)
+    # XOR this orbit with the flag to get the hexed flag plaintext
+    flag_plaintext = xor_bytes(flag, aes_orbit)
+    print('Flag:', flag_plaintext.decode())
+    
+    print('IV:', iv.hex())
+
+if __name__ == '__main__':
+    main()

default.nix

@@ -0,0 +1,10 @@
+let
+  sources = import ./nix/sources.nix;
+  pkgs = import sources.nixpkgs {};
+  # Let all API attributes like "poetry2nix.mkPoetryApplication"
+  # use the packages and versions (python3, poetry etc.) from our pinned nixpkgs above
+  # under the hood:
+  poetry2nix = import sources.poetry2nix {inherit pkgs;};
+  myPythonApp = poetry2nix.mkPoetryApplication {projectDir = ./.;};
+in
+  myPythonApp

examples/cryptohack-ecboracle.py

@@ -0,0 +1,46 @@
+import requests
+
+from imp.constants import PRINTABLE
+from imp.attacks import paddingoracle
+
+from Crypto.Util.Padding import pad
+
+import string
+
+NIBBLESET = [n.to_bytes() for n in range(256)]
+
+HOST = 'https://aes.cryptohack.org'
+ENDPOINT = '/ecb_oracle/encrypt/{0}/'
+URI = HOST + ENDPOINT
+
+CHARSET = [c.encode() for c in string.printable]
+# CHARSET = NIBBLESET # OVERRIDE
+
+FLAG_LEN = 26  # flag length, calculated by hand
+SPACER = b'\x0f' # arbitrary spacing character
+
+BLOCK_BYTES = 16
+BLOCK_NIBBLES = 32 # measured in nibbles
+
+
+def mkreq(hextext: str) -> dict[str, str]:
+    resp = requests.get(URI.format(hextext))
+    if resp.status_code != 200:
+        raise Exception(f'[!] resp failed! {resp} : {resp.text}')
+    return resp.json()
+
+def encrypt(b: bytes) -> bytes:
+    resp = mkreq(b.hex())
+    return bytes.fromhex(resp['ciphertext'])
+
+def main() -> None:
+    paddingoracle.crack(encrypt, pad, CHARSET, 16, batch_size=20, debug=True)
+
+               
+
+if __name__ == '__main__':
+    try:
+        main()
+    except (KeyboardInterrupt, EOFError):
+        print('\n[!] Interrupt')
+

examples/local-ecboracle.py

@@ -0,0 +1,28 @@
+import string
+
+from imp.attacks import paddingoracle
+
+from Crypto.Cipher import AES
+from Crypto.Util.Padding import pad
+
+CHARSET = [c.encode() for c in string.printable]
+
+KEY = b'you wont get me!'
+FLAG = b'imbaud{omg_you_catched_me}'
+CIPHER = AES.new(KEY, AES.MODE_ECB)
+
+def encrypt(b: bytes, debug=False) -> bytes:
+    padded = pad(b + FLAG, 16)
+    if debug:
+        print(padded)
+    # print(padded)
+    return CIPHER.encrypt(padded)
+
+def main() -> None:
+    paddingoracle.crack(encrypt, pad, CHARSET, 16, batch_size=50, debug=True)
+
+if __name__ == '__main__':
+    try:
+        main()
+    except (KeyboardInterrupt, EOFError):
+        print('\n[!] Interrupt')

imp/attacks/paddingoracle.py

@@ -0,0 +1,106 @@
+from math import inf, ceil
+from typing import Callable
+
+from imp.math.util import clamp_max
+
+SPACER = b'\xff' # arbitrary spacing character
+
+class DecryptFailed(Exception):
+    pass
+    
+def round_to_blocks(n: int, block_size: int) -> int:
+    return ceil(n / block_size)
+
+def crack_secret_len(cipher: Callable[[str], str], 
+                     max_iters: int = inf) -> int | None:
+    # calculate length for i = 1
+    init_len = len(cipher(SPACER))
+    secret_len = None
+    i = 2
+    while True:
+        if i - 2 > max_iters:
+            break
+        elif len(cipher(SPACER*i)) != init_len:
+            secret_len = init_len - i
+            break
+        i += 1
+    return secret_len
+
+'''
+
+NOTE: pad_if_perfect exists for PKCS#7 which will add a full block
+NOTE: of padding if the input is perfectly alligned to the blocks already. 
+'''
+def crack(cipher: Callable[[str], str],
+          padfn: Callable[[bytes, int], bytes],
+          charset: list,
+          block_size: int,
+          max_secret_iters: int = inf,
+          batch_size: int = 1,
+          pad_if_perfect: bool = True,
+          debug: bool = False) -> str | None:
+    if len(charset) % batch_size:
+        raise ValueError(f'batch_size={batch_size} does not divide len(charset)={len(charset)}')
+    # calculate the secret length
+    secret_len = crack_secret_len(cipher, max_iters=max_secret_iters)
+    if debug:
+        print(f'[+] Found secret length: {secret_len}')
+
+    # calculate how many blocks the secret stretches over
+    # NOTE: secret_block_len - secret_len represents the number of
+    # NOTE: bytes required to make the secret fill the blocks with no padding
+    secret_block_len = round_to_blocks(secret_len, block_size) * block_size
+    default_push = (secret_block_len - secret_len)
+    known = b''
+    while True:
+        # the "full tail" is all characters we know + the 1 we're cracking (target)
+        # the "current tail" is the characters in the same block as the target
+        full_tail_bytes = len(known) + 1
+        tail_bytes = clamp_max(full_tail_bytes, block_size - 1)
+        # generate ALL possible tails (avoid padding if no padding required)
+        tails = [c + known[:tail_bytes] for c in charset]
+        if len(tails[0]) != block_size:
+            tails = [padfn(tail, 16) for tail in tails]
+        # calculate the "push" applied to the secret
+        push_size = (default_push + full_tail_bytes) % block_size
+
+        matched = False
+        NUM_BATCHES = len(tails) // batch_size
+        for i in range(NUM_BATCHES):
+            if debug:
+                print(f'{int(i/NUM_BATCHES*100)}%', end='\r')
+            batch = tails[i*batch_size : (i+1)*batch_size]
+            batch = b''.join(batch) + (SPACER * push_size) # apply spacing
+
+            # encrypt batch and split the ciphertext into blocks
+            ciphertext = cipher(batch)
+            num_blocks = len(ciphertext)//block_size
+            blocks = [ciphertext[i*block_size : (i+1)*block_size] for i in range(num_blocks)]
+
+            oracle_pos = round_to_blocks(full_tail_bytes, block_size)
+            if pad_if_perfect and (push_size + secret_len) % block_size == 0:
+                oracle_pos += 1
+            
+            for j, cipher_block in enumerate(blocks[:batch_size]):
+                if cipher_block == blocks[-oracle_pos]:
+                    char = charset[i*batch_size + j]
+                    known = char + known
+                    if debug:
+                        print(f'[*] Found Tail: {known}')
+                    matched = True
+                    break
+            if matched:
+                break
+        if not matched:
+            break
+        elif len(known) == secret_len:
+            if debug:
+                print('[+] SUCCESS')
+            return known
+    # if we reached the end (no return)
+    # then the attack failed
+    err_msg = 'Padding oracle attack failed'
+    if not debug:
+        raise DecryptFailed(err_msg)
+    print(f'\n[!] {err_msg}')
+                

imp/constants.py

@@ -9,6 +9,7 @@ ALPHA_UPPER = 'ABCDEFGHIJKLMNOPQRSTUVWXYZ'
 ALPHA = ALPHA_LOWER + ALPHA_UPPER
 ALPHANUM = ALPHA + DIGITS
 SYMBOLS = '!\"#$%&\'()*+,-./:;<=>?@[\\]^_`{|}~'
+PRINTABLE = ALPHANUM + SYMBOLS
 # Other
 DIGITS_BIN = '01'
 DIGITS_OCT = '01234567'

imp/crypto/hash.py

@@ -0,0 +1,7 @@
+import hashlib
+
+def sha256(data: bytes, as_bytes: bool = False) -> bytes:
+    hasher = hashlib.sha256()
+    hasher.update(data)
+    hash = hasher.digest()
+    return hash if as_bytes else int.from_bytes(hash)

imp/crypto/rsa.py

@@ -0,0 +1,18 @@
+'''
+Simplification of Euler's Totient function knowing
+the prime factorisation for the public key N value.  
+'''
+def _totient(p: int, q: int) -> int:
+    return (p - 1) * (q - 1)
+
+'''
+Implements RSA encryption as modular exponentiation. 
+'''
+def encrypt(plaintext: int, e: int, N: int) -> int:
+    return pow(plaintext, e, N)
+def decrypt(ciphertext: int, d: int, N: int) -> int:
+    return pow(ciphertext, d, N)
+
+def gen_private_key(e: int, p: int, q: int) -> int:
+    return pow(e, -1, _totient(p, q))
+

imp/math/factor/__init__.py

@@ -0,0 +1,2 @@
+from .pftrialdivision import trial_division
+from .factordb import DBResult, FType, FCertainty

imp/math/factor/factordb.py

@@ -0,0 +1,161 @@
+'''
+Simple interface for https://factordb.com inspired by
+https://github.com/ihebski/factordb
+
+TODO:
+1. Implement primality certificate generation, read this:
+https://reference.wolfram.com/language/PrimalityProving/ref/ProvablePrimeQ.html
+'''
+
+import requests
+from enum import Enum, StrEnum
+
+_FDB_URI = 'https://factordb.com'
+# Generated by https://www.asciiart.eu/text-to-ascii-art
+# using "ANSI Shadow" font and "Box drawings double" border with 1 H. Padding
+_BANNER = '''
+╔═══════════════════════════════════════════════════╗
+║ ███████╗ ██████╗████████╗██████╗ ██████╗ ██████╗  ║
+║ ██╔════╝██╔════╝╚══██╔══╝██╔══██╗██╔══██╗██╔══██╗ ║
+║ █████╗  ██║        ██║   ██████╔╝██║  ██║██████╔╝ ║
+║ ██╔══╝  ██║        ██║   ██╔══██╗██║  ██║██╔══██╗ ║
+║ ██║     ╚██████╗   ██║   ██║  ██║██████╔╝██████╔╝ ║
+║ ╚═╝      ╚═════╝   ╚═╝   ╚═╝  ╚═╝╚═════╝ ╚═════╝  ║
+╚═══════════════════════════════════════════════════╝
+╚═══ cli by imbored ═══╝
+'''.strip()
+
+# Enumeration of number types based on their factorisation
+class FType(Enum):
+    Unit      = 1
+    Composite = 2
+    Prime     = 3
+    Unknown   = 4
+
+class FCertainty(Enum):
+    Certain = 1
+    Partial = 2
+    Unknown = 3
+
+# FactorDB result status codes
+class DBStatus(StrEnum):
+    C    = 'C'
+    CF   = 'CF'
+    FF   = 'FF'
+    P    = 'P'
+    PRP  = 'PRP'
+    U    = 'U'
+    Unit = 'Unit' # just for 1
+    N    = 'N'
+    Add  = '*'
+
+    def is_unknown(self) -> bool:
+        return (self in [DBStatus.U, DBStatus.N, DBStatus.Add])
+
+    def classify(self) -> tuple[FType, FCertainty]:
+        return _STATUS_MAP[self]
+    
+    def msg_verbose(self) -> str:
+        return _STATUS_MSG_VERBOSE[self]
+
+# Map of DB Status codes to their factorisation type and certainty 
+_STATUS_MAP = {
+    DBStatus.Unit: (FType.Unit,      FCertainty.Certain),
+    DBStatus.C:    (FType.Composite, FCertainty.Unknown),
+    DBStatus.CF:   (FType.Composite, FCertainty.Partial),
+    DBStatus.FF:   (FType.Composite, FCertainty.Certain),
+    DBStatus.P:    (FType.Prime,     FCertainty.Certain),
+    DBStatus.PRP:  (FType.Prime,     FCertainty.Partial),
+    DBStatus.U:    (FType.Unknown,   FCertainty.Unknown),
+    DBStatus.N:    (FType.Unknown,   FCertainty.Unknown),
+    DBStatus.Add:  (FType.Unknown,   FCertainty.Unknown),
+}  
+
+# Reference: https://factordb.com/status.html
+# NOTE: my factor messages differ slightly from the reference
+_STATUS_MSG_VERBOSE = {
+    DBStatus.Unit: 'Unit, trivial factorisation',
+    DBStatus.C:    'Composite, no factors known',
+    DBStatus.CF:   'Composite, *partially* factors',
+    DBStatus.FF:   'Composite, fully factored',
+    DBStatus.P:    'Prime',
+    DBStatus.PRP:  'Probable prime',
+    DBStatus.U:    'Unknown (*but in database)',
+    DBStatus.N:    'Not in database (-not added due to your settings)',
+    DBStatus.Add:  'Not in database (+added during request)',
+}
+
+# Struct for storing database results with named properties
+class DBResult:
+    def __init__(self, 
+                 status: DBStatus, 
+                 factors: tuple[tuple[int, int]]) -> None:
+        self.status = status
+        self.factors = factors
+        self.ftype, self.certainty = self.status.classify()
+
+def _make_cookie(fdbuser: str | None) -> dict[str, str]:
+    return {} if fdbuser is None else {'fdbuser': fdbuser}
+
+def _get_key(by_id: bool):
+    return 'id' if by_id else 'query'
+
+def _api_query(n: int, 
+               fdbuser: str | None, 
+               by_id: bool = False) -> requests.models.Response:
+    key = _get_key(by_id)
+    uri = f'{_FDB_URI}/api?{key}={n}'
+    return requests.get(uri, cookies=_make_cookie(fdbuser))
+
+def _report_factor(n: int,
+                   factor: int,
+                   fdbuser: str | None,
+                   by_id: bool = False) -> requests.models.Response:
+    key = _get_key(by_id)
+    uri = f'{_FDB_URI}/reportfactor.php?{key}={n}&factor={factor}'
+    return requests.get(uri, cookies=_make_cookie(fdbuser))
+
+'''
+Attempts a query to FactorDB, returns a DBResult object 
+on success, or None if the request failed due to the
+get request raising a RequestException.
+'''
+def query(n: int, 
+          token: str | None = None, 
+          by_id: bool = False,
+          cli: bool = False) -> DBResult | None:
+    if cli:
+        print(_BANNER)
+    try:
+        resp = _api_query(n, token, by_id=by_id)
+    except requests.exceptions.RequestException:
+        return None
+    content = resp.json()
+    result = DBResult(
+        DBStatus(content['status']),
+        tuple((int(F[0]), F[1]) for F in content['factors'])
+    )
+    if cli:
+        print(f'Status: {result.status.msg_verbose()}')
+        print(result.factors)
+
+    # ensure the unit has the trivial factorisation (for consistency)
+    if result.status == DBStatus.Unit:
+        result.factors = ((1, 1),)
+    return result
+
+'''
+Reports a known factor to FactorDB, also tests it is
+actually a factor to avoid wasting FactorDBs resources. 
+'''
+def report(n: int, 
+           factor: int, 
+           by_id: int,
+           token: str | None = None) -> None:
+    try:
+        resp = _report_factor(n, factor, token)
+    except requests.exceptions.RequestException:
+        return None
+    content = resp.json()
+    print(content)
+

imp/math/factor/pftrialdivision.py

@@ -0,0 +1,46 @@
+'''
+The trial division algorithm is essentially the idea that
+all factors of an integer n are less than or equal to isqrt(n),
+where isqrt is floor(sqrt(n)).
+
+Moreover, if p divides n, then all other factors of n must
+be factors of n//p. Hence they must be <= isqrt(n//p).
+'''
+from math import isqrt # integer square root
+
+# Returns the "multiplicity" of a prime factor
+def pf_multiplicity(n: int, p: int) -> int:
+    mult = 0
+    while n % p == 0: 
+        n //= p
+        mult += 1
+    return n, mult
+
+'''
+Trial division prime factorisation algorithm.
+Returns a list of tuples (p, m) where p is
+a prime factor and m is its multiplicity.
+'''
+def trial_division(n: int) -> list[tuple[int, int]]:
+    factors = []
+
+    # determine multiplicity of the only even prime (2)
+    n, mult_2 = pf_multiplicity(n, 2)
+    if mult_2: factors.append((2, mult_2))
+    # determine odd factors and their multiplicities
+    p = 3
+    mult = 0
+    limit = isqrt(n)
+    while p <= limit:
+        n, mult = pf_multiplicity(n, p)
+        if mult:
+            factors.append((p, mult))
+            limit = isqrt(n) # recalculate limit
+            mult = 0 # reset
+        else:
+            p += 2
+    # if n is still greater than 1, then n is a prime factor
+    if n > 1:
+        factors.append((n, 1))
+    return factors
+            

imp/math/primes.py

@@ -1,67 +0,0 @@
-from math import gcd
-
-'''
-Euler's Totient (Phi) Function
-'''
-def totient(n: int) -> int:
-    phi = int(n > 1 and n)
-    for p in range(2, int(n ** .5) + 1):
-        if not n % p:
-            phi -= phi // p
-            while not n % p:
-                n //= p
-    #if n is > 1 it means it is prime
-    if n > 1: phi -= phi // n 
-    return phi
-
-'''
-Tests the primality of an integer using its totient.
-NOTE: If totient(n) has already been calculated 
-      then pass it as the optional phi parameter. 
-'''
-def is_prime(n: int, phi: int = None) -> bool:
-    return n - 1 == (phi if phi is not None else totient(n))
-
-'''
-Prime number generator function.
-Returns the tuple (p, phi(p)) where p is prime
-    and phi is Euler's totient function.
-'''
-def prime_gen(yield_phi: bool = False) -> int | tuple[int, int]:
-    n = 1
-    while True:
-        n += 1
-        phi = totient(n)
-        if is_prime(n, phi=phi):
-            if yield_phi:
-                yield (n, phi)
-            else:
-                yield n
-
-'''
-Returns the prime factorisation of a number.
-Returns a list of tuples (p, m) where p is
-a prime factor and m is its multiplicity.
-NOTE: uses a trial division algorithm
-'''
-def prime_factors(n: int) -> list[tuple[int, int]]:
-    phi = totient(n)
-    if is_prime(n, phi=phi):
-        return [(n, 1)]
-    factors = []
-    for p in prime_gen(yield_phi=False):
-        if p >= n:
-            break
-        # check if divisor
-        multiplicity = 0
-        while n % p == 0:
-            n //= p
-            multiplicity += 1
-        if multiplicity:
-            factors.append((p, multiplicity))
-            if is_prime(n):
-                break
-    if n != 1:
-        factors.append((n, 1))
-    return factors
-            

imp/math/primes/__init__.py

@@ -0,0 +1,48 @@
+from math import inf, isqrt # integer square root
+from itertools import takewhile, compress
+
+SMALL_PRIMES = (2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59)
+
+'''
+Euler's Totient (Phi) Function 
+Implemented in O(nloglog(n)) using the Sieve of Eratosthenes.
+'''
+def eulertotient(n: int) -> int:
+    phi = int(n > 1 and n)
+    for p in range(2, isqrt(n) + 1):
+        if not n % p:
+            phi -= phi // p
+            while not n % p:
+                n //= p
+    #if n is > 1 it means it is prime
+    if n > 1: phi -= phi // n 
+    return phi
+
+'''
+Tests the primality of an integer using its totient.
+NOTE: If totient(n) has already been calculated 
+      then pass it as the optional phi parameter. 
+'''
+def is_prime(n: int, phi: int = None) -> bool:
+    return n - 1 == (phi if phi is not None else eulertotient(n))
+
+# Taken from Lucas A. Brown's primefac.py (some variables renamed)
+def primegen(limit=inf) -> int:
+    ltlim = lambda x: x < limit
+    yield from takewhile(ltlim, SMALL_PRIMES)
+    pl, prime = [3,5,7], primegen()
+    for p in pl: next(prime)
+    n = next(prime); nn = n*n
+    while True:
+        n = next(prime); ll, nn = nn, n*n
+        delta = nn - ll
+        sieve = bytearray([True]) * delta
+        for p in pl:
+            k = (-ll) % p
+            sieve[k::p] = bytearray([False]) * ((delta-k)//p + 1)
+        if nn > limit: break
+        yield from compress(range(ll,ll+delta,2), sieve[::2])
+        pl.append(n)
+    yield from takewhile(ltlim, compress(range(ll,ll+delta,2), sieve[::2]))
+
+

imp/math/util.py

@@ -1,2 +1,22 @@
+def clamp(n: int, min: int, max: int) -> int:
+    if n < min:
+        return min
+    elif n > max:
+        return max
+    return n
+
+def clamp_max(n: int, max: int) -> int:
+    return max if n > max else n
+
+def clamp_min(n: int, max: int) -> int:
+    return min if n < min else n
+
 def digits(n: int) -> int:
     return len(str(n))
+
+# NOTE: assumes A and B are equal length
+def xor_bytes(A: bytes, B: bytes) -> bytes:
+    return b''.join([(a ^ b).to_bytes() for (a, b) in zip(A, B)])
+def xor_str(A: str, B: str) -> str:
+    return ''.join([chr(ord(a) ^ ord(b)) for (a, b) in zip(A, B)])
+

poetry.lock

@@ -0,0 +1,220 @@
+# This file is automatically @generated by Poetry 1.8.4 and should not be changed by hand.
+
+[[package]]
+name = "certifi"
+version = "2025.6.15"
+description = "Python package for providing Mozilla's CA Bundle."
+optional = false
+python-versions = ">=3.7"
+files = [
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+    {file = "certifi-2025.6.15.tar.gz", hash = "sha256:d747aa5a8b9bbbb1bb8c22bb13e22bd1f18e9796defa16bab421f7f7a317323b"},
+]
+
+[[package]]
+name = "charset-normalizer"
+version = "3.4.2"
+description = "The Real First Universal Charset Detector. Open, modern and actively maintained alternative to Chardet."
+optional = false
+python-versions = ">=3.7"
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pyproject.toml

@@ -0,0 +1,16 @@
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+
+
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